Research ArticleGait Planning and Stability Control of a Quadruped Robot

Junmin Li1 Jinge Wang1 Simon X Yang2 Kedong Zhou1 and Huijuan Tang1

1School of Mechanical Engineering Xihua University No 999 Jinzhou Road Jinniu District Chengdu Sichuan China2Advanced Robotics and Intelligent Systems Laboratory School of Engineering University of Guelph Guelph ON Canada N1G 2W1

Correspondence should be addressed to Jinge Wang wangjgmailxhueducn

Received 24 November 2015 Revised 14 February 2016 Accepted 16 March 2016

Academic Editor Paolo Del Giudice

Copyright copy 2016 Junmin Li et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to realize smooth gait planning and stability control of a quadruped robot a new controller algorithm based on CPG-ZMP(central pattern generator-zero moment point) is put forward in this paper To generate smooth gait and shorten the adjustingtime of the model oscillation system a new CPG model controller and its gait switching strategy based on Wilson-Cowan modelare presented in the paper The control signals of knee-hip joints are obtained by the improved multi-DOF reduced order controltheory To realize stability control the adaptive speed adjustment and gait switch are completed by the real-time computing of ZMPExperiment results show that the quadruped robotrsquos gaits are efficiently generated and the gait switch is smooth in the CPG controlalgorithm Meanwhile the stability of robotrsquos movement is improved greatly with the CPG-ZMP algorithm The algorithm in thispaper has good practicability which lays a foundation for the production of the robot prototype

1 Introduction

The coordinated movement control of multilegged robot hasbeen a difficult problem [1 2] in the field of robot because arobot needs tomake a quick response to the change of externalenvironment and various stimulusThe control strategy basedon biological induction is a new control idea that has beengradually carried out in the multilegged robot researches [3ndash12] in which the alternate rhythmic movement of each leg ofthe quadruped robot is the most common Biological studiesshow that rhythmic movement is usually achieved by CPG(central pattern generator) and can be applied to four-leggedrobot motion control [13 14]

The issues concerning the architecture of a CPG modelare the choice of type and number of oscillators to use Mat-suoka [15] first achieved CPG output by the use of oscillatormodel regulation And this oscillator can only provide a pos-itive output signal which often makes it difficult to meet theneeds of engineering control object On the basis of Mat-suokarsquos CPG oscillator Kimura adopted two neurons flexorand extensor muscles to simulate the movement of thenervous system of animals and to achieve quadruped robotgait control [16] In addition he improved the functions of theoscillators by introducing plenty of additional reflex feedback

to the controller and performed successful walking tests ofTekken in several terrains Similar works using these oscilla-torswere introduced byBailey [10] for controlling insect loco-motion and also by Liu et al [17] for controlling AIBO robotHuang et al built mutual suppression oscillator model andcontrol networks of quadruped robot joints based on Mat-suokarsquos neuron and obtained the CPG network parameters ofquadruped gait control [2] But only a single CPGwas consid-ered to realize single joint control which lacks systematic net-work behavior and is cumbersome to parameter adjustment

The Hopf oscillator is also popular for modeling the CPGto control legged robots CPG unit model based on Hopfoscillator was constructed by Santos and Matos [13] whichrealizes the controllable conditioning of hip drive signals andgait switch of quadruped robot but it has no effective CPGregulatory networks to control the movement of the otherjoints directly or indirectly However when four Hopf oscil-lators are connected to obtain phase entrainments the wave-forms of the outputs are changed accordingly The deforma-tion in the waveforms depends on the connection structure(or the gait) and the connecting weights Explicit examplescan be found elsewhere [18] In different approaches insteadof generating periodic outputs directly from the dynamicoscillators (Matsuoka andHopf oscillators) other researchers

Hindawi Publishing CorporationComputational Intelligence and NeuroscienceVolume 2016 Article ID 9853070 13 pageshttpdxdoiorg10115520169853070

2 Computational Intelligence and Neuroscience

du va

b

c

Excitatory connectionInhibitory connection

Figure 1 Wilson-Cowan central nervous oscillator model

focused on producing stable phase entrainments using phaseoscillators Tsujita et al [19] introduced an example of phaseoscillators for controlling a quadruped robot Aoi et alintroduced similar oscillators to control a quadruped robot[20] to perform several locomotion tasks including dynamicwalking and gait transitions Maufroy et al [21] used phasemodulations to control the posture and rhythmic motions ofa quadruped robot

The Wilson-Cowan neural oscillator is also popular formodeling the CPG to control legged robots Li et al presentedtheWilson-Cowan neural oscillator controller for quadrupedrobot rhythmic locomotion control which is known as aweakly neural network that generates rhythmic movementsin locomotion of animals [22] The harmony motion of oneleg from the others is controlled with four Wilson-Cowanneural oscillators The period and amplitude of the CPGmodel are easy to control for generating various gaits butthe real time of adjusting the model oscillation system andstability control need to further improve

In stability control methods Liu and Chen proposedstability control method of gait based on ZMP (zero momentpoint) theory to control a quadruped robot which achievessome success in stability control but lacks efficiency andflexibility of gait planning and gait switch [23]

In this work a new controller algorithm based on CPG-ZMP (central pattern generator-zero moment point) is putforward in order to realize smooth gait planning and stabilitycontrol at the same time At first a newCPGmodel controllerand its gait switching strategy based onWilson-Cowanmodelare presented in order to generate smooth gait and shorten theadjusting time of the model oscillation system The controlsignals of knee-hip joints are obtained by the improvedmulti-DOF reduced order control theory And then adaptivespeed adjustment and gait switch are completed by real-timecomputing of ZMP to realize stability control Simulationresults show that quadruped robotrsquos gait planning is efficientlygenerated and the gait switch is smooth in the CPG controlalgorithm Meanwhile the stability of the robot movement isimproved greatly with CPG-ZMP algorithm The algorithmhas been applied on joint quadruped robot which greatlyimproves the stability of movement and the flexibility of gaitgeneration and switch

2 Improved Central NervousOscillators Model

The oscillator model presented by Wilson and Cowan isshown in Figure 1 which is composed of excitatory neuron 119906

and inhibitory neuron V A stable limit cycle shock is formedby the intercoupling of 119906 and V

The model can be described by the following differentialequation [22]

119879119906

119889119906

119889119905

+ 119906 = 119891120583(119886119906 minus 119887V + 119878

119906)

119879119906

119889V119889119905

+ V = 119891120583(119888119906 minus 119889V + 119878V)

119891120583(119909) = tanh (120583119909)

(1)

where 119886 is the excitatory connection strength of neuron and119889 is the inhibitory connection strength of neuron 119887 is theinhibitory connection strength of V to 119906 119888 is the excitatoryconnection strength of 119906 to V 119878

119906and 119878V are the external

signals and the119863119862 inputs usually119879119906is the rise-time constant

of step input 119879V is the fatigue time constant 119891120583(119909) is the

coupling function and 120583 is the gain of 119891120583(119909)

In order to applyWilson-Cowan nervous oscillator on thegait control of quadruped robot the model is improved asfollows

(1) 119901 is introduced as amplitude limiting coefficient toadjust the outputs of 119906 and V119910out is an output of linearsynthesis to control the movement of correspondingleg

(2) Every leg is controlled by a CPG oscillator which isbuilt by weighted directed graph with graph theory

(3) External feedback of CPG control network is intro-duced where 119904

119894119896is the reflection information 119892

119896is

coefficient of 119904119894119896 and 119906 and V are the adverse vectors

of refection coefficients

Then the improved oscillator model is described asfollows

119879119906119894

119889119906119894

119889119905

+ 119906119894

= 119891120583(119886119906119894minus 119887V119894+

119899

sum

119895=1

119908119894119895120583119895+

119898

sum

119896=1

119904119894119896119892119896+ 119878119906119894)

119879V119894119889V119894

119889119905

+ V119894

= 119891120583(119888119906119894minus 119889V119894+

119899

sum

119895=1

119908119894119895V119895minus

119898

sum

119896=1

119904119894119896119892119896+ 119878V119894)

Computational Intelligence and Neuroscience 3

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(a)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(b)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(c)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(d)

Figure 2 Output curves of walk gait (a) Left front leg (b) Rightfront leg (c) Right hind leg (d) Left hind leg

119891120583(119909) = tanh (120583119909)

119910119894

out = 119901 (119906119894 minus V119894)

119894 119895 = 1 2 3 4 119896 = 1 2 3 119898

(2)

where 119894 and 119895 are the numbers of central neural oscillators119908119894119895

is the connection weight between oscillators and119882 isin 1198774times4

is a matrix composed of 119908119894119895

Output curves of walk gait with the improved centralnervous oscillatormodel are shown in Figure 2The adjustingtime of the improved model is less than 05 T but that of thetraditional Wilson-Cowan model is about 15 T [22] so theadjusting time of the improved model is shortened greatly

3 Typical Gaits Planning andTransition of Quadruped Robot

Two typical gaits are discussed in this paper including walkand trot Walk belongs to a still gait and each leg puts up anddown in turn the phase difference between legs is a quartercycle Trot means that the two diagonal legs put up anddown at the same time and is better at energy consumptionand belongs to dynamic gait of which the phase differencebetween legs is half of cycle

1 2

4 3

minus01 minus01minus01 minus01

minus01

minus01

HL HR

FRFL

Figure 3 Walk network connection topology structure

1 2

4 3

HL HR

01 01

FRFL

minus01minus01

minus01

minus01

Figure 4 Trot network connection topology structure

31 Typical Gaits Planning The connection weight matrixes119882walk and119882trot are described as follows

119882walk =

[

[

[

[

[

[

0 minus01 minus01 minus01

minus01 0 minus01 minus01

minus01 minus01 0 minus01

minus01 minus01 minus01 0

]

]

]

]

]

]

119882trot =

[

[

[

[

[

[

0 minus01 +01 minus01

minus01 0 minus01 +01

+01 minus01 0 minus01

minus01 +01 minus01 0

]

]

]

]

]

]

(3)

The relative displacement between two legs is a quarterof walk cycle during walking and each connection amongoscillators is inhibitory connection in a full symmetric CPGnetwork But excitatory connections are adopted in trotThus let the excitatory connection value be +01 which is asmaller positive value in119882 and let the inhibitory connectionvalue be minus01 which is a smaller negative value The networktopological structure is shown in Figures 3 and 4 respectively

CPG equation is solved by using the four-order Runge-KuttaThe initial values ofmatrix are randomnumbers whichare one order of magnitude larger than 119878

119906and 119878V

1205830= [

1205831120583212058331205834

V1

V2

V3

V4

] = [

01 025 01 018

01 021 02 027

] (4)

The parameters in (2) are set in Table 1

32 Typical Gaits Transition Because there are direct corre-spondences between the connection weight matrix and gait

4 Computational Intelligence and Neuroscience

Table 1 Parameters of the CPG differential equations

119879119906 119879V 119886 119889 119887 119888 119878

119906 119878V 120583 119901 119898 119892

119896

02 56 minus24 56 24 002 1 05 1 01

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(a)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(b)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(c)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(d)

Figure 5 Gait transition from walk to trot (a) Left front leg (b)Right front leg (c) Right hind leg (d) Left hind leg

we can realize gaits transition by replacing the connectionweight matrix Gait transition curves from walk to trot areshown in Figure 5 Gait transition begins at the time 119905 = 8 sTransition process takes about 05 T but that of the traditionalWilson-Cowan is about 15 T [22] Because the adjusting timeof the improved central nervous oscillator model is shortgaits transition is rapid and smooth

4 Multi-DOF Lower-Order ControlMethod of Quadruped Robot

Lower-order control method of joints in eightDOFs quadru-ped robot is shown in Figure 6 which builds intercouplingmapping relations between hip joint and knee joint Thecontrol signals of CPGoutput are used to control the four cor-responding hips directly and control the four knee joints indi-rectly by coupling relationship CPG oscillation control sys-tem couples with hip joints and hip joints couple with corre-sponding knee jointsThismakes up the intercoupling controlsystem

41 Construction ofMotionMapping Functions Themappingfunction of knee joint is defined as formula (5) which indi-cates that the knee joint has movement in swing phase and

4 3

2

6

78

5

1

CPG

(1 2 3 4) hip joints(5 6 7 8) knee joints(f) mapping function from hip joints to knee joints

f 120579h 997888rarr 120579k

Figure 6 Lower-order control model of quadruped robot

has only tiny passive movement in support phase as a half-wave function The tiny movement of knee joint in supportphase is ignored in order to simplify control algorithm

120579119896(119905) =

0 (120579ℎlt 0)

sgn (120593) 120572119896119860119896[1 minus (

120579ℎ(119905)

120572ℎ119860ℎ

)

2

] (120579ℎge 0)

120593 =

1 (elbow joint)

minus1 (knee joint)

(5)

where 120579ℎ 119860ℎ and 120572

ℎrepresent the signals of hip joint and its

corresponding amplitude and correction factor respectively120579119896 119860119896 and 120572

119896represent the signals of knee joint and its

corresponding amplitude and correction factor respectivelyand sgn (120593) is the multiplier of joint configuration form 120579

ℎ

is obtained by the Wilson-Cowan neural oscillators 120572119896and

120572ℎare positive correlation relationship to 120579

119896(119905)and are used

to keep the knee joints from touching the ground and obtainmapping signals from the hip joints

42 Motion Trajectory Planning of Single Leg The duty ratioof walk gait is 34 and themotion order of four legs is 1-3-2-4which realizes reciprocating motion of four legsThe supportphase of every leg costs three quarters of the cycle time andswing phase costs a quarter of the cycle time The duty ratioof trot gait is 05 which means the time of support phase andthe time of swing phase are the sameThe other two legs swaywhen the diagonal two legs step on the ground The wholeprocesses from the beginning of support phase to the end ofswing phase for walk gait and trot gait are shown in Figures 7and 8 respectively

43 Motion Parameter Determination of Single Leg In thevirtual prototype of quadruped robot in this paper thelengths of thigh and shank are 119897 = 014m the speed of walkgait is V = 012msminus1 and the motion cycle is 119879 = 15 s

It can be known by analyzing one legrsquos motion track thatthe hip jointrsquos rotor angle is always increasing from supportphasersquos beginning to the end and then is decreasing when

Computational Intelligence and Neuroscience 5

A

B

A1 A2 A3

B1 B2B3

CC2 C3

s

3s4 s4

Figure 7 Single leg motion graphic of walk gait

s2 s2

A

B

A1 A2 A3

B1 B2 B3

C

C2 C3

s

Figure 8 Single leg motion graphic of trot gait

the leg is in swing phase The knee joint has tiny passiverotation range in the support phase so the knee jointrsquos rotorangle becomes the biggest when the support phase ends andthen gets into the swing phase immediately The knee jointrsquosrotor angle becomes the smallest when the height above theearth for sway leg is in swing phasersquos midpoint 119862

2

As a matter of experience let the height of leg raise ℎ =001m Formula (6) can be obtained on the basis of Figure 7

119904 = V times 119879

119860119896= ang119860

11198611119862 minus ang119860

211986121198622

119860ℎ=

120587

2

minus ang11986011986011198611

(6)

Hip jointrsquos swing amplitude 119860ℎis 1550∘ and knee jointrsquos

swing amplitude 119860119896is 1112∘ by trigonometric function

relationshipsWhen the robot is in trot let speed V = 024msminus1 and let

motion cycle 119879 = 12 s and let the highest height of leg raiseabove the earth ℎ = 005m Hip jointrsquos swing amplitude119860

ℎis

45∘ and knee jointrsquos swing amplitude 119860119896is 142∘ as the same

theory

44Motion Track Simulation of Joint Theconfiguration formof the robot joint is an inward knee-elbow form The walkgait matrix 119882 is 119882walk The motion tracks of hip joints arecontrolled byCPGandknee joints are controlled by half-wavefunctionsThemovement curves of hip-knee joints are shownin Figure 9 by MATLAB simulation

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04minus03minus02minus01

001020304

120579(r

ad)

t (s)

HipKnee

(d)

Figure 9 Movement curves of hip-knee joints for walk gait (a) Leftfront leg (b) Right front leg (c) Right hind leg (d) Left hind leg

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

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Electrical and Computer Engineering

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Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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httpwwwhindawicom Volume 2014

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Multimedia

International Journal of

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ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

2 Computational Intelligence and Neuroscience

du va

b

c

Excitatory connectionInhibitory connection

Figure 1 Wilson-Cowan central nervous oscillator model

focused on producing stable phase entrainments using phaseoscillators Tsujita et al [19] introduced an example of phaseoscillators for controlling a quadruped robot Aoi et alintroduced similar oscillators to control a quadruped robot[20] to perform several locomotion tasks including dynamicwalking and gait transitions Maufroy et al [21] used phasemodulations to control the posture and rhythmic motions ofa quadruped robot

The Wilson-Cowan neural oscillator is also popular formodeling the CPG to control legged robots Li et al presentedtheWilson-Cowan neural oscillator controller for quadrupedrobot rhythmic locomotion control which is known as aweakly neural network that generates rhythmic movementsin locomotion of animals [22] The harmony motion of oneleg from the others is controlled with four Wilson-Cowanneural oscillators The period and amplitude of the CPGmodel are easy to control for generating various gaits butthe real time of adjusting the model oscillation system andstability control need to further improve

In stability control methods Liu and Chen proposedstability control method of gait based on ZMP (zero momentpoint) theory to control a quadruped robot which achievessome success in stability control but lacks efficiency andflexibility of gait planning and gait switch [23]

In this work a new controller algorithm based on CPG-ZMP (central pattern generator-zero moment point) is putforward in order to realize smooth gait planning and stabilitycontrol at the same time At first a newCPGmodel controllerand its gait switching strategy based onWilson-Cowanmodelare presented in order to generate smooth gait and shorten theadjusting time of the model oscillation system The controlsignals of knee-hip joints are obtained by the improvedmulti-DOF reduced order control theory And then adaptivespeed adjustment and gait switch are completed by real-timecomputing of ZMP to realize stability control Simulationresults show that quadruped robotrsquos gait planning is efficientlygenerated and the gait switch is smooth in the CPG controlalgorithm Meanwhile the stability of the robot movement isimproved greatly with CPG-ZMP algorithm The algorithmhas been applied on joint quadruped robot which greatlyimproves the stability of movement and the flexibility of gaitgeneration and switch

2 Improved Central NervousOscillators Model

The oscillator model presented by Wilson and Cowan isshown in Figure 1 which is composed of excitatory neuron 119906

and inhibitory neuron V A stable limit cycle shock is formedby the intercoupling of 119906 and V

The model can be described by the following differentialequation [22]

119879119906

119889119906

119889119905

+ 119906 = 119891120583(119886119906 minus 119887V + 119878

119906)

119879119906

119889V119889119905

+ V = 119891120583(119888119906 minus 119889V + 119878V)

119891120583(119909) = tanh (120583119909)

(1)

where 119886 is the excitatory connection strength of neuron and119889 is the inhibitory connection strength of neuron 119887 is theinhibitory connection strength of V to 119906 119888 is the excitatoryconnection strength of 119906 to V 119878

119906and 119878V are the external

signals and the119863119862 inputs usually119879119906is the rise-time constant

of step input 119879V is the fatigue time constant 119891120583(119909) is the

coupling function and 120583 is the gain of 119891120583(119909)

In order to applyWilson-Cowan nervous oscillator on thegait control of quadruped robot the model is improved asfollows

(1) 119901 is introduced as amplitude limiting coefficient toadjust the outputs of 119906 and V119910out is an output of linearsynthesis to control the movement of correspondingleg

(2) Every leg is controlled by a CPG oscillator which isbuilt by weighted directed graph with graph theory

(3) External feedback of CPG control network is intro-duced where 119904

119894119896is the reflection information 119892

119896is

coefficient of 119904119894119896 and 119906 and V are the adverse vectors

of refection coefficients

Then the improved oscillator model is described asfollows

119879119906119894

119889119906119894

119889119905

+ 119906119894

= 119891120583(119886119906119894minus 119887V119894+

119899

sum

119895=1

119908119894119895120583119895+

119898

sum

119896=1

119904119894119896119892119896+ 119878119906119894)

119879V119894119889V119894

119889119905

+ V119894

= 119891120583(119888119906119894minus 119889V119894+

119899

sum

119895=1

119908119894119895V119895minus

119898

sum

119896=1

119904119894119896119892119896+ 119878V119894)

Computational Intelligence and Neuroscience 3

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(a)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(b)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(c)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(d)

Figure 2 Output curves of walk gait (a) Left front leg (b) Rightfront leg (c) Right hind leg (d) Left hind leg

119891120583(119909) = tanh (120583119909)

119910119894

out = 119901 (119906119894 minus V119894)

119894 119895 = 1 2 3 4 119896 = 1 2 3 119898

(2)

where 119894 and 119895 are the numbers of central neural oscillators119908119894119895

is the connection weight between oscillators and119882 isin 1198774times4

is a matrix composed of 119908119894119895

Output curves of walk gait with the improved centralnervous oscillatormodel are shown in Figure 2The adjustingtime of the improved model is less than 05 T but that of thetraditional Wilson-Cowan model is about 15 T [22] so theadjusting time of the improved model is shortened greatly

3 Typical Gaits Planning andTransition of Quadruped Robot

Two typical gaits are discussed in this paper including walkand trot Walk belongs to a still gait and each leg puts up anddown in turn the phase difference between legs is a quartercycle Trot means that the two diagonal legs put up anddown at the same time and is better at energy consumptionand belongs to dynamic gait of which the phase differencebetween legs is half of cycle

1 2

4 3

minus01 minus01minus01 minus01

minus01

minus01

HL HR

FRFL

Figure 3 Walk network connection topology structure

1 2

4 3

HL HR

01 01

FRFL

minus01minus01

minus01

minus01

Figure 4 Trot network connection topology structure

31 Typical Gaits Planning The connection weight matrixes119882walk and119882trot are described as follows

119882walk =

[

[

[

[

[

[

0 minus01 minus01 minus01

minus01 0 minus01 minus01

minus01 minus01 0 minus01

minus01 minus01 minus01 0

]

]

]

]

]

]

119882trot =

[

[

[

[

[

[

0 minus01 +01 minus01

minus01 0 minus01 +01

+01 minus01 0 minus01

minus01 +01 minus01 0

]

]

]

]

]

]

(3)

The relative displacement between two legs is a quarterof walk cycle during walking and each connection amongoscillators is inhibitory connection in a full symmetric CPGnetwork But excitatory connections are adopted in trotThus let the excitatory connection value be +01 which is asmaller positive value in119882 and let the inhibitory connectionvalue be minus01 which is a smaller negative value The networktopological structure is shown in Figures 3 and 4 respectively

CPG equation is solved by using the four-order Runge-KuttaThe initial values ofmatrix are randomnumbers whichare one order of magnitude larger than 119878

119906and 119878V

1205830= [

1205831120583212058331205834

V1

V2

V3

V4

] = [

01 025 01 018

01 021 02 027

] (4)

The parameters in (2) are set in Table 1

32 Typical Gaits Transition Because there are direct corre-spondences between the connection weight matrix and gait

4 Computational Intelligence and Neuroscience

Table 1 Parameters of the CPG differential equations

119879119906 119879V 119886 119889 119887 119888 119878

119906 119878V 120583 119901 119898 119892

119896

02 56 minus24 56 24 002 1 05 1 01

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(a)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(b)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(c)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(d)

Figure 5 Gait transition from walk to trot (a) Left front leg (b)Right front leg (c) Right hind leg (d) Left hind leg

we can realize gaits transition by replacing the connectionweight matrix Gait transition curves from walk to trot areshown in Figure 5 Gait transition begins at the time 119905 = 8 sTransition process takes about 05 T but that of the traditionalWilson-Cowan is about 15 T [22] Because the adjusting timeof the improved central nervous oscillator model is shortgaits transition is rapid and smooth

4 Multi-DOF Lower-Order ControlMethod of Quadruped Robot

Lower-order control method of joints in eightDOFs quadru-ped robot is shown in Figure 6 which builds intercouplingmapping relations between hip joint and knee joint Thecontrol signals of CPGoutput are used to control the four cor-responding hips directly and control the four knee joints indi-rectly by coupling relationship CPG oscillation control sys-tem couples with hip joints and hip joints couple with corre-sponding knee jointsThismakes up the intercoupling controlsystem

41 Construction ofMotionMapping Functions Themappingfunction of knee joint is defined as formula (5) which indi-cates that the knee joint has movement in swing phase and

4 3

2

6

78

5

1

CPG

(1 2 3 4) hip joints(5 6 7 8) knee joints(f) mapping function from hip joints to knee joints

f 120579h 997888rarr 120579k

Figure 6 Lower-order control model of quadruped robot

has only tiny passive movement in support phase as a half-wave function The tiny movement of knee joint in supportphase is ignored in order to simplify control algorithm

120579119896(119905) =

0 (120579ℎlt 0)

sgn (120593) 120572119896119860119896[1 minus (

120579ℎ(119905)

120572ℎ119860ℎ

)

2

] (120579ℎge 0)

120593 =

1 (elbow joint)

minus1 (knee joint)

(5)

where 120579ℎ 119860ℎ and 120572

ℎrepresent the signals of hip joint and its

corresponding amplitude and correction factor respectively120579119896 119860119896 and 120572

119896represent the signals of knee joint and its

corresponding amplitude and correction factor respectivelyand sgn (120593) is the multiplier of joint configuration form 120579

ℎ

is obtained by the Wilson-Cowan neural oscillators 120572119896and

120572ℎare positive correlation relationship to 120579

119896(119905)and are used

to keep the knee joints from touching the ground and obtainmapping signals from the hip joints

42 Motion Trajectory Planning of Single Leg The duty ratioof walk gait is 34 and themotion order of four legs is 1-3-2-4which realizes reciprocating motion of four legsThe supportphase of every leg costs three quarters of the cycle time andswing phase costs a quarter of the cycle time The duty ratioof trot gait is 05 which means the time of support phase andthe time of swing phase are the sameThe other two legs swaywhen the diagonal two legs step on the ground The wholeprocesses from the beginning of support phase to the end ofswing phase for walk gait and trot gait are shown in Figures 7and 8 respectively

43 Motion Parameter Determination of Single Leg In thevirtual prototype of quadruped robot in this paper thelengths of thigh and shank are 119897 = 014m the speed of walkgait is V = 012msminus1 and the motion cycle is 119879 = 15 s

It can be known by analyzing one legrsquos motion track thatthe hip jointrsquos rotor angle is always increasing from supportphasersquos beginning to the end and then is decreasing when

Computational Intelligence and Neuroscience 5

A

B

A1 A2 A3

B1 B2B3

CC2 C3

s

3s4 s4

Figure 7 Single leg motion graphic of walk gait

s2 s2

A

B

A1 A2 A3

B1 B2 B3

C

C2 C3

s

Figure 8 Single leg motion graphic of trot gait

the leg is in swing phase The knee joint has tiny passiverotation range in the support phase so the knee jointrsquos rotorangle becomes the biggest when the support phase ends andthen gets into the swing phase immediately The knee jointrsquosrotor angle becomes the smallest when the height above theearth for sway leg is in swing phasersquos midpoint 119862

2

As a matter of experience let the height of leg raise ℎ =001m Formula (6) can be obtained on the basis of Figure 7

119904 = V times 119879

119860119896= ang119860

11198611119862 minus ang119860

211986121198622

119860ℎ=

120587

2

minus ang11986011986011198611

(6)

Hip jointrsquos swing amplitude 119860ℎis 1550∘ and knee jointrsquos

swing amplitude 119860119896is 1112∘ by trigonometric function

relationshipsWhen the robot is in trot let speed V = 024msminus1 and let

motion cycle 119879 = 12 s and let the highest height of leg raiseabove the earth ℎ = 005m Hip jointrsquos swing amplitude119860

ℎis

45∘ and knee jointrsquos swing amplitude 119860119896is 142∘ as the same

theory

44Motion Track Simulation of Joint Theconfiguration formof the robot joint is an inward knee-elbow form The walkgait matrix 119882 is 119882walk The motion tracks of hip joints arecontrolled byCPGandknee joints are controlled by half-wavefunctionsThemovement curves of hip-knee joints are shownin Figure 9 by MATLAB simulation

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04minus03minus02minus01

001020304

120579(r

ad)

t (s)

HipKnee

(d)

Figure 9 Movement curves of hip-knee joints for walk gait (a) Leftfront leg (b) Right front leg (c) Right hind leg (d) Left hind leg

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

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International Journal of

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Distributed Sensor Networks

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International Journal of

ReconfigurableComputing

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

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Computational Intelligence and Neuroscience 3

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(a)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(b)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(c)

0 1 2 3 4 5 6 7 8 9 10minus1

minus050

051

120579(r

ad)

t (s)

(d)

Figure 2 Output curves of walk gait (a) Left front leg (b) Rightfront leg (c) Right hind leg (d) Left hind leg

119891120583(119909) = tanh (120583119909)

119910119894

out = 119901 (119906119894 minus V119894)

119894 119895 = 1 2 3 4 119896 = 1 2 3 119898

(2)

where 119894 and 119895 are the numbers of central neural oscillators119908119894119895

is the connection weight between oscillators and119882 isin 1198774times4

is a matrix composed of 119908119894119895

Output curves of walk gait with the improved centralnervous oscillatormodel are shown in Figure 2The adjustingtime of the improved model is less than 05 T but that of thetraditional Wilson-Cowan model is about 15 T [22] so theadjusting time of the improved model is shortened greatly

3 Typical Gaits Planning andTransition of Quadruped Robot

Two typical gaits are discussed in this paper including walkand trot Walk belongs to a still gait and each leg puts up anddown in turn the phase difference between legs is a quartercycle Trot means that the two diagonal legs put up anddown at the same time and is better at energy consumptionand belongs to dynamic gait of which the phase differencebetween legs is half of cycle

1 2

4 3

minus01 minus01minus01 minus01

minus01

minus01

HL HR

FRFL

Figure 3 Walk network connection topology structure

1 2

4 3

HL HR

01 01

FRFL

minus01minus01

minus01

minus01

Figure 4 Trot network connection topology structure

31 Typical Gaits Planning The connection weight matrixes119882walk and119882trot are described as follows

119882walk =

[

[

[

[

[

[

0 minus01 minus01 minus01

minus01 0 minus01 minus01

minus01 minus01 0 minus01

minus01 minus01 minus01 0

]

]

]

]

]

]

119882trot =

[

[

[

[

[

[

0 minus01 +01 minus01

minus01 0 minus01 +01

+01 minus01 0 minus01

minus01 +01 minus01 0

]

]

]

]

]

]

(3)

The relative displacement between two legs is a quarterof walk cycle during walking and each connection amongoscillators is inhibitory connection in a full symmetric CPGnetwork But excitatory connections are adopted in trotThus let the excitatory connection value be +01 which is asmaller positive value in119882 and let the inhibitory connectionvalue be minus01 which is a smaller negative value The networktopological structure is shown in Figures 3 and 4 respectively

CPG equation is solved by using the four-order Runge-KuttaThe initial values ofmatrix are randomnumbers whichare one order of magnitude larger than 119878

119906and 119878V

1205830= [

1205831120583212058331205834

V1

V2

V3

V4

] = [

01 025 01 018

01 021 02 027

] (4)

The parameters in (2) are set in Table 1

32 Typical Gaits Transition Because there are direct corre-spondences between the connection weight matrix and gait

4 Computational Intelligence and Neuroscience

Table 1 Parameters of the CPG differential equations

119879119906 119879V 119886 119889 119887 119888 119878

119906 119878V 120583 119901 119898 119892

119896

02 56 minus24 56 24 002 1 05 1 01

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(a)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(b)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(c)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(d)

Figure 5 Gait transition from walk to trot (a) Left front leg (b)Right front leg (c) Right hind leg (d) Left hind leg

we can realize gaits transition by replacing the connectionweight matrix Gait transition curves from walk to trot areshown in Figure 5 Gait transition begins at the time 119905 = 8 sTransition process takes about 05 T but that of the traditionalWilson-Cowan is about 15 T [22] Because the adjusting timeof the improved central nervous oscillator model is shortgaits transition is rapid and smooth

4 Multi-DOF Lower-Order ControlMethod of Quadruped Robot

Lower-order control method of joints in eightDOFs quadru-ped robot is shown in Figure 6 which builds intercouplingmapping relations between hip joint and knee joint Thecontrol signals of CPGoutput are used to control the four cor-responding hips directly and control the four knee joints indi-rectly by coupling relationship CPG oscillation control sys-tem couples with hip joints and hip joints couple with corre-sponding knee jointsThismakes up the intercoupling controlsystem

41 Construction ofMotionMapping Functions Themappingfunction of knee joint is defined as formula (5) which indi-cates that the knee joint has movement in swing phase and

4 3

2

6

78

5

1

CPG

(1 2 3 4) hip joints(5 6 7 8) knee joints(f) mapping function from hip joints to knee joints

f 120579h 997888rarr 120579k

Figure 6 Lower-order control model of quadruped robot

has only tiny passive movement in support phase as a half-wave function The tiny movement of knee joint in supportphase is ignored in order to simplify control algorithm

120579119896(119905) =

0 (120579ℎlt 0)

sgn (120593) 120572119896119860119896[1 minus (

120579ℎ(119905)

120572ℎ119860ℎ

)

2

] (120579ℎge 0)

120593 =

1 (elbow joint)

minus1 (knee joint)

(5)

where 120579ℎ 119860ℎ and 120572

ℎrepresent the signals of hip joint and its

corresponding amplitude and correction factor respectively120579119896 119860119896 and 120572

119896represent the signals of knee joint and its

corresponding amplitude and correction factor respectivelyand sgn (120593) is the multiplier of joint configuration form 120579

ℎ

is obtained by the Wilson-Cowan neural oscillators 120572119896and

120572ℎare positive correlation relationship to 120579

119896(119905)and are used

to keep the knee joints from touching the ground and obtainmapping signals from the hip joints

42 Motion Trajectory Planning of Single Leg The duty ratioof walk gait is 34 and themotion order of four legs is 1-3-2-4which realizes reciprocating motion of four legsThe supportphase of every leg costs three quarters of the cycle time andswing phase costs a quarter of the cycle time The duty ratioof trot gait is 05 which means the time of support phase andthe time of swing phase are the sameThe other two legs swaywhen the diagonal two legs step on the ground The wholeprocesses from the beginning of support phase to the end ofswing phase for walk gait and trot gait are shown in Figures 7and 8 respectively

43 Motion Parameter Determination of Single Leg In thevirtual prototype of quadruped robot in this paper thelengths of thigh and shank are 119897 = 014m the speed of walkgait is V = 012msminus1 and the motion cycle is 119879 = 15 s

It can be known by analyzing one legrsquos motion track thatthe hip jointrsquos rotor angle is always increasing from supportphasersquos beginning to the end and then is decreasing when

Computational Intelligence and Neuroscience 5

A

B

A1 A2 A3

B1 B2B3

CC2 C3

s

3s4 s4

Figure 7 Single leg motion graphic of walk gait

s2 s2

A

B

A1 A2 A3

B1 B2 B3

C

C2 C3

s

Figure 8 Single leg motion graphic of trot gait

the leg is in swing phase The knee joint has tiny passiverotation range in the support phase so the knee jointrsquos rotorangle becomes the biggest when the support phase ends andthen gets into the swing phase immediately The knee jointrsquosrotor angle becomes the smallest when the height above theearth for sway leg is in swing phasersquos midpoint 119862

2

As a matter of experience let the height of leg raise ℎ =001m Formula (6) can be obtained on the basis of Figure 7

119904 = V times 119879

119860119896= ang119860

11198611119862 minus ang119860

211986121198622

119860ℎ=

120587

2

minus ang11986011986011198611

(6)

Hip jointrsquos swing amplitude 119860ℎis 1550∘ and knee jointrsquos

swing amplitude 119860119896is 1112∘ by trigonometric function

relationshipsWhen the robot is in trot let speed V = 024msminus1 and let

motion cycle 119879 = 12 s and let the highest height of leg raiseabove the earth ℎ = 005m Hip jointrsquos swing amplitude119860

ℎis

45∘ and knee jointrsquos swing amplitude 119860119896is 142∘ as the same

theory

44Motion Track Simulation of Joint Theconfiguration formof the robot joint is an inward knee-elbow form The walkgait matrix 119882 is 119882walk The motion tracks of hip joints arecontrolled byCPGandknee joints are controlled by half-wavefunctionsThemovement curves of hip-knee joints are shownin Figure 9 by MATLAB simulation

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04minus03minus02minus01

001020304

120579(r

ad)

t (s)

HipKnee

(d)

Figure 9 Movement curves of hip-knee joints for walk gait (a) Leftfront leg (b) Right front leg (c) Right hind leg (d) Left hind leg

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

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Distributed Sensor Networks

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ReconfigurableComputing

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

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RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

4 Computational Intelligence and Neuroscience

Table 1 Parameters of the CPG differential equations

119879119906 119879V 119886 119889 119887 119888 119878

119906 119878V 120583 119901 119898 119892

119896

02 56 minus24 56 24 002 1 05 1 01

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(a)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(b)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(c)

0 2 4 6 8 10 12 14 16minus1

minus050

051

t (s)

120579(r

ad)

(d)

Figure 5 Gait transition from walk to trot (a) Left front leg (b)Right front leg (c) Right hind leg (d) Left hind leg

we can realize gaits transition by replacing the connectionweight matrix Gait transition curves from walk to trot areshown in Figure 5 Gait transition begins at the time 119905 = 8 sTransition process takes about 05 T but that of the traditionalWilson-Cowan is about 15 T [22] Because the adjusting timeof the improved central nervous oscillator model is shortgaits transition is rapid and smooth

4 Multi-DOF Lower-Order ControlMethod of Quadruped Robot

Lower-order control method of joints in eightDOFs quadru-ped robot is shown in Figure 6 which builds intercouplingmapping relations between hip joint and knee joint Thecontrol signals of CPGoutput are used to control the four cor-responding hips directly and control the four knee joints indi-rectly by coupling relationship CPG oscillation control sys-tem couples with hip joints and hip joints couple with corre-sponding knee jointsThismakes up the intercoupling controlsystem

41 Construction ofMotionMapping Functions Themappingfunction of knee joint is defined as formula (5) which indi-cates that the knee joint has movement in swing phase and

4 3

2

6

78

5

1

CPG

(1 2 3 4) hip joints(5 6 7 8) knee joints(f) mapping function from hip joints to knee joints

f 120579h 997888rarr 120579k

Figure 6 Lower-order control model of quadruped robot

has only tiny passive movement in support phase as a half-wave function The tiny movement of knee joint in supportphase is ignored in order to simplify control algorithm

120579119896(119905) =

0 (120579ℎlt 0)

sgn (120593) 120572119896119860119896[1 minus (

120579ℎ(119905)

120572ℎ119860ℎ

)

2

] (120579ℎge 0)

120593 =

1 (elbow joint)

minus1 (knee joint)

(5)

where 120579ℎ 119860ℎ and 120572

ℎrepresent the signals of hip joint and its

corresponding amplitude and correction factor respectively120579119896 119860119896 and 120572

119896represent the signals of knee joint and its

corresponding amplitude and correction factor respectivelyand sgn (120593) is the multiplier of joint configuration form 120579

ℎ

is obtained by the Wilson-Cowan neural oscillators 120572119896and

120572ℎare positive correlation relationship to 120579

119896(119905)and are used

to keep the knee joints from touching the ground and obtainmapping signals from the hip joints

42 Motion Trajectory Planning of Single Leg The duty ratioof walk gait is 34 and themotion order of four legs is 1-3-2-4which realizes reciprocating motion of four legsThe supportphase of every leg costs three quarters of the cycle time andswing phase costs a quarter of the cycle time The duty ratioof trot gait is 05 which means the time of support phase andthe time of swing phase are the sameThe other two legs swaywhen the diagonal two legs step on the ground The wholeprocesses from the beginning of support phase to the end ofswing phase for walk gait and trot gait are shown in Figures 7and 8 respectively

43 Motion Parameter Determination of Single Leg In thevirtual prototype of quadruped robot in this paper thelengths of thigh and shank are 119897 = 014m the speed of walkgait is V = 012msminus1 and the motion cycle is 119879 = 15 s

It can be known by analyzing one legrsquos motion track thatthe hip jointrsquos rotor angle is always increasing from supportphasersquos beginning to the end and then is decreasing when

Computational Intelligence and Neuroscience 5

A

B

A1 A2 A3

B1 B2B3

CC2 C3

s

3s4 s4

Figure 7 Single leg motion graphic of walk gait

s2 s2

A

B

A1 A2 A3

B1 B2 B3

C

C2 C3

s

Figure 8 Single leg motion graphic of trot gait

the leg is in swing phase The knee joint has tiny passiverotation range in the support phase so the knee jointrsquos rotorangle becomes the biggest when the support phase ends andthen gets into the swing phase immediately The knee jointrsquosrotor angle becomes the smallest when the height above theearth for sway leg is in swing phasersquos midpoint 119862

2

As a matter of experience let the height of leg raise ℎ =001m Formula (6) can be obtained on the basis of Figure 7

119904 = V times 119879

119860119896= ang119860

11198611119862 minus ang119860

211986121198622

119860ℎ=

120587

2

minus ang11986011986011198611

(6)

Hip jointrsquos swing amplitude 119860ℎis 1550∘ and knee jointrsquos

swing amplitude 119860119896is 1112∘ by trigonometric function

relationshipsWhen the robot is in trot let speed V = 024msminus1 and let

motion cycle 119879 = 12 s and let the highest height of leg raiseabove the earth ℎ = 005m Hip jointrsquos swing amplitude119860

ℎis

45∘ and knee jointrsquos swing amplitude 119860119896is 142∘ as the same

theory

44Motion Track Simulation of Joint Theconfiguration formof the robot joint is an inward knee-elbow form The walkgait matrix 119882 is 119882walk The motion tracks of hip joints arecontrolled byCPGandknee joints are controlled by half-wavefunctionsThemovement curves of hip-knee joints are shownin Figure 9 by MATLAB simulation

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04minus03minus02minus01

001020304

120579(r

ad)

t (s)

HipKnee

(d)

Figure 9 Movement curves of hip-knee joints for walk gait (a) Leftfront leg (b) Right front leg (c) Right hind leg (d) Left hind leg

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 5

A

B

A1 A2 A3

B1 B2B3

CC2 C3

s

3s4 s4

Figure 7 Single leg motion graphic of walk gait

s2 s2

A

B

A1 A2 A3

B1 B2 B3

C

C2 C3

s

Figure 8 Single leg motion graphic of trot gait

the leg is in swing phase The knee joint has tiny passiverotation range in the support phase so the knee jointrsquos rotorangle becomes the biggest when the support phase ends andthen gets into the swing phase immediately The knee jointrsquosrotor angle becomes the smallest when the height above theearth for sway leg is in swing phasersquos midpoint 119862

2

As a matter of experience let the height of leg raise ℎ =001m Formula (6) can be obtained on the basis of Figure 7

119904 = V times 119879

119860119896= ang119860

11198611119862 minus ang119860

211986121198622

119860ℎ=

120587

2

minus ang11986011986011198611

(6)

Hip jointrsquos swing amplitude 119860ℎis 1550∘ and knee jointrsquos

swing amplitude 119860119896is 1112∘ by trigonometric function

relationshipsWhen the robot is in trot let speed V = 024msminus1 and let

motion cycle 119879 = 12 s and let the highest height of leg raiseabove the earth ℎ = 005m Hip jointrsquos swing amplitude119860

ℎis

45∘ and knee jointrsquos swing amplitude 119860119896is 142∘ as the same

theory

44Motion Track Simulation of Joint Theconfiguration formof the robot joint is an inward knee-elbow form The walkgait matrix 119882 is 119882walk The motion tracks of hip joints arecontrolled byCPGandknee joints are controlled by half-wavefunctionsThemovement curves of hip-knee joints are shownin Figure 9 by MATLAB simulation

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04minus03minus02minus01

001020304

120579(r

ad)

t (s)

HipKnee

(d)

Figure 9 Movement curves of hip-knee joints for walk gait (a) Leftfront leg (b) Right front leg (c) Right hind leg (d) Left hind leg

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Computational Intelligence and Neuroscience

0 2 4 6 8 10minus04

minus02

0

02

04120579

(rad

)

t (s)

HipKnee

(a)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(b)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(c)

0 2 4 6 8 10minus04

minus02

0

02

04

120579(r

ad)

t (s)

HipKnee

(d)

Figure 10 Movement curves of hip-knee joints for trot gait (a) Left front leg (b) Right front leg (c) Right hind leg (d) Left hind leg

The zero lines ofmotion curves in Figure 9 are the balancestates of joints Swing amplitude of hip joints near the balancestate is 119860

ℎ while unilateral swing amplitude of knee joints is

119860119896 The motion curves of front legsrsquo knee joints are in the

positive axis and those of the hind legs are in the negativeaxis The movement curves of hip-knee joints for trot gait areshown in Figure 10 when gait matrix119882 is119882trot

5 ZMP Model of Quadruped Robot

Over the past 35 years there have been many theoretical andexperimental studies on the ZMP To summarize the ZMPcriterion states that if the ZMP is within the support polygonmade between the foot and the ground then stable dynamicwalking is guaranteed [23]The schematic diagram of ZMP isshown in Figure 11

Assume that the barycentre of robot is in its geometriccenter and the ground is plane so the height coordinate 119910

119892of

robot centroid above the earth is a constant and coordinatesof ZMP can be obtained by the following formula

119909ZMP = 119909119892 minus119892

119892119910

sdot 119910119892

119885ZMP = 119885119892 minus119885119892

119892119910

sdot 119910119892

(7)

Inertia force

Resultant forceGravity

xZMPGravity point Ground

y

z

Figure 11 The schematic diagram of ZMP

where 119909119892is robot barycentre coordinate of 119909-axis 119910

119892is

robot barycentre coordinate of 119910-axis 119911119892is robot barycentre

coordinate of 119911-axis 119892is the acceleration of 119909-axis and

119892

is the acceleration of 119910-axisIn the case of trot gait the ZMP trajectory analysis is

shown in Figure 12ZMP is in the upper left of support diagonal when the left

hind leg 2 and the right front leg 4 are the supporting legsZMP is in the upper right of support diagonal when the leftfront leg 1 and the hind front leg 3 are the supporting legs SoZMP crosses support diagonal twice in one movement cycle

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 7

1

4

3

2

3

2

4

1

4

4

3

2

1

2

3

1

3

4

2D

irect

ion

of m

otio

n

ZMP

i + 3rd cycle

i + 2nd cycle

i + 1st cycle

ith cycle

Figure 12 ZMP trajectory analysis diagram for trot gait

The change of ZMP in 119885 direction is in 119878 curve which showspose of robot is adjusted in the right or the left continually

6 Hybrid CPG-ZMP Control System

The flow chart of hybrid CPG-ZMP control algorithm isshown in Figure 13 The motion track of each joint is gener-ated by the improved CPG and motion mapping meanwhilewe specify the global threshold of CPG (119892 in) Rhythmicmotion of robot is realized by CPG gait generator and CPGcan receive feedback signal from body sensor while working

ZMP can be calculated by datum from force sensor andgyroscope The control system can tell whether the ZMP isoutside of safe area If true but still not up to the criticalpoint of turnover ZMP detector sends a signal to reducethe global threshold quickly for restraining roll and then theneural signal activity in CPG is lowered If not outside of safe

area the control systemwill detect whether the current globalthreshold is smaller than the preset value if true the systemwill increase the global threshold If ZMP is outside of safearea and the robot is in the state of turnover which is mainlymade by external impact anddisturbance CPG stopsworkingand the control system will recalculate balanced foothold Torecover the pose of robot the angle of robotrsquos each joint isrecalculated by inverse kinematics And CPG is back to workuntil robot pose is normal The theory of ZMP not only canbe used as the stability criterion of robot gait but also can beused to plan the corresponding gait when robot is in the stateof turnover

7 Experiment Study

71 Simulation Experiment The flow chart of gait plan sim-ulation based on Webots is shown in Figure 14 The key

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Computational Intelligence and Neuroscience

No

CPG gait generator

ZMP outside safety zone

Current global excitation

Increase global excitation

In overturning stateReset the globalexcitation

Stop CPG workingcalculate balanced foothold

Replanning foot track

Recalculate angle of each jointby inverse kinematics

Joint control instruction

Adjust duty ratioreplace gait weight

matrix

Gait keeping or switching

Yes

No

Yes

Yes

No

Multi-DOF reduced order control based onhip-knee joints motion mapping

lt g_in

Figure 13 Flow chart of hybrid CPG-ZMP control algorithm

Modeling

Set parameters

Programme and debug

Simulation

Figure 14 Webots simulation flow chart

parameters of walk gait and trot gait are shown in Table 2 bycut-and-try method

711Walk Gait Thewalk gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 15 Quadruped robot walks in the 1-3-2-4order (1 left foreleg 2 right foreleg 3 right hind leg and 4left hind leg) and there are three legs on the ground whichare in stand phase at any time from the simulation chartThe simulation of walk shows that robot moves at a constantvelocity and the pose is steady so the algorithm has goodpracticability

Table 2 Parameters of the two kinds of gaits

119860ℎ

119860119896

120572ℎ

120572119896

119901

Walk 1550∘ 1112∘ 127 175 025Trot 4500∘ 190∘ 100 211 050

712 Trot Gait The trot gait simulation of quadruped robotbased on Webots with the improved CPG in the paper isshown in Figure 16 The left foreleg and the right hind leg arein support phase when the right front leg and the left hind legare in swing phase The simulation shows that the speed ofrobot in trot is obviously higher than the speed in walk butthe stability of body is lower

713 Typical Gaits Transition Gaits transition from walk totrot is shown in Figure 17 (V = 024msminus1) The adjusting timeis about 05 T Gaits transition is rapid and smooth

714 Stability Simulation of CPG Control The simulationresult is shown in Figure 18 The stability of robot decreaseswhen the speed is higher When the speed is up to 13V(V = 024msminus1) gaits become disordered because robotrsquos

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 9

(a)

(b)

(c)

(d)

Figure 15 Movement orders of legs in walk gait (a) Left foreleg inswing phase (b) Right hind leg in swing phase (c) Right foreleg inswing phase (d) Left hind leg in swing phase

inertia and the impact force of toes increase And thenthe body jolts violently in the direction of move Finallythe robot is in rollover after about one motion cycle Theheight change of robot centroid in the direction of 119910-axisduring the movements is shown in Figure 19

(a)

(b)

Figure 16 Movement orders of diagonal legs in gait trot (a) RF andLH in swing phase (b) LF and RH in swing phase

715 Stability Simulation of CPG-ZMP Control The simu-lation results are shown in Figure 20 The robotrsquos stabilitydecreases when the speed is higher But the robot adjustsgait adaptively by CPG-ZMP control and is kept from fallingover and the rollover effectively The height change of robotcentroid in the direction of 119910-axis during the movements isshown in Figure 21

When the speed is up to 0312msminus1 (13V) the robotjolts violently in the direction of move and then the robotbecomes unstable gradually CPG stops working and gaitsof robot are replanned by inverse kinematics when ZMP ofrobot is out of the safe range and is turning over After aboutone and a half motion cycles the CPG restarts working whenZMP is in safe range then the robotrsquos gait becomes normal

72 Real Experiment For testing our proposed controllerwe designed a robot which has 16DOFs and each leg has3 actuated rotary joints Each rotary joint is controlled bya steering engine In addition an IMU sensor is attachedto the robotrsquos body to measure the orientation (roll-pitch-yaw angles) body linear acceleration and rotational velocityFurthermore each leg is equippedwith a load cell To evaluatethe efficiency of the proposed controller we performed sometests under rough terrain using a walk gait The desiredvelocity is set to 008msminus1 The robot can adaptively adjustvelocity from 003msminus1 to 008msminus1 according to movementenvironment and its posture Experiment results show theCPG-ZMP controller adapts to the environment change verywell The overview is shown in Figure 22

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Computational Intelligence and Neuroscience

(a)

(b)

(c)

(d)

Figure 17 Gaits transition fromwalk to trot (a)Walk (b) Transientstate 1 (c) Transient state 2 (d) Trot

8 Conclusions

We conclude the following

(1) The improved CPG system based on Wilson-Cowanmodel shortens the oscillation time and makes thesystem respond quickly and enhances the real timemeanwhile the gait switch is more smooth and rapid

(a)

(b)

(c)

(d)

(e)

Figure 18 Simulation of trot gait controlled only by CPG (a) V =024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severeinstability (V = 0312msminus1) (e) Rollover (V = 0312msminus1)

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 11

0 1 2 3 4 5 6 7 8015

02

025

03

035

04

y(m

)

x (m)

Figure 19 Height change of robot centroid in 119910-axis with displacement in 119909-axis

(a) (b) (c)

(d) (e) (f)

(g) (h)

Figure 20 Trot simulation controlled by CPG-ZMP (a) V = 024msminus1 (b) V = 0288msminus1 (c) V = 0312msminus1 (d) Severe instability (V =0312msminus1) (e) Stop CPG and replan gait (f) Adjusting joint angle (g) Restart CPG working (h) Recover normal gait

(2) The intercoupling mapping relations between the hipjoint and the knee joint are built by the improvedmulti-DOF reduced order control theory whichimproves the efficiency of control and the real timeA quadruped robot takes 8DOFs to realize rhythmicmovements so if 8DOFs are controlled by CPG

CPG nets are too complex to influence the real-timeperformance of system

(3) The robot adjusts gait adaptively and the stability ofrobotrsquos movement is improved greatly by CPG-ZMPcontrol

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

12 Computational Intelligence and Neuroscience

0 1 2 3 4 5 6 7 8 9 10 1102

025

03

035

04

y(m

)

x (m)

Figure 21 Height change of robot centroid in 119910-axis with displacement in 119909-axis

Figure 22 The overview of the motion in a rough terrain

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (51575456) the Spring Plan of Ministryof Education of China (Z2012014) theKey Scientific ResearchFund of Xihua University (Grant no z1420210) and theOpen Research Fund of Key Laboratory of Manufacture andAutomation Laboratory (Xihua University szjj2015-082)

References

[1] H Kimura Y Fukuoka and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on natural ground based on bio-logical conceptsrdquoThe International Journal of Robotics Researchvol 26 no 5 pp 475ndash490 2007

[2] B Huang Y F Yao and L Sun ldquoQuadruped robot gait controlbased on central pattern generatorrdquo Journal of MechanicalEngineering vol 46 no 7 pp 1ndash6 2010

[3] M A Lewis F Tenore and R Etienne-Cummings ldquoCPGdesign using inhibitory networksrdquo in Proceedings of the IEEEInternational Conference on Robotics andAutomation pp 3682ndash3687 Barcelona Spain April 2005

[4] S Grillner ldquoBiological pattern generation the cellular andcomputational logic of networks inmotionrdquoNeuron vol 52 no5 pp 751ndash766 2006

[5] S Rossignol R Dubuc and J-P Gossard ldquoDynamic sensori-motor interactions in locomotionrdquo Physiological Reviews vol86 no 1 pp 89ndash154 2006

[6] J H Barron-Zambrano C Torres-Huitzil and B GirauldquoPerception-driven adaptive CPG-based locomotion for hexa-pod robotsrdquo Neurocomputing vol 170 no 25 pp 63ndash78 2015

[7] V Matos and C P Santos ldquoOmnidirectional locomotion ina quadruped robot a CPG-based approachrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems (IROS rsquo10) pp 3392ndash3397 IEEE Taipei TaiwanOctober 2010

[8] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forQuadruped Robotsrdquo IEEE Transactions on Systems Man andCybernetics Part B Cybernetics vol 41 no 3 pp 867ndash880 2011

[9] L Righetti and A J Ijspeert ldquoDesign methodologies for centralpattern generators an application to crawling humanoidsrdquo inProceedings of the Robotics Science and Systems pp 191ndash198Philadelphia Pa USA 2006

[10] S A Bailey Biomimetic control with a feedback coupled non-linear oscillator insect experiments design tools and hexapedalrobot adaptation results [PhD thesis] Stanford UniversityStanford Calif USA 2004

[11] V Matos C P Santos and C M A Pinto ldquoA brainstem-like modulation approach for gait transition in a quadrupedrobotrdquo in Proceedings of the IEEERSJ International Conferenceon Intelligent Robots and Systems (IROS rsquo09) vol 84 no 12 pp2665ndash2670 St Louis Mo USA October 2009

[12] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 Pasadena Calif USAMay2008

[13] C P Santos and V Matos ldquoGait transition and modulationin a quadruped robot a brainstem-like modulation approachrdquoRobotics and Autonomous Systems vol 59 no 9 pp 620ndash6342011

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience 13

[14] D T Tran I M Koo Y H Lee et al ldquoCentral pattern generatorbased reflexive control of quadruped walking robots using arecurrent neural networkrdquo Robotics and Autonomous Systemsvol 62 no 10 pp 1497ndash1516 2014

[15] K Matsuoka ldquoMechanisms of frequency and pattern control inthe neural rhythm generatorsrdquo Biological Cybernetics vol 56no 5 pp 345ndash353 1987

[16] Y Fukuoka H Kimura and A H Cohen ldquoAdaptive dynamicwalking of a quadruped robot on irregular terrain basedon biological conceptsrdquo The International Journal of RoboticsResearch vol 22 no 3-4 pp 187ndash202 2003

[17] C Liu Q Chen and D Wang ldquoCPG-inspired workspacetrajectory generation and adaptive locomotion control forquadruped robotsrdquo IEEE Transactions on Systems Man andCybernetics vol 41 no 3 pp 867ndash880 2011

[18] L Righetti and A J Ijspeert ldquoPattern generators with sensoryfeedback for the control of quadruped locomotionrdquo in Pro-ceedings of the IEEE International Conference on Robotics andAutomation (ICRA rsquo08) pp 819ndash824 IEEE Pasadena CalifUSA May 2008

[19] K Tsujita K Tsuchiya and A Onat ldquoAdaptive gait patterncontrol of a quadruped locomotion robotrdquo in Proceedings ofthe IEEERSJ International Conference on Intelligent Robots andSystems pp 2318ndash2325 Maui Hawaii USA November 2001

[20] S Aoi T Yamashita A Ichikawa and K Tsuchiya ldquoHysteresisin gait transition induced by changing waist joint stiffnessof a quadruped robot driven by nonlinear oscillators withphase resettingrdquo in Proceedings of the IEEERSJ InternationalConference on Intelligent Robots and Systems (IROS rsquo10) pp1915ndash1920 Taipei Taiwan October 2010

[21] C Maufroy H Kimura and K Takase ldquoIntegration of postureand rhythmicmotion controls in quadrupedal dynamicwalkingusing phase modulations based on leg loadingunloadingrdquoAutonomous Robots vol 28 no 3 pp 331ndash353 2010

[22] B Li Y Li and X Rong ldquoGait generation and transitionsof quadruped robot based on Wilson-Cowan weakly neuralnetworksrdquo in Proceedings of the IEEE International Conferenceon Robotics and Biomimetics (ROBIO rsquo10) pp 19ndash24 TianjinChina December 2010

[23] F Liu and X P Chen ldquoGait evolving method of quadrupedrobot using zero-moment point trajectory planningrdquoRobot vol32 no 3 pp 398ndash404 2010

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014