locomotion of a quadruped robot using cpg

7/25/2019 Locomotion of a Quadruped Robot Using CPG

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Locomotion

of

a

Quadruped Robot

Using

CPG

Takayuki

ISHII,

Seiji MASAKADOand

K a m o

ISHII

Dept. of Brain Science and Engineering, Kyush u Institute ofTechnolo gy

Kitakyushu, Fukuoka

8084196

JAPAN

E-mail:

[email protected]

Abst ract - It is well known that the rhythm generator

mechanism called Central Pattern Gene rato r (CPG)

controls rhythmic activities, such as locnmotion,

respiration, heart heat, etc in biological systems, and

various neuron models are proposed. The CPC has

attractive features such that (i)it generates periodical

signals persistently, @)return to the original oscillation

if

disturbances are removed, (i) the mathematical

conditions for oscillation are proved, and so

on.

In this

paper, a CPG network, which consists of the Matsuoka

model neurons, is introduced to realize the locomotion

of a quadruped walking robot and the response to

disturbances is discussed. The outputs of neurons are

utilized as the target angles of corresponding joints and

the efficiency of the proposed method is examined

through experiments with a qua druped walking robot.

1.

INTRODUCTION

Legged robots are expected

as

attractive tools to

transport in various environment such as rough terrain,

nuclear reactors, etc [ I]. The mobile capabilities of human

beings or deers in mountains attract us

in

spite

of

the

difficulties of contml and show

the

possibility of motion

control strategy imitating the processing of nervous

control mechanism.

The

rhythm generator mechanism called Central Pattern

Generator (CPG) [2][3] has been proven to be involved in

rhythmic activities, such

as

locomotion, respiration,

heartbeat, etc. Locomotion employing CPG attracts the

attention because the motion of each joint can be modeled

as the interaction between a nervous system and a

mechanical system.

The

CPG is a model to represent the

mutual inhibition among neurons, such that a neuron's

excitation suppresses other neurons' excitations. Matsuoka

[4]

proposed a mathematical model, and showed some

mathematical conditions of mutual inhabitation networks

represented by a continuous-variable neuron model that

make oscillations. Taga et. a1.[5] proposed the principle of

adaptive control of locomotion system, where nervous,

musculo-skeletal, and sensory systems behave

cooperatively to adapt to unpredictable environments.

In

this paper, a CPG network, which consists of the

Matsuoka model neurons, is introduced to realize

locnmotion

of

a quadruped walking robot and responses to

disturbances are discussed. The outputs of neurons are

utilized as the target of each joint angle, and the efficiency

of the proposed method is examined through experiments

with a quadruped walking robot.

11. CENTRAL PATTERN GENERATOR

CPG is the biological rhythmic system, and consists of

neural oscillators where

a

mutual inhibition among

neurons is modeled such that a neuron's excitation

suppresses others neurons' excitations. Beers et. al [6]

shows that the six legged robot takes reflective action

with a small number of instruction signal and simple

sensor inputs by imitating the nervous system of

cockroach. It is shown that CPG, which generates the

walk rhythm of a vertebrate, exists in a spine, and walk is

autonomously generated in the neuron system of

comparatively a low level below the midbrain [7][8].

In this paper, the mathematical model

of

CPG

proposed by Matsuoka[4]

is

introduced into

the

locomotion of a quadruped robot.

The

model among n

neurons with adaptation is expressed in continuous-

variable form as shown in I) .

7 i =

- , - / ~ : - ~ ~ ~ ? * ~ , , . ~ ~ ~ ~ d ,

1 )

,

r i

- r,

. .

.

=

intixi< .

us

Here, is a potential

of

the

neuron, v

is the variable that

represents the degree of the adaptation, T. T and

j?

are

parameters that specify the time course

of

the adaptation,

the wg indicates the strength of the inhibitory connection

between

the

neurons.

uo

is

an external input with a

constant rate, and feed; is a feed back signal. The

mathematical conditions to generate oscillations are

analyzed precisely in the reference [4]. The attractive

feature is that a CPG can adapt to extraneous signals from

the sensory system, the nervous system and unpredictable

environment, and the outputs of CPG return to the

rhythmical oscillation with the same frequency. A neural

oscillator[5] is illustrated in Fig.

I .

A neural oscillator

Fe

*,


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0 -2.0

-1.0

0 -1.0 0

-1.0 0

-

- 2 . 0

0

0

-1.0

0

-1.0

0

-1.0

-1.0 0 0

- 2 . 0 - 1 . 0

0 -1.0

0

0 - 1 . 0 - 2 . 0

0

0 -1.0

0

-1.0

-1.0

0

-1.0

0

0

- 2 . 0 - 1 . 0

0

0 -1.0 0 -1.0-2.0 0 0 -1.0

-1.0

0

-1.0 -1.0

0

-2.0

0

-1.0

0 -1.0 0 -1.0

-2.0

w. .

=

Fig. 2. Wave gait diagram ofduty factor 0.75.

I S i O

#

P f m r m

.......................

co,din.,ilUr

cOffiaQc-1

...................

Wiuiilx

CoKirirnt:-2

Fig. 3. The CPG network for walk gait of a quadmped

walking robot.

, .......... .........

i

m

t l

U

m

-.I.

Fig. 4. The output of the CPG network. The four neural

oscillators fire successively.

The numbers

,2

correspond to the neurons of left fore leg

(LEGI), 3,4 for the right fore leg (LEGZ),

5 6

far the left

rear leg

LEG3),

and

7 ,

8

for the right rear leg (LEG4),

respectively. The w12 is the weight between the extensor

neuron and the flexor neuron of LEG1 and w13 is the

weight between the extensor neuron of LEG1 and the

extensor neuron of LEGZ. If the w is positive, the

connection excites the other neuron, and if negative, the

connection suppresses the other. Zero means no

connection.

C.

Duty factor and walk phase

In order to generate a stable walk similar with wave gait,

the signal in Fig. 4 are utilized as the switching signal to

change legs from the supported leg phase to the swing leg

phase, and vise versa. If the corresponding signal is larger

than a certain threshold, the

leg

becomes in the swing

phase, and if smaller, the leg becomes in the supported

phase. By changing this threshold, walk gait in various

duty factors can be realized. The precise procedure of

walk gait generation for a quadruped walking robot is

described in the followings.

First, it supposed that one cycle consists of 200 steps. It

divides into the number

of

steps

of

a support leg and the

3 1 x 0

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B 0.5

1- B

B

VB= -V , (4)

0.6 0 7 0.75 0.8

0.9

Changing duty factor while walking can control the

walking speed. However, the robot becomes unstable if

the duty factor is changed rapidly. For example, a horse

changes walk gait according to walk speed and the change

of walk gait is completed within one cycle from a certain

walk gait

tu

another.

In

this research, the transition of walk

gait is realized within one walk cycle by changing the

threshold Th as shown in the following equation.

Th,, = Thvjd Th, hdd)'T

5 )

Here, Th,, is the new gait, Thholds the old gait and Tis the

period of one walk cycle.

E. Adaptation to disturbances

The generation of walk gait and the gait-transition can he

realized by employing the periodical signal

of

the CPG

network. The feature that the CPG network generates

oscillation signal robustly against disturbances, which is

one of interesting feature of CPG network,

is

utilized to

realize an adaptive walking.

The flow chart to deal with the disturbance on foot, the

contact to uneven ground, is shown in Fig. 5 . The

algorithm supposes that a contact of object occurs before

the scheduled time

to

contact the ground. If the touch

sensor of each foot reacts, a feedback signal is given

to

the

Feed, in

I) .

The trajectory of a leg which had a contact signal is shown

in Fig.6. A leg follows the trajectory

I )

to S ) , if there is

no disturbance. If the robot recognizes a level difference in

( 6 ) ,

the

Feed,

makes the leg change

f

he swing phase

to the support phase. If the output of CPG becomes larger

Feed =

- Oufppuf;

( 6 )

Th

0

Fig. 5 . Flow chart for adaptation to disturbances

0.11 0.25 0.3 0.38 0.5

Fig. 6. Trajectory ofleg.

than threshold at 7), it changes

to

the swing phase

between (8) to

9).

Then if there

is

no level difference, a

leg will return

to

I ) and takes the basic trajectory. Since

the mutual control combination of the CPG network, the

output of corresponding leg becomes, and the outputs of

other CPG become larger than threshold compulsorily, this

causes the support phase of other legs longer.

IV.

XP RIM NTS

The following three points are discussed in generating

walk gait of a quadruped robot.

The robot can walk, while it had kept the

posture stable.

The robot can change to various walk gaits

according to a situation.

The robot can be adapted tu disturbance.

(i)

(ii)

(iii)

A.Quadruped walking robot

A quadruped walking robot [9]

is

shown in Fig.

7.

As the

mechanical part, the TITAN-VI11 is introduced and each

leg has 3 DOF. As the sensors, a silicon retina sensor

[IO]

is mounted as the vision system

on

the top of robot, a

touch sensor is attached on each foot, and an attitude

sensor fur rolling, pitching, and heading is in the center of

body. The robot weights about 20 kg and the size

is

approximately

60 x 60

x

50

cm.

Fig. 8 shows the hardware architecture. In this research,

DIA hoards and the serial port are used tu control actuators.

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The target angles of each joint and pan-tilt camera system

are transmined through the DIA board into the DC motor

driver, and from serial port to a servo motor control driver,

respectively. And rolling, pitching and heading angles are

measured with TCMZ sensor and obtained through a serial

port. The image of silicon retina is captured with a image

processing board IP5000, and the touch signals are from a

PI0 board. Fig.9 shows the software architecture. The

RTLinuxver.2.2 (http:llw.rtlinux.org/) is used as the

realtime operating system for the software development.

The RTLinux

is

one of the real-time operating system and

can be available as the Open Source Software. The APIs to

handle the

IiO

data, scheduling and hardware interrupt are

prepared, therefore, the hardware level programming of

the robot is suitable. The low level software such as

sensing, actuation and control are developed as the real-

time threads (kernel module) because this process should

be scheduled in real-time. The image processing is carried

out as the normal Linux process (user program). The data

transmission to each leg of the robot that needs a real-time

control is overated on

the kemel side. and, additionallv, it

Fig. 7. A quadruped walking

robot

Fig.8. Hardware architecture of a quadmped walking

robot.

Fig.9. Software architecture of a quadruped walking

robot.

develops

as

a program

on

the user side. Moreover, the data

of the user program is exchanged for the kernel module

through FIFO and Shared-Memory.

B.

Experimental results

Walk gait in various duty factors can be realized using the

signal from the CPG network, and the relation between

duty factor and speed is investigated. The times to walk 2

[m] long are measured at duty factor 0.75, 0.85, 0.75 ->

0.85 and 0.85 -> 0.75, respectively.

In

the third and fourth

experiments, the duty factor

is

changed after I[m] walk.

The walk time in each duty factor is shown in Table 2.In

the experiments, one cycle time is fixed to 4 [sec],

therefore the robot moves faster when the duty factor is

small.

Table 2. Speed change with various duty factors.

-Change speed by changing duty factor

I

time(sec)

I

46.508

I

53.221

I

49.085 49.845

I

-Adaptation to disturbances

In order to investigate the efficiency of the proposed

method, the experiments are carried out that the robot

carries over a bump with height of 20 [mm] in front of the

left leg (LEGI).

In

the normal condition, the robot lifts up

legs 50 [mm].

Fie.10 shows the outout of the CPG network. In the

points of LEG1 (blue line) indicated with red circles, the

touch sensor of the LEG1 reacted to the bump and

feedback signals are given to the CPG network. Therefore,

the output signals corresponding to LEG1 become small

,......... ~~ ..............................

:-,..


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and other signals are excited. The

Z

position of each foot

is shown in Fig. 11 In the normal state, the Z position is

250 [mm] in the body coordinate. And the Z position of

LEG1 keeps small values while carrying over the bump,

and that of LEG3 becomes small successively. The rolling

and pitching angles of center of body using proposed

method are shown in Fig. 12. Fig. 13 is the resulton

condition that the feedback signals are

not

given to the

CPG network. Comparing the rolling angle with and

without feedback signals, the offset can be observed in

Fig.l3(a). In spite that the robot leans positive direction

around x-axis in the experiment without feedback signal,

the robot keeps the stability utilizing feedback signals. As

for pitching angle, the same results can be observed. The

average and distribution

of

rolling and pitching angle

while the robot having ridden on a bump is shown in Table

3.

It

is shown that the proposed method works as we

expected and keeps the robot stable.

...

.

uw

(a) Rolling angle

* I

..... _ ,

..

..............................

1 1.

OM

5

U

.

*.>

z

a

i:

U

.)I.-

M

.e, i . . . . . . . . I

...... .

I .

Epr

(b) Pitching angle

Fig.12. The experimental results with feedback signals.

1V.

CONCLUSIONS

In this paper, the generation of walk gait using the

Central Pattern Generator (CPG) is proposed and the

efficiency of the adaptation method against disturbances is

examined through the experiments.

Consequently, the walk gait for a quadruped robot can be

generated in various duty factors using CPG. And it is

shown that the walk gait can be changed smoothly by

changing threshold. Furthermore, it is shown that the robot

can keep the posture stable using feedback signal from

touch sensors while carrying over a bump. The CPG

network works as we expected.

In this paper, we discussed a walk gait to a convex

environment. The CPG network should be extended to the

various environments. Moreover, the feedback signal from

vision sensors is under consideration.

References

[I] S.Song, K.J.Waldron, Machines That Walk, The

Adaptive Suspension Vehicle, MIT Press, 1989

[2] G.S.Stent, W.B.Jr.Kristan, W.D.Friesen, C.A.A. Ort,

M.Poon and R.L.Carabrese, Neuronal Generation of the

Leech Swimming Movement, Science, Vol.2W, pp.1348-

1357, 1978

[3] J.T.Bachanam and S.Grillner, Newly Identified

Glutamate Interneurons and Their Role in Locomotion in

Lamprey Spinal Cors Science, Vo1.236, pp. 312-314,

1987

[4] K.Matsuoka: Sustained Oscillations Generated by

Mutually Inhibiting Neurons with Adaptation Biological

Cybemetics Vo1.52 pp.367-376,1985

[ 5 ] G.Taga, Y.Yamaguchi and H.Shimizu: Self-organized

. . . . . . . .

I.,

,

,.

....

......

I_

I

.. i

................................................................................................

c

(a) Rolling angle

. I ... ... ... .. ............... .............. ...... ....

uy

(b) Pitching angle

Fig.

13.

Experimental results without feedback

signals.

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control of bipedal locomotion by neural oscillators in

unpredictable environment Biological Cybernetics vo1.65

[6] RD.Beer, H.J.Chil and L.S.Sterling: An Artificial

1nsectAmerican Scientist Vo1.79 pp.444452, 1991

[7] M.L.Shik and G.N.Orlovsky: Neurophysiology of

Locomotor Automatism Physiol. Review 56, pp.465-501,

1976

[8]

S.Grillner Control of locomotion in bipeds, tetrapods

and

fish

In Handbook of Physiology, volume I I ,

American Physiol. Society, Bethesda,

MD,

pp.1179-1236,

1981

[9] T.Ishii, K.Ishii, Geneartion

of

Walk Gait for the

Quardruped Robot Using Neural Oscillator, Proc. of RSJ

Conf. 2002, 1119,2M)2,pp.

70-71, 2002

[ O ]

K.Shimonomura, . Kame&, K.1shii and T.Yagi, A

Novel Robot Vision Employing a Silicon Retina, Journal

ofRohotics and Mechatoronics, vol. 13. No.4, pp.614-620,

2001

Appeudir

-

Example ofneura l oscillators

The neural oscillators with two to five neurons are

examined.Here T=12.0 T=l.O ~=2.5 andu0=l.O.

The weighting parameters

wv

are set to the same values

for

inhibition. The zero means

no

connection between

neurons.

(i) Two neurons

pp1138-1145,1991

w. .

=

I

.............................................................

. ......

r...w>:

...-i/

.. .

- 0 -1.5

0

-1.5-

-1.5 0 -1.5

0

0

-1.5 0 -1.5

-1.5

0 1.5

0

Fig.A-I. CPG with two neurons.

(ii) Three neurons

-2.5 -2.5

-2.5 -2.5

. . .

-.-.-I

. . . . . . . . . . . .

. .

......

-2.5

0

-2.5 -2.5

I

- 2 . 5 - 2 . 5 0 -2.5

-2.5 -2.5 - 2 . 5

0

w =

Fig.A-2. CPG with three neurons.

wv

=

3184

-2.5

0

-2.5 -2.5 -2.5

-2.5

-2.5

0

-2.5 -2.5

-2.5

-2.5

-2.5 0

-2.5

(iii) Four neurons a)

-.-

Fig. A-5 CPG with five neurons

locomotion of a quadruped robot using cpg

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