Self-adaptive Wheel-side Independent Driving System with Active Suspension

CHEN Wei Institute of Mechanical Science and Engineering,

Jilin University Changchun 130022, China

chenweichx@126.com

LIU Xin-hui Institute of Mechanical Science and Engineering,

Jilin University Changchun 130022, China liuxinhui8015@163.com

Abstract—A new traction-balanced driving vehicle steering in complicated cross country terrains was developed to improve the synchronous driving vehicle steering in complicated terrains low traction efficiency. The vehicle driving system traction-balanced was achieved through hydraulic-resistance control technology applied to the single-side wheel-side hydraulic driving motor and securing the tyro grounding by hydraulic active suspension. The semi-rail vehicle driving system model was set up based on the methods of estimating wheel–terrain contact angles of mobile robots using simple on-board sensors and principle of the pump-control-motor. The simulation showed that when the wheel grounding was secured, the vehicle traction efficiency was improved with the hydraulic-resistance control in different complicated terrains and the vehicle cross-country performance was improved further.

Keywords—self-adaptive wheel-side driving; hydraulic-resistance control; traction-balance

I. INTRODUCTION Cross-country performances is one of important

specifications in cross-country vehicle. The wheel-leg whole-hydraulic rover robots with the advantages of simple control, motion stabilizing, high energy utilization efficiency and so on are put into practice quickly. Currently, the researches of whole-hydraulic cross-country robots are carried out in many countries, such as “Polar Bear” [1] robot developed by University of Alberta in Canada having strong power and ability to adapt various complicated terrains by application of indenpent suspensition system supported by hydraulic cylinder and drived by variable pump. Another instance is “T4”[2] robot developed by Utah State University in USA, having strong motion ability and cross-country performance.

At present, the whole-hydraulic driving vehicles have various driving systems. In many real engineering vehicles, the synchronous driving of each wheel-side driving motor with same rotation rate is realized by compulsive shunt of the pump flow through shunt or twin-lock system [3] shunt. However, due to the uneven terrain in the field environment, the routes of each wheel going across at the same time are different. Thus, the average shunt system would lead to slip

in a wheel or some wheels during the vehicle treading and low traction efficiency.

A new whole-hydraulic driving vehicle technical scheme was introduced in this paper, that is, in order to realize traction-balanced driving, the active suspension system with hydraulic oil cylinder and the hydraulic-resistance control strategy among the wheel-driving motors in same side are adopted. By establishing the semi-rail driving system model and simulating this driving system, the new driving scheme are shown to be able to improve the vehicle power and driving performances.

II. HYDRAULIC DRIVING SYSTEM ANALYSIS The six-wheel hydraulic independent driving system is a

system in which the six wheels were driven by one motor respectively and the six motors were equally divided into left and right group. The driving motor power came from the flow rate controlled by the constant power variable piston pump by two electro-hydraulic proportional controller. In order to insure the vehicle stability as steering in line, the driving wheels in two sides could self-adapt the terrain by adjusting the active suspension to make the wheel keep contact with ground all the time if there is slip in a wheel or some wheels in icy or unsmooth terrain. In addition, by adopting hydraulic-resistance technology to make flow distributed automatically, the balanced-traction in the wheels of two sides is achieved, therefore improving the working efficiency of the vehicle hydraulic driving system. The so-called hydraulic-resistance control technology is to realize the motor flow self-adjustment through the serial-connection of the same throttle orifice in the shunt outlet. It is necessary to monitor each driving motor working state so that the corresponding adjustments could be made under the control system. The schematic of vehicle single side wheel independent driving hydraulic system is shown in Fig.1.

III. VEHICLE DRIVING SYSTEM MODEL During the vehicle steering on cross country terrain, the

different resistances derived from the rugged roads were overcome through the motor torque provided by the inner hydraulic system, so the analysis of the driving system and hydraulic system should be carried out respectively to determine the vehicle dynamic system model. The assumption is made in this paper that under the control of

International Conference on Computer Modeling and Simulation

978-0-7695-3562-3/09 $25.00 © 2009 IEEE

DOI 10.1109/ICCMS.2009.58

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active suspension, each wheel grounding pressure of this 6x6 whole hydraulic driving engineering vehicle is the same during the simulation all time.

A. Driving Dynamic Model

First, the vehicle traction iT and normal pressure iN

should meet the following requirements, and then the rigid

wheel could steer in non-normal rigid terrain normally

0>iN ， ni 1=

maxminLiiLi TrTT ≤≤ ， ni 1=

ii NT μ= ， ni 1=

In which: iT —wheel torque； r —wheel radius； μ —rolling friction from the ground.

As shown in Fig.2, there is an n-wheel vehicle on an unknown road, only the force distribution in x-y plane was considered conjunction with the assumption that the rigid-wheel steers on hard road and all forces in each wheel,

iM ( { }ni ,,1= ), concentrate on one point. And in

Figures: [ ]Tyi

xi VV=iV ( { }ni ,,1= ), expresses Vehicle

vector from the centroid to the iM point in { }xyz space;

[ ]TZyx MFF=F , expresses 3x1 force matrixes in inertia space, including vehicle weight, inertial force, and forces generated in the operation process and others natural forces outside etc; [ ]T

ii NT=iF ( { }ni ,,1= ), expresses force derived from the contact point between each wheel and the ground, this force is the composition of the traction force, iT ,

and the obverse pressure, iN ,in { }xyz space; iα expresses the angle between the tangent of the wheel and ground contact point and horizontal line.

The vehicle with the speed considered in dynamics can

not pass through big obstacles, when the vehicle steers in cross-country roads, so the over-barrier study belongs to the region of statics [7], and the vehicle quasi-static forces equilibrium equation according to Fig.1 and Fig.2 is [6，8]:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎦

⎤⎢⎣

⎡

−−

z

y

x

n

xn

yn

nxyxy

MFF

F

F

VVVVVV

10

22

20

11

10 EEE

(1)

In which: jiE : 2x2 angle matrix between the wheel and the

ground. According to (1), the quasi-static force equilibrium

equation of the 6x6 whole hydraulic driving engineering vehicle is

1. Filter 2. Variable piston pump 3. Relief valve 4. Shunt

5. Throttle orifice 6. Direction-change valve

7. Braking valve block 8. Hydraulic motor

Figure 1. Schematic of the traction-balanced hydraulic control system.

Figure 2. N-wheel vehicle steering on Non-normal rigid roads

295

( )( )

( )( )

( )( )

( )( )

( )( )

( )( )

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−

−

−

−

−

−

z

y

x

xyxyxy

MFF

NTNTNT

VVVVVV

3

3

2

2

1

1

3

3

3

3

3

3

2

2

2

2

2

2

1

1

1

1

1

1

cossin

sincos

cossin

sincos

cossin

sincos

αα

αα

αα

αα

αα

αα

(2)

B. Hydraulic System Model As shown in Fig.1, the flow loss in shunt and direction-

change valve was ignored and the motor was assumed as ideal motor:

tmmtp QPVqPCQ ++=−0

0

βθ (3)

ppppp knqnQ γ== (4)

Lmmfm

mmmmm TGqPCBJPq ++++= θ

θθθθ (5)

In which: mq — motor displacement mθ — motor shaft

rotational angle 0V —single cavity volume P —motor load

pressure tC —total leakage coefficient 0β —effective bulk

spring modulus tQ —flow generated in throttle orifices pn—pump speed pq —variable piston pump displacement γ— pump variable mechanic swinging angle pk — pump

displacement grads J — inertia of motor and load mB —

viscous damping coefficient fC — motor inner friction

coefficient, dimensionless G —load spring stiffness LT —

arbitrary outer load torque. And the throttle equation between the featheredge small

orifices among the motors is:

( )LHdt PPAcQ −′=ρ2

0 (6)

In which: dc′ —flow coefficient 0A —over-flow section area

in the orifice mouth HP 、 LP —pressure before and after throttle ρ —fluid density

After (6) was linearized and this equation was combined with pump-control motor equation, the equation with

Laplace transform in traction-balanced semi-rail vehicle hydraulic system is:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

++−

−+++−

−++

+

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

++−

−+++−

−++

+++⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

3

2

1

40

04

3320

02

110

0

3

2

1

40

04

3320

02

110

0

2

3

2

12

0

0

0

0

)

(333

L

L

L

t

t

t

m

m

m

t

t

t

m

m

m

m

mppm

TTT

ksV

Ck

kkksV

Ck

kksV

C

ksV

Ck

kkksV

Ck

kksV

C

G

sBJssqknq

β

β

β

θθθ

β

β

β

θθθ

γγγ

(7)

In which: 1k 、 2k 、 3k 、 4k —constants after the throttle equation linearization.

IV. DRIVING SYSTEM SIMULATION

A. Driving System Model Parameter The corresponding system model was set up according to

the “Vehicle Driving System Model”. The vehicle was assumed to steer with constant speed, which means the obliquity between the engine speed and piston pump diagonal plate keeps unchanged. The white noise curves were used to replace the terrain conditions to be input to the wheel. One cycle of the gaussin white noise was chosen to illustrate in the simulation curve.

TABLE I. TABLE TYPE STYLES

pump displacement 38mL/r engine speed 2000r/min

motor displacement 468mL/r throttle hole diameter 1mm

flow coefficient 0.661

B. Simulation Curve Analysis The stoke of the active suspension system studied in this

paper was ±250mm, so do the while noise input curves, as shown in Fig.3.

As shown in Fig.4, during the vehicle steering, the pressures in three motors varied and fluctuated according to the terrain white noise input curves in certain ranges. If the

296

pressure rises or decreases in one or two motors, the flow to motor will also vary correspondingly under the self-adjustment of the throttle hole controlled by hydraulic-resistance technology, which means that the wheel rotation speed increases or decreases as the terrain condition changes, as shown in Fig.5 (Fig.6). Consequently, there is no extra driving resistance added resulting from the limitation of the hydraulic driving system in the synchronous driving system.

V. CONCLUSIONS A new whole-hydraulic driving vehicle technical scheme

was introduced in this paper, that is, in order to realize traction-balanced driving, the active suspension system with hydraulic oil cylinder and the hydraulic-resistance control strategy among the wheel-driving motors in same side are adopted. Furthermore, the semi-rail driving system model was set up. The calculation results showed that on the basis of insuring the tyre grounding (realized through active suspension), the vehicle traction balanced driving can be achieved in complicated terrains by the hydraulic-resistance control technology. Thus, the vehicle power and driving performances were further improved.

ACKNOWLEDGMENT The authors wish to show appreciation to the National

Ministry of Science and Technology HI-Tech Research and Development Program of CHINA (863:2007AA04Z208 ).

REFERENCES [1] William G. Agnew, “University of Alberta Autonomous Robotic

Vehicle Project “Polar Bear” Technical Report”, 8th Intelligent Ground Vehicle Competition, June, 2000.

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[3] Wang Qian.“TWIN-LOCK SYSTEM — A SIMPLE SOLUTION TO DIFFICULT TASK[J].FIFTH INTERNATIONAL CONFERENCE ON FLUID POWER TRANSMISSION AND CONTROL (ICFP2001)” .3-5 April, 2001 Hangzhou, China.

[4] Karl Iagnemma, Adam Rzepniewski, Steven Dubowsky and Paul Schenker, “Control of Robotic Vehicles with Actively Articulated Suspensions in Rough Terrain”, Autonomous Robots,2003:14-16.

[5] L.V.V. Gopala Rao, S. Narayanan, “Preview control of random response of a half-car vehicle model traversing rough road”, Journal of Sound and Vibration, doi:10.1016/j.jsv.2007.08.004.

[6] Karl Iagnemma, Steven Dubowsky, “Traction Control of Wheeled Robotic Vehicles in Rough Terrain with Application to Planetary

Figure 3. Road inputs.

Figure 4. The motor pressure curve of three wheels on the ipsilateral

side.

Figure 5. The motor flow curve of three wheels on the ipsilateral

side.

Figure 6. Speeds of the three ipsilateral motors.

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Rovers”, The International Journal of Robotics Research.23, 2004:1029-1040.

[7] Bekker G., “Introduction to Terrain-Vehicle Systems”, University of Michigan Press, 1969.

[8] Karl Iagnemma, Steven Dubowsky, “MOBILE ROBOT ROUGH-TERRAIN CONTROL (RTC) FOR PLANETARY

EXPLORATION”, Proceedings of 2000 ASME IDETC/CIE: 26th Biennial Mechanisms and Robotics Conference, September 2000:10-13.

[9] Seo J., et al, “Feedback linearization based control of a rotational hydraulic drive”, Control Engineering Practice , doi:10.1016/j.conengprac, 2007.02.009.

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