Steering Control for Car Cornering by Means of Learning Using Neural Network and Genetic Algorithm

Copyright © IFAC Intelligent Components for Vehicles, Seville, Spain, 1998

STEERING CONTROL FOR CAR CORNERING BY MEANS OF LEARNING USING NEURAL NETWORK AND GENETIC ALGOR.I1HM

AkihikoShimura' and Kazuo Yoshida"

, Graduate School of Science and Technology, Keio University " Department of System Design Engineering, Faculty of Science and Technology, Keio University

3-14-1 , Hiyoshi, Kohoku, Yokohama, Kanagawa, Japan Fax +81 455601783, Tel +81455601289, E-mail [email protected]

Abstract: Car drivers learn steering operation with exercises, but car dynamics is nonlinear at high speed situation on rough roads or low friction roads. Although skillful drivers might control cars for such nonlinear dynamics, it is difficult for ordinary drivers to control cars for such a situation. In this paper, steering operation for cornering is learned by using a neural network (NN) and a genetic algorithm (GA). The NN controller drives car autonomously with visual information and car states. The inputs to the NN controller are the direction and the curvature of the object path, and the lateral position, the yaw rate and the slip angle of the car. The output from the NN controller is the front steering angle. 4 wheel nonlinear car model with the magic formula of pure cornering is used for an analytical model. The NN controller acquires the driving operation on the curved road as a result of 30 generations iteration of the GA learning. It drives the car successfully on learned and non-learned curved roads. And, it shows the operation that is similar to the counter steering operation which is used by World Rally Championship drivers at tight curved roads. It achieves higher manoeuvrability than any other positive steering controller by using the counter steering. As a result, the availability of the NN controller learns by the GA algorithm for vehicle autonomous driving in nonlinear region is shown. Copyright © 1998 IFAC Keywords: Automotive control, Genetic algorithms, Learning algorithms, Neural networks, Nonlinear control

I,INTRODUCTION

sis that the counter steering is useful for cornering steering (Ono, et aI., 1995). Therefore, it is possible to enhance drive performance with steering control only.

From the viewpoints of safety, comfortably and traffic efficiency, vehicle motion control is important. Cars have nonlinear dynamics, because of the characteristic of force between road and tire is saturated at large slip situation. There are many approaches and available technologies in linear region, but there are not so many in nonlinear region. Generally, combined control of steering and traction is significant in nonlinear region, because it is difficult to control cornering force at the large slip region. On the other hand, many 2WD cars match evenly with 4WD cars in World Rally Championship. And, it was demonstrated by a mathematical analy-

Driving situation always changes, and car drivers' operation aren't so exactly. The neural network (NN) is suitable to learn the operation of drivers, since it is robust and smooth (Kageyama, et al., 1994). But, it is hard to make teaching signals at various roads for the NN, and car drivers learn steering operation by trialand-error. The Genetic Algorithms (GA) learning doesn't require teaching signals and learns by trial-and-error. Therefore, the driver's learning process is similar to the GA learning.

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Table 1 Specifications of Car Parameters

Value

Mass [kg)

2002

Yaw Moment of Inertia [kg m 2 ]

2882

Front Wheel to G.c. [m]

1.126

Rear Wheel to G.c. [m]

1.171

Tread [m)

1.4

Cornering Power in Linear Region (approx .)[N/rad]

F: 39000 R: 46000

Operation

Feel

Object Path

Obj ect ,........""'"-----'----, Path

Output

Input

,--....1..----1.---,

Fig. 2 Relation of Driver / NN Controller and Car 20rn

theta I ..... ' . . ..... . .

4500

Srn

-+-+~r-I.=.. '

d I

Object Path

Fig. 3 Visual Information to NN Controller

1== 0.05

0.1

0,15

0.2

Table 2 Car Driver's Feel and Operation and NN Controller's VO

~!

0.25

Driver's Feel

0.3

Shp Angle {radj

Input to NN

Car Lateral Position in Lane

dl

Fig. 1 Characteristic of Road-Tire Force

Direction of Object Path

theta I

Curvature of Object Path

theta 2

In this paper, nonlinear steeling control strategy with NN is learned with GA. And its usefulness is examined by carrying out computer simulations.

Changing Rate of Car Direction

Yaw Rate

Direction of Slip

Slip Angle

Driver's Operation

Output from NN

Steering Wheel

Front Steering Angle

2. DESIGN OF CONTROL SYSTEM 2.1 Car model

Yaw

Rate--C:~

Slip Angle

The vehicle model (Abe, 1992) is a 4 wheels, 2WS and 3 D.O.F. model with nonlinear road-tire force characteristics. The parameters of the vehicle model are based on the measured data of a small truck on paved road. The specifications of the model are shown in Table I. The road-tire force model is the pure cornering magic formula (Bakker, et al. , 1989). The characteristic of the road-tire force model is shown in Fig. 1. The initial speed of the car is 20 mls. There is not any traction force in the pure cornering model , so that the vehicle speed decreases gradually due to the cornering resistance.

d I

=::::0-- Steering Angle theta I theta 2 I (constant)---,.----

o

Linear OIF Neuron

o Sigmoidal OIF Neuron OIF : Output Function

Fig. 4 Structure of NN Controller car driver'S operation. Table 2 shows the car driver's feel and operation, and the NN controller's I/O. The visual information to the NN controller include the information that is used by a conventional driver model. In addition, the usage of car states in the NN controller enables expanding controllable region in slip angle yaw rate plane (Drive Envelope). The NN controller is a 3 layered NN as shown in Fig. 4. The hidden layer has tangential sigmoid output function with a constant input for offset. The output layer has linear output function, and doesn't have constant input, because of NN controller'S symmetry. A driver's steering operation is symmetric with right and left of curvature and car motion, thus NN controller's steering operation and structure must be also symmetric. The inputs and output are normalized from -1.0 to 1.0.

2.2 NN controller The NN controller drives a car like a car driver as shown in Fig. 2, and then it must sense information and operate like the car driver. The car driver senses direction and curvature of object path, the car position and motion with vision and feeling of car states. The inputs to the NN controller are two angles of object path, lateral position of the car, yaw rate and slip angle as shown in Fig. 3. These inputs include the dominant information that the car driver senses. The output from the NN controller is the steering angle of front wheel as well as

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2.3 GA learning strategy

points fitness. It drives the car successfulIy at tight and loose corner on learned and non-learned roads. At the tight corner where the radius is over 40m, it can drive a car successfully, and the large slip angle and the negative steering operation appeared and look like the counter steering. Fig. 12 shows that the slip angle and the yaw rate locus at the tight corner are out of drive envelope with a positive steering operation. The drive envelope is a limit of controllable region with a positive steering operation (Inagaki, et aI., 1994). It shows that

The evolutionary process of the GA is shown in Fig. 5. In the initial step, 30 individuals are generated at randomly. But, individuals that don't steer straight at straight road are eliminated and regenerated. The distribution range of weight from input layer to hidden layer is -5.0 to 5.0. The distribution range of weight from hidden layer to output layer is -2.0 to 2.0. In the selection step, individuals are selected by the stochastic universal sarnpling method (Baker, 1987). Also the elitist individuals (Elite) are selected by the elitist preserving selection. In the crossover step, the Elite and some other individuals survive as they are, but majority individuals are replaced with children. The parents individuals of the children are selected randomly from all individuals. The children's weights of hidden and output layer neurons are generated with the I-point crossover method (Charnbers, 1995) from parents' weights. In the mutation step, some individuals mutate. Also the Elite never mutate. The mutation changes weights of a selected neuron randomly at a probability. The neuron is selected randomly in hidden layer or output layer.

Fig. 5 GA Learning Flow

The fitness index is defined as the sum of scores of numerical simulations on ten object paths. The paths are simple curved roads as shown in Fig. 6, and their radius and angle are shown in Table 3. The simulation period is 12 seconds. On all object paths, the car can pass out the curves in 12 seconds. The score of each simulation is the sum of tracing score and reaching score. The tracing score is the sum of scores of each 0.2 sec in simulation period. The score of each time period is inverse squared distance from the running trajectory to object path. If the distance is less than 1.0, the score of each time period is 1.0. Then the maximum of the tracing score is 59. The tracing score leads the running trajectories to be along the object paths. The reaching score is the sum of scores at two points shown in Fig. 6. The score of point A is 10 (15 at point B) times of inverse squared distances from the running trajectory to the point. If the distance is short enough, the score of point A is 11 (15 at point B). Then the maximum of reaching score is 26. The reaching score leads the running trajectory to reach exit of the curve. Therefore, the maximum score of each road is 85, and the maximum fitness index of each individual is 850.

Simulation Start Po~ition

50m

Object Path

Fig. 6 Object Path Figure Table 3 Object Path Figure No. Radiu s (mJ

'000

1.2

80

Angle (deg) 45 (right.left)

3,4

65

45 (right.left)

5,6

65

7,8

45

90 (right,left) 45 (right,left)

9,10

40

90

(ri~ht,left)

1

800 ~ )(

I

~ 600 ~ ",,,,,, "'"' u::

3. Simulation results

S

200

After 30 generations learning, some individuals get cornering operation successfully. The learning history of the fitness is shown in Fig. 8. The running trajectory, direction and steering angle of the car with the GA learned NN controller on learned roads are shown in Fig. 9 and 10. These on non-learned roads are shown in Fig. 11. In Fig. 9 and 11, the slip angle and the steering angle are magnified 5 times. The NN controller gets 832

30

JO

Individual

0

Generation

Fig. 8 Learning History of Fitness Index

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100,-----~----_,~------~----__, 0 .8

Unstabilizable region y positi ve steering

0.6

:a

50

I

04

~ O.2

>-

2a!

c

0

c::

.g '(ii 0

:;: -0'

~ -o.~

0

a..

C)

(3

-o.6r

:.E C)

>

-o.~

-50

Unstabilizable region by positive steering

:h':... ., ---o~.'----:--0.':-3---0:':2----:-o.~ ' --'--:0 --'-:-0.:-'---:0"""::" .2 --:':0.3C----:-0.~.~ o.,

Slip Angle [rad]

Fig. 12 Slip Angle - Yaw Rate Locus at Tight Corner (Radius: 40m, Angle: 90deg(right,left»

-100 ~------~----~~------~----~

o

-50

50

100

150

Vehicle Position X [m]

the NN controller achieves higher yaw rate and more agile maneuver than any other controllers that use positive steering only. The NN controller learned and acquired the counter steering operation.

Fig. 9 Car Running Trajectory on Learned Roads

_:::t;;:;/-----.,I O~K;: r

~.~~-----;: '~r-----1'f

-:~'

O~~'

-0.05 -

.

4. Conclusions By applying the GA learning, the NN controller acquires human driver's steering operation on curved roads successfull y. The inputs and output are given corresponding to human driver's senses and operation. The NN controller is learned on various simple curved roads. As a result, it is shown that the NN based on GA learning can acquire nonlinear and skillful human driver's steering operation.

-O . 05~ -----...,---___:-----'·

J;; · " 1~==: ·

-O. 05~----...,---___:----...J

-0.05 -

~:bfi o

4

" ~Et

8

12

0

Time [sec]

4

r r

8

12

Time [sec]

References

Fig. 10 Steering Angle on Learned Roads Abe, M. (1992). Vehicle Dynamics and Control, Chap. 3. Sankai-do, Tokyo Bakker. E, et al. (1989). A New Tire Model with an Application in Vehicle Dynamics Studies. In: SAE paper, No. 890087 Baker, 1. E. (1987). Reducing bias and inefficiency in the selection algorithm . In : Proc. Second Interna tional Conference on Genetic Algorithms, pp. 1421. Chambers, L. ( 1995). Practical Handbook of Genetic Algorithms: Applications, Vol. 1, Chap. 4. CRC Press, Boca Raton Doi, S., E. Ono, and S. Hosoe ( 1995). Anti-Spin Control by Hoc Control. In: Proc. lSAE, No. 954, pp. 141144. Inagaki, S., et al.( 1994). Analysis on Vehicle Stability in Critical Cornering Using Phase-Plane Method. In: Proc. of the International Symposium on Advanced Vehicle Control, pp. 287-292 Kageyama, I., et al . (1994). Modeling of Driver-Vehicle System with Neural Network. In: 1. oflSAE, VoI. 48, No. 12, pp. 5-11.

100 1

I 50

I

>c

g '(ii 0

a..

0

C)

(3

:.E

CD

>

-50

-100L-----~------~------~----~

-50

o

50

100

150

Vehicle Position X [m]

Fig. II Car Running Trajectory on Non-learned Roads

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