A Lateral Control Algorithm for Vision-Based Vehicles with a Moving Target in the Field of View Sadayuki Tsugawa

Abstract |

Hiroaki Mori, and Shin Kato

This paper describes a new lateral con-

trol algorithm that provides steering control to drive a vision-based, autonomous vehicle to hit a target point positioned in a road scene captured with a machine vision system on the vehicle. The control is found with a current location and heading of the vehicle, and a location of the target point and a desirable heading of the vehicle there. The target point, which is updated in every control period, is appropriately positioned to guide the vehicle along a path and to avoid obstacles.

The

algorithm is applicable to various maneuvers including lane following, obstacle avoidance, lane changing, and parking.

Simulation studies have been conducted to

show the feasibility and characteristics of the algorithm.

Keywords |

vision-based vehicle, lateral control, ITS,

AVCSS, AHS, automated driving.

I. Introduction

Lateral control plays an essential role in automated driving systems[1]. It can be classi ed to two types: one is in autonomous vehicles including vision-based vehicles, and the other is in vehicles based on cooperation between intelligence on vehicles and that on infrastructure including vehicles guided with a series of magnetic markers embedded on a roadway. The features of vision-based autonomous vehicles are freedom of design of a vehicle path[2] as well as availability of preview information on paths, which is indispensable to vehicle lateral control[3]. This paper proposes a new lateral control algorithm for a vision-based vehicle. The algorithm uses a moving target in a eld of view available, where the target is appropriately positioned, and the vehicle is guided as if it chased the target. Lateral control algorithms for vision-based vehicles usually employ road boundaries or lane markings, but this algorithm uses a target point in the eld of view. It leads to freedom of design of a path for the vehicle not only on lane following and lane changing but also on obstacle avoidance and parking. The lateral control in this algorithm is found with a current location and heading of the vehicle, and a location of the target point and a desirable heading of the vehicle there. The origin of the algorithm is a dead reckoning-based algorithm[4], which has open loop structure, but the algorithm proposed here has S. Tsugawa and S. Kato are with Mechanical Engineering Laboratory, MITI, Japan, and H. Mori is a student at Graduate School, University of Tsukuba, Japan. E-mail: ftsugawa, hiroaki,[email protected]

Fig. 1. Derivation of the target point following algorithm.

closed loop structure, which makes it feasible. This paper describes derivation of the algorithm, and simulation studies to show the characteristics and feasibility of the algorithm. II. Lateral Control Algorithm

The origin of the algorithm presented here is an algorithm for an automated vehicle with a localization function including the dead reckoning, named the target point following algorithm. If the localization function uses the dead reckoning, the control system has an open loop structure, which is not desirable for the control. The algorithm addressed here is extension of the target point following algorithm for use on a visionbased automated vehicle. A. Target Point Following Algorithm

The target point following algorithm is applied to an automated vehicle driving along a path discretely de ned by a series of points and the heading of the vehicle at each point on a map in the onboard controller. The vehicle is steered to hit a point one after the other with the designated heading. The points are referred as target points, and the algorithm is named after it. Fig. 1 shows the vehicle and a present target point in two coordinate frames. Let (X0; Y0 ) and 20 be the current location and heading of the vehicle in the xed reference frame or in the X 0Y system, and let (X1 ; Y1 ) be the present target point and 21 be the desirable

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heading of the vehicle at the point. In the new coordinate system or in the x0y system, where the location of the vehicle is at the origin and its heading is zero after translation and rotation of the xed reference frame, let (x1 ; y1) be the present target point and 1 be the heading assuming that 1 6= =2. With data from a localization function, (x1 ; y1) and 1 can be calculated with (X1 ; Y1 ) and 21 . In the derivation of the algorithm, the dynamics of a vehicle is described with equations: 8 >
: _

= = =

vx cos  vx sin  vx tan  `

(1)

where (x; y ) is the location of the vehicle,  is the heading of the vehicle, vx is the speed of the vehicle,  is the front wheel steering angle and ` is the wheelbase of the vehicle. The relations hold when the vehicle drives without slip. When there exists a curve that goes through the origin and the target point in the x 0 y system, and the headings of the vehicle at the origin and at the target point are tangential angles of the curve, the curve is assumed to be a path of the vehicle. Because y(0), y (0), y(x1 ), and y (x1 ) have been given, the curve y = y(x) is a cubic curve. The cubic curve is uniquely de ned as follows: y = ax3 + bx2 (2) where a = (x1 tan 1 0 2y1 )=x31 ; b = (3y1 0 x1 tan 1 )=x21: (3) Use of the dynamics in (1) and the cubic curve in (2) and (3) will provide a front wheel steering angle  at the origin in the x 0 y system that leads the vehicle to hit the point (x1; y1 ) with the heading 1 as follows:  = arctan 2`b (4) Equation (4) shows that the front wheel steering angle is a function of the present target point and the expected heading of the vehicle there. There is some limitation on the location of a target point and heading there, but it is not a practical hindrance to application of the algorithm. The procedure for steering the vehicle consists of the translation and rotation of the xed reference frame, and calculation of the steering angle. It is repeated in each control period. When a vehicle arrives at the present target point, the point is replaced with the next one. 0

0

Fig. 2. The moving target point following algorithm.

vehicle. The vision system captures the road scene in front of the vehicle. If a target point and a expected heading of the vehicle there are appropriately de ned in the road scene in the eld of view of the vehicle by an onboard controller as shown in Fig. 2, a current front wheel steering angle can be calculated with Equation (4) to drive the vehicle towards the point. The position of the target point in the eld of view may be updated in every control period, or may be xed for a while. In the former case, the point is relatively still in the eld of view, and in the latter case, the point is relatively approaching the vehicle. In this study, the position of the point and the heading there are updated in every control period. In both cases, the target point moves eventually in front of the vehicle to guide it, and the algorithm is named the moving target point following algorithm. The feature of the algorithm is in exible design of a path for an automated vehicle. This algorithm can, therefore, be applied to not only lane following, lane changing, and obstacle avoidance at high speed driving, but also complicated maneuvers including parking and backing-up at low speed driving. This paper addresses the feasibility of the algorithm and investigates the static and transient characteristics of the algorithm with simulation studies. III. Vehicle Model For Simulation

The lateral control algorithm was derived with a veThe target point following algorithm will be ex- hicle model in (1) based on a geometric relation withtended to an algorithm for a vision-based automated out any consideration on cornering stiness. Before B. Moving Target Point Following Algorithm

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Fig. 3. The notation of the vehicle model.

the investigation of the characteristic of the algorithm, comparison of two vehicle models will be made. One Fig. 4. A simulation result of obstacle avoidance with the algorithm: the vehicle velocity is 5 [m/sec] and the look-ahead model is described in (1). The other shown in Fig. 3 distance is 10 [m]. is based on forces acting on front and rear tires with consideration on cornering stiness, and is described with following variables and parameters: algorithm, named the line following algorithm, is apv: velocity vector (vx ; vy ), plicable to various maneuvers including not only lane f ; r : side slip angles of the front and rear tires, following but also lane changing and obstacle avoid: vehicle yaw angle within a xed frame, ance[2]. Feasibility of the moving target following al: front wheel steering angle, gorithm proposed here will be shown here with a simple m: total mass of the vehicle, I : total inertia of the vehicle around center of grav- example. Fig. 4 shows a simulation result on obstacle avoidity (CG), ance with a vision-based vehicle described by the `f ; `r : distance of the front and rear axles from CG, model in (5). The vehicle is autonomously driving on `: the wheelbase, ` = `f + `r , and the left lane at a speed of 5 [m/sec] by putting a moving cf ; cr : cornering stiness of the front and rear tires. target point at a look-ahead distance of 10 [m]. The The state equations are expressed as: expected direction at the point is straight ahead. The 2 3 a1 0mvx2 + a2       control period is 0.05 [sec] and the point is updated in d vy b1  every control period. When it nds an obstacle ahead, 6 0 mvx 7 vy mvax = + 4 5 a _ _ 3 4 b2   dt a new target point is put on the right lane with the 0I v 0I v  x  x direction as before to make the vehicle change (5) same lanes. After passing the obstacle, the vehicle returns where a1 = cf + cr , a2 = cr `r 0 cf `f , a3 = 0`f cf + `r cr , to the original lane by putting a point on the left lane a4 = `2f cf + `2r cr , b1 = cf =m, b2 = `f cf =I . again. The trajectory the vehicle in Fig. 4 will During the simulation studies, the model in (5) will indicate feasibility of theofalgorithm. be employed, although the algorithm was derived with the model in (1). Trajectories of a vehicle described V. Characteristics of the Algorithm with the two models in (1) and (5) were compared for choice of an appropriate vehicle model, when a si- The characteristics of the algorithm will be investinusoidal input was applied to the front wheels of the gated regarding both static and dynamic performances vehicle models[5]. The results show that there is a with simulation studies. The static performance will little dierence between the trajectories of the two ve- be measured by moving a target point along a circle hicle models. The results were obtained under open- to drive the vehicle also along it, and the dynamic one loop control of a vehicle. Since even open-loop con- will be measured by making a sudden lateral shift of a trol yielded a little dierence, the dierence would be target point to feed a step input to the steering of the vehicle. smaller, if feedback control was employed. Parameters for a vehicle used in the simulation stud- A. Static Performance ies are m=1590 [kg], I =2920 [kg 1m2], `f =1.22 [m], `r =1.62 [m], cf = cr = 2 2 60000 [N/rad], which have The static performance is measured by driving a vebeen cited from a test vehicle[6]. The distance between hicle along a circle at a constant speed. As shown in the front edge of the vehicle and CG is 2.14[m]. Fig. 5, the target point is put on the circle, and the direction is set to be that of a tangent there. The charIV. Feasibility of the Algorithm acteristics are investigated by varying the radius of the A lateral control algorithm for a vision-based au- circle, the vehicle velocity, and the look-ahead distance tonomous vehicles based on the target point following to the point from the vehicle, L. 1998 IEEE International Conference on Intelligent Vehicles

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Fig. 7. Maximum velocity at which the tracking error is within 0.3 [m].

Fig. 5. Evaluation of static performance.

Fig. 6. Maximum velocity at which the vehicle can drive along the circle.

When a target point moves on the circle, the vehicle is possibly steered along the circle. Fig. 6 shows maximum velocities when a vehicle is steered with stability (beyond that velocity the vehicle loses control) by varying the look-ahead distance, L. The result shows the algorithm is feasible under normal velocities. It may, however, contain some errors due to lack of validity of the vehicle model when the radius is small and the velocity is high. When the vehicle drives along the circle by following a moving target point, there remains some tracking error. Fig. 7 shows maximum velocities when the tracking error is kept within 0.3 [m] by varying the lookahead distance, L. The longer the look-ahead distance, L, becomes, the larger the tracking error becomes.

Fig. 8. Evaluation of the dynamic performance.

B. Dynamic Performance

The dynamic performance is measured by making a sudden lateral shift of a target point keeping the same direction to cause the vehicle to change the paths as shown in Fig. 8. This is a kind of step response of the lateral control system of the vehicle. The characteristics are investigated by varying the vehicle velocity, and the look-ahead distance to the point from the vehicle, L. As shown in Fig. 4 and Fig. 8, the vehicle will possibly follow the shift of the point. In Fig. 8, the distance of the shift is 0.5 [m], the vehicle velocity is 5 [m/sec], and the look-ahead distance is 10 [m].

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VI. Conclusion

Fig. 9. Maximum lateral acceleration when the path is laterally shifted.

A lateral control algorithm for a vision-based autonomous vehicles has been proposed and the characteristics have been investigated with simulation studies. The algorithm is featured by exibility in design of a path of a vehicle. It is applicable to lane following, lane changing and obstacle avoidance, and will be possibly to complicated maneuvering including parking. The characteristics have been investigated regarding a static performance and a dynamic one. The static performance shows the algorithm is applicable to high speed autonomous driving along a roadway with small curvature. The dynamic performance indicates an appropriate look-ahead distance of 10 to 15 [m] when the algorithm is employed to the path of a step. The optimal location of a target point and the direction there in the eld of view will be a important issue for application of the algorithm to various maneuvers. References

[1] Shladover, S. E., Review of the State of Development of Advanced Vehicle Control Systems (AVCS), Vehicle System Dynamics, Vol.24,1995, pp.551-595. [2] Tsugawa, S. et al., A Lateral Control Algorithm for VisionBased Vehicles Applicable to Various Maneuvers, Proceedings of 4th ITS World Congress (CD-ROM), October, 1997. [3] Guldner, J. et al., Analysis of Automatic Steering Control [4]

for Highway Vehicles with Look-down Lateral Reference System, Vehicle System Dynamics, Vol.26, 1996, pp.243-269. Tsugawa, S. et al., Steering Control Algorithm for Autonomous Vehicle, Proceedings of 1990 Japan - U. S. A.

Symposium on Flexible Automation, July, 1990, pp.143-146. [5] Tsugawa, S. et al., Optimal Design of Vision System for Lateral Control of Autonomous Vehicle, Proceedings of 4th International Symposium on Advanced Vehicle Control, September, 1998. [6] Kosecka, J. et al., Vision-Based Lateral Control of Vehicles, Proceedings of IEEE Conference on ITS, 1997, pp.900-905. Fig. 10. Settling distance after the path is laterally shifted.

Fig. 9 shows a relation between maximum acceleration and the look-ahead distance, L, when the vehicle changes the paths by a distance of 0.5 [m]. The longer the look-ahead distance becomes, the smaller the acceleration becomes. After the vehicle changes the paths, the behavior of the vehicle may be oscillatory, and the oscillation usually decays as the vehicle proceeds. Fig. 10 shows a relation between a distance where the oscillation decays and settles within 0.005 [m] and the look-ahead distance, L, when the vehicle changes the paths also by a distance of 0.5 [m]. The longer the look-ahead distance becomes, the larger the distance becomes in general. The results in Fig. 9 and Fig. 10 indicate an appropriate look-ahead distance. The appropriate distance will be 10 to 15 [m], if the ride quality expressed by the acceleration and the tracking error expressed by the settling distance are compromised. 1998 IEEE International Conference on Intelligent Vehicles

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