Lateral Vehicle Control for Semi-Autonomous Valet Parking with Consideration of Actuator Dynamics

In this paper, the lateral control algorithm for semi-autonomous valet parking is presented and its feasibility is demonstrated via field driving tests. With the assumptions of low speed driving and s mall slip angle, a vehicle model with kinemat ic constraints of a steering actuator is proposed todesign the lateral controller. A model-based nonlinear control technique called dynamic surface control is applied to developa lateral control law for forward driving and backward parallel parking maneuvers. Furthermore, the previewcontrol and filteringtechniquesare incorporated in the lateral controller to improve the tracking performance. Since there is measurement noiseregarding position and yaw angle and model uncertainty, it is necessary for the proposed lateral controller to be robust enough to compensate for noise and disturbance. Finally the performance of the lateral controller is validated experimentally v ia field testsas well as simulat ions.


Introduction
The growing attention has been paid to a parking assistance system (PAS) to provide more safety and convenience to a driver. The PASallows the driver to park a car without manual steering control and has been commercializedrecently by many automakers [1]. Furthermore, the advanced parking assistance system (APAS) (o r called self-parking), which makes a vehicle parked autonomously, has been developed [2,3].For instance, autonomous driving including autonomous valet parking (A VP) was demonstrated in the Urban Challengein 2007, wh ich is an autonomous vehicle co mpetition [4,5]. Whereas it succeeded in showing the feasibility of autonomous drivingwith many additional sensors such as radars, lidars, cameras, and u ltrasonic sensors to recognize lane, obstacles, and a parking lot, it is interesting to remark that the detection range to identify an availab le parking lot in a public parking structure is still limited.
Another approach is to develop an intelligent parking infrastructure wh ichprovides usefully driving information such as position of the vehicle, obstacles and location of anavailable parking space to either a driver or a vehicle w ir e les s ly v ia v eh ic le to in f ras t ru ctu r e ( V2 I ) co mmu n icat io n. Since a parking gu idan ce syst em to identify an optimal parking lot and guide the route to the driver has been already developed [6], the develop ment of the intelligent parking infrastructure is feasible if the positions of all vehicles in the parking structure can be measured or estimated.
One possible approach to obtain this information is to use a set of infrastructure sensors such as lidars and cameras, which are imp lemented in the parking structure, not on the vehicle [7]. That is,the infrastructure sensors detect all vehicles within their detection range, and positions of vehicles are estimated by co mb ining all measurements of sensors and location of sensors centrally in an intelligent parking server.
In this paper, a semi-autonomous valet parking (SA VP) system with the cooperation of the intelligent parking infrastructure is considered under the assumption that a driver is in a vehicle and the velocity is controlled manually. Only steering control is performed automatically for forward driv ing to a parking lot and backward parking maneuvers. Furthermore, it is assumed that an optimal parking lot is identified and the corresponding route, i.e., a set of waypoints, is planned by the intelligent parking server, and the corresponding information is sent to the vehicle via V2I co mmunicat ion.
Among many challenging problems for SA VP in the area of perception, planning, commun ication, and control, a lateral control problem is only focused in this paper. More specifically speaking, the challenging control problems to be solved in this paper are summarized as follo ws: •Both measurement noise (especially in position and heading angle) and model uncertainty are considered.
•Various driving maneuvers (e.g., forward driving, temporary stop, and backward parking) need to be conducted in a unified framework of lateral control.
•The driving performance should reflect the behavior of a human driver. Thus, the movement of steering is slow enough to satisfy kinematic constraints of a steering actuator.

Driving Scenario and Hardware
As shown in Fig. 1, it is assumed that the driving scenario for SA VP includes a series of driving maneuvers, i.e., forward driv ing on a straight and curved road (see a waypoint A to B in Fig. 1), temporary stop (at B in the figure), backward parallel parking (B to C in the figure), and complete stop at the waypoint C. Moreover, it is assumed that an available parking location is determined by an SA VP server wh ich monitors all vehicles in a dedicated intelligent parking infrastructure. Then, the corresponding waypoints (refer to the circles in Fig. 1) are delivered to the vehicle controller via V2I co mmunications.  To conduct the given driving maneuvers for SA VP, a test vehicle shown in Fig. 2 has the follo wing capabilit ies: •The steering wheel angle can be controlled by external commands determined fro m the vehicle controller. In fact, it is feasible if a motor drive power steering system (MDPS) which is already co mmercialized is availab le.
•Both position and heading angle of the vehicle with measurement noise are provided. It is noted that a DGPS is used for experimental validation of the proposed lateral controller as shown in Fig.2 although it will be rep laced by infrastructure sensors in the near future.
•There is an electronic control unit (ECU) or processor to compute a steering angle command based on information via V2I co mmunicat ions.
• Gear engagement and wheel speed are measured by in-vehicle sensors and the information is sent to ECU v ia controller area network (CAN).

Lateral Control
The lateral controller to provide the desired steering wheel angle for SA VP needs both trajectory for different driving maneuvers and control laws. A kinemat ic vehicle model subject to kinematic constraints of the steering actuator is proposed and the model-based nonlinear control technique is applied for the controller design.

Trajectory Generation
To perform different driv ing maneuvers such as forward driving and backward parallel parkingas illustrated in Fig. 1, the corresponding trajectory is necessary for the lateral controller. Th ree approaches for the trajectory generation have been found main ly in the literature: a co mbination of lines and circles [8,9], curve fitting [10], and clothoids [11]. In this section, both the combination of circles and curve fitting techniques are used for trajectory generation.
In the case of forward driv ing, the trajectory generation is interpreted as curve interpolation between two given waypoints. Suppose two waypoints are given as p 0 (or a point A) and p 3 (or a point B) as seen in Fig. 3. Ifa cubic Bezier curve interpolation approach is appliedwith two additional control points, p 1 and p 2 , the trajectory for the forward driv ing isdetermined as follows: is the desired trajectory(or a set of reference points) between two waypoints with respect to a local coordinate originated at p 0 , , and the vectors a, b, and c are defined as The shape and smoothness of the trajectory in (1) depends on the selection of two control point points(see p 1 and p 2 in Fig. 3). The control points are written in the coordinate fro m as follows: wherel is a constant which determines the smoothness of trajectory,ψis the yaw angle of the vehicle, and 2 φ is the angle between p 3 and next waypoint. However, it is noted that 2 φ is a predefined angle when the vehicle reaches the waypoint where the parking maneuver begins (refer to a waypoint B in Fig. 3).
For the backward parallel parking, one of the simplest trajectory generation techniques is to use two circles based on Ackermann steering geometry of the vehicle [6]. When the vehicle arrives at an available parking location, i.e., near Parking with Consideration of Actuator Dynamics a waypoint Bin Fig. 3, it is assumed that a parking end point, i.e., a waypoint C in Fig. 3, is given via V2I communicat ion.To generate two circles for parallel parking, an intersection point of two circles, Q in Fig. 3, is first calculated under the assumption that two circles with the same radius are used. Since a circle is uniquely determined when two points on the circle are known, a center and radius of the circle passing a current position near a waypoint B and Q can be determined as follows: Since the center of the second circle, T, can be obtained similarly, the trajectory for the parallel parking can be summarized as follows: where the subscript dstands for thedesired trajectory, and thesubscripts x and y are the positions with respect to x and y directions respectively.

Vehicle Model
A bicycle model has been used widely for design of the lateral controller for highway driving [12]. It is assumed that all system parameters of tire stiffness are known and all wheel angles are small. However, a large amount of wheel angle is generated for parking and it is not easy to identify the system parameters for various types of vehicles.
For the SA VP, the vehicle is driving at low speed and thus sideslip angle is neglected in this study. Thus, the kinemat ic model can be used for both driv ing and parallel parking.The equation of motion is written as follows [13,14] where x and y are the longitudinal and lateral positions of the vehicle, v is the vehicle speed, and δis the steering angle. In addition, the subscript i represents the driving maneuver, i.e., f is forward driving and b is backward driv ing. It is noted that the effective length of wheelbase, L i , instead of the length of wheelbase (L), is used with respect to driving maneuver. Furthermore, the kinemat ic constraints of a steering actuator are considered and they are written as where δ max , ω max are the maximu m steering angle and angular velocity respectively. Suppose a set of parameters in (4) and (5) (4) and (5) are co mpared with experimental data using a test vehicle shown in Fig. 2. The vehicle is driven forward manually fro m 0 to about 75 second, stopped temporarily to changegear engagement for backward driving, and d riven backward fro m about 78 to 110 second (see the first plot in Fig. 4). The corresponding steering angle is shown in the second plot of Fig. 4. Around 78 second, the maximu m steering angle is required for backward parking and the maximu m angular velocity of the steering angle is shown at that time. The angular velocity is approximated by use of difference of the steering angle of five samp les as follows: When the same velocity and steering angle satisfying the constraints in (5) are assigned, it is shown in the fourth and fifth plots of Fig. 4 that both responses of fo rward driving and backward parking are quite similar with the maximu m error deviation of 0.11(rad) and 0.01(rad/s) in terms o f the yaw angle and rate respectively

Lateral Control Law
A model-based nonlinear control technique called dynamic surface control is applied to design alateral controllerat most of speed range [14,15].First, the error surface is defined as follo ws (see also in Fig. 5) [14]: where the lateral error e y is defined as the shortest distance from the current position to the desired trajectory, e d , is calcu lated as andP d comes fro m (1) for forward driv ing and (3) backward parking respectively. Furthermore, the sign of the lateral error in (7) is defined as follo ws: Where [x pd y pd ] T is the preview point and m i is a constant but two different values are assigned for forward driving and backward parking. When the vehicle is placed as in Fig. 5, c is negative and the lateral error in (7) beco mes positive. Then, the positive (or counterclockwise) steering angle co mmand will be determined by the lateral control law which will be discussed later. Furthermo re, d i and ψ d in (6) (6) [8].
After differentiat ing S i in (6) and co mbin ing it with (4), the time derivative of S i is To make S i go to zero, let where K i is acontroller gain. Then the desired steering angle is obtained as Ne xt, two possible cases which may ma ke the control law in (10) vio late the actuator constraints in (5) are considered.
First, the desired steering angle in (10) can be changed rapidly due to the assignment of a large controller gain K i or inclusion of measurement noise. Then the actual steering angle cannot follow the desired steering angle. To solve this problem, the lateral controller is redesigned by introducing a first order low-pass filter. That is, if the desired steering wheel is calculated after passing through as follows: (0) (0) des des des g g g g g τ + = =  (11) the desired steering angle is determined as ) ( tan 1 des des g − = δ (12) It is remarked that g in (9) rather thanδ des in (10) is filtered and it allows us to analyze the stability more easily and clearly [15].
For the second case, since the velocity is controlled manually by a driver, it can be very low or even zero. In this case, the desired steering angle in (10) becomes greater than δ max , thus resulting in saturation of the actuator regardless of the lateral error or S i in (6). Thus, two control laws are switched depending on velocity, i.e., a proportional controller is used when the velocity is very low. Otherwise, the lateral control law in (12) is used. Finally, the modified lateral control law is summarized as follows: whereK pi is a proportional controller gain and εis a velocity threshold.

Validation Results
Suppose 21 waypoints are given as shown in Fig 6. The forward driv ing is required fro m the first to 20 th waypoint (A to B in the figure) and the backward parallel parking is asked fro m 20 th to 21 st waypoint (B to C in the figure). The proposed lateral controller is validated via a vehicle simu lator called CarSim [16] and field tests using a test vehicle shown in Fig. 2. Parking with Consideration of Actuator Dynamics First, the tracking performance of the lateral control law in (13) is validated via simu lations with considerations of measurement noise and kinematic constraints of a steering actuator. Before evaluating the performance, it is shown in Fig 6 that trajectory for forward driving and backward parallel parking is generated appropriately. When measurement noise of position and yaw angle is not considered, the performance of the lateral controller in (10) is shown in Fig. 6 and 7. It is validated in Fig. 7 that two different driving maneuvers can be conducted by the single lateral controller with the maximu m lateral error deviation of about 0.2 (m) (see the top plot in Fig. 7).
However, it is shown in the bottom plot of Fig 7 that the steering angle does not track the desired steering angle sometimes due to the kinematic constraint of the steering angular velocity. If the control law in (13) is used, it is shown in Fig. 8 that the desired steering angle does not violate the kinemat ic constraints much less than one in (10) without any performance degradation in the term of lateral error.  respectively. While the performance of the lateral controller in (10) is degraded with the maximu m lateral error of about 0.5 (m) as shown in Fig. 9, one of the redesigned controller in (13) is not much in the presence of measurement noise and the kinemat ic constraints of the steering actuator (refer to Fig.  10). Fig. 11 shows the snapshot of forward following in the CarSim vehicle simu lator.   The proposed lateral controller is imp lemented in a real vehicle as shown in Fig. 2 and its performance is evaluated via field driving tests. For the given 21 waypoints (see circle marks in Fig. 12), it is shown that the vehicle follows the desired trajectory with a maximu m lateral error deviation of about 0.3 (m)(see also the second plot in Fig.  13).Furthermore, the corresponding time responses of the lateral controller are shown in Fig. 13. It is shown that the vehicle arrives at 20 th waypoint at about 65 second and waits until the gear is shifted to backward. Then, the parallel parking maneuver begins at about 78 second. Finally, snapshots of forward d riv ing, temporary stop, and backward parallel parking are shown in Fig. 14.

Conclusions
The lateral vehicle control algorith mbased on the vehicle model with kinematic constraints of the steering actuator was proposed. It was incorporated with the preview control, switching of mult iple controllers, and filtering of the steering command to compensate for performance degradation due to measurement noise and manual control of velocity.Finally, it was validated via simu lations and field tests that the proposed controller could be applied to conduct two different driv ing maneuvers,i.e., fo rward driv ing and parallel backward parking.
In the near future, it is necessary to consider more various parking maneuvers such as perpendicular and/or mult i-step parking, forward parking, and effect of time delay and packet loss when V2I co mmunication is used.