Backstepping Control Design and Its Applications to Vehicle Lateral Control in Automated Highway Systems

Backstepping Control Design and Its Applications to Vehicle Lateral Control in Automated Highway Systems by Chieh Chen Doctor of Philosophy in Engineering-Mechanical Engineering University of California at Berkeley Professor Masayoshi Tomizuka, Chair In this dissertation the e ort is to explore new aspects of recursive backstepping design methodology from both theoretical and application point of view. Three main topics are investigated in this dissertation from a backstepping perspective: control of multivariable nonlinear systems whose vector relative degrees are not well de ned, steering control of light passenger vehicles on automated highways, and coordinated steering and braking control of commercial heavy vehicles on automated highways. For a class of a ne multivariable nonlinear systems with an equal number of inputs and outputs, if the decoupling matrix is singular, the vector relative degree is not well de ned. If the mutivariable nonlinear system is strongly invertible and strongly accessible, the vector relative degree of the system can be achieved by adding chains 2 of integrators to the input channels. Several versions of dynamic extension algorithms have been proposed to identify the input channels where dynamic compensators (or integrators) are needed to achieve the nonsingularity of the decoupling matrix. Once the vector relative degree is well de ned by adding dynamic compensators in the input channel, the multivariable nonlinear system can be decoupled in the inputoutput sense. In this dissertation, instead of decoupling the nonlinear system by adding chains of integrators in the input channels, we modify the dynamic extension algorithm by incorporating backstepping design methods to partially close the loop in each design step. The resulting control law by this new approach is a static state feedback law. Although the nal closed loop form of the nonlinear system is not decoupled, each output is controlled to the desired value asymptotically. Backstepping design methodology is utilized for lateral control of light passenger vehicles and commercial heavy vehicles in Automated Highway Systems (AHS). The steering control algorithm for light passenger vehicles is designed by utilizing the robust backstepping technique, whereas the coordinated steering and braking control algorithm for commercial heavy vehicles is designed by applying the backstepping technique for multivariable nonlinear systems without vector relative degrees. For lateral control of light passenger vehicles, the lateral tracking error is a ected by the relative yaw angle of the vehicle with respect to the road centerline. Then the relative yaw angle is controlled by the front wheel steering command. Intuitively, this backstepping control procedure resembles the human driver behavior. Mathe3 matically, there is no internal dynamics in this design; i.e., both the lateral and the yaw dynamics are under control. Another advantage of the backstepping controller is that the road disturbance, which does not satisfy the matching condition, can be attenuated e ectively. Thus the backstepping design e ectively utilizes the feedforward information of the road curvature to generate the feedforward part of the steering command. To satisfy both the ride comfort and safety requirements, we introduce a nonlinear spring term (nonlinear position feedback) which exhibits lower gains at small tracking errors and higher gains at larger tracking errors. Furthermore, to cope with nonsmoothness of the road disturbance, robust backstepping control methodology will be utilized. For lateral control of commercial heavy vehicles, a control oriented dynamic modeling approach for articulated vehicles is proposed. A generalized coordinate system is introduced to describe the kinematics of the vehicle. Equations of motion of a tractor-semitrailer vehicle are derived based on the Lagrange mechanics. Experimental studies are conducted to validate the e ectiveness of this modeling approach. Two lateral control algorithms are designed for a tractor-semitrailer vehicle. The baseline steering control algorithm is designed utilizing input-output linearization, whereas the coordinated steering and braking control algorithm is designed based on the multivariable backstepping technique.