Fixed Settling Time Robust Control for Self-Driving Car

Abstract

Self-driving cars are at the center stage of research and development in autonomous systems. The objective of achieving driving autonomy is linked to passenger safety since human driving errors constitute a significant source of loss of life around the globe. Moreover, with the advancements in perception and path planning algorithms for self-driving cars, the vehicle control system is required to become more sophisticated than the erstwhile driving assistance systems like lane following and cruise control. Therefore, self-driving cars’ control under physical constraints, safety-critical time-bound maneuvering constraints at high speeds, and computational time constraints for real-time implementation is a challenging and promising research direction in control systems. This dissertation provides a novel control scheme for self-driving cars under practical constraints. To address the problem, first, a theoretical contribution is presented, which is, a robust fixed settling time sliding mode control (FSTSMC) scheme for a class of nonlinear systems. This approach guarantees that the tracking error reaches a predefined error margin within a known fixed settling time, in the presence of modeling uncertainties and external disturbances. The barrier Lyapunov function is used in conjunction with linear sliding mode control to constraint the nonlinear system within desired bound. The Lyapunov theory-based fixed settling time convergence analysis of the proposed control scheme is also presented. It is worth noting that the existing literature on nonlinear control lacks robust fixed settling time control using a linear sliding manifold. In terms of the contribution toward the self-driving car application, the proposed FSTSMC method is employed to design the longitudinal and lateral controller. The longitudinal control ensures that the reference longitudinal speed is achieved within the fixed settling time for both acceleration and deceleration modes. The lateral control for the self-driving car is rather complex. The steering angle is the input, whereas the yaw angle and lateral position are the outputs, rendering the system as a single-input multi-output (SIMO) underactuated system. However, comparing the time constants, the yaw angle is the fast state, and the lateral position is the slow state. Consequently, the lateral dynamics of the self-driving car are modeled as a iv two-timescale system. The proposed FSTSMC is modified for two timescale systems and implemented to control the lateral dynamics. The trajectory tracking control for combined longitudinal and lateral dynamics under output constraints for a self-driving car is also presented. The tire forces and road friction are treated as unknown external disturbances. To validate the proposed FSTSMC, a software in loop (SIL) evaluation is performed using the Carsim simulator. The proposed FSTSMC control scheme performance is evaluated through Carsim-MATLAB co-simulations. Under output constraints, the fixed settling time controller demonstrates its effectiveness for coupled longitudinal and lateral dynamics in the presence of modeling uncertainties and external disturbances.