Trajectory tracking and stability control via MPC with adaptive control barrier functions

Abstract

This paper addresses the trade-off between trajectory tracking performance and vehicle stability in front-wheel steering vehicles without differential braking capability and develops a dynamic equilibrium control approach to achieve an adaptive balance between them. The stability phase-plane is constructed using the two-degree-of-freedom vehicle model based on the Dugoff tire model and is partitioned into extensional, classical, and unstable domains using extension theory, serving both to define constraint for the controller and to evaluate the effectiveness of stability control. Subsequently, the Model Predictive Control (MPC) framework is designed, which integrates Control Barrier Function (CBF) and terminal Attraction Region (AR) constraints. Two individual CBFs are formulated, one for the lateral error to constrain trajectory tracking and the other for the yaw rate to maintain vehicle stability. To resolve conflicts between CBFs, the deep deterministic policy gradient (DDPG) is used to dynamically balance their effects. Model-in-the-loop (MIL) and driving simulator (DS) tests show that, compared with a conventional MPC, the proposed method reduces peak lateral error by 37.5%, sideslip angle by 9.3%, and time in unstable domain by 2.6% on high-curvature roads. These results demonstrate that the proposed method effectively enhances lateral control accuracy while maintaining vehicle stability.