Coordinated Vehicle Path Tracking and Stability Control with Stability Region Estimation Using Sum-of-Squares Programming

This paper presents a coordinated control algorithm which integrates path tracking performance with stability through direct yaw moment control by regulating motor torque distribution for distributed drive electric vehicle. The control architecture comprises longitudinal and lateral controllers with torque distribution modules. The longitudinal controller utilizes sliding mode control (SMC) to derive desired acceleration, subsequently computing total longitudinal force through vehicle dynamics modeling before distributing specific forces to each wheel. The lateral controller employs model predictive control (MPC) to generate optimal steering angles and yaw moments while accounting for constraints and dynamic state variations. Regarding coordinated stability and tracking control, vehicle stability is quantified through estimation of sideslip angle and yaw rate attraction regions using sum-of-squares (SOS) programming. An adaptive weight adjustment mechanism is designed for the cost function, dynamically prioritizing stability metrics when approaching instability thresholds. Simulation verification confirmed the algorithm's effectiveness in maintaining stability under extreme conditions while preserving tracking accuracy.