Computing variable convex for automated vehicle dynamic trajectory planning

Abstract To address the problems of poor convex quality in single-neighborhood search and inferior controllability during multi-convex-shape transitions for automated vehicles, a dynamic trajectory planning method based on Variable Differential Neighborhood Search (VDNS) is proposed. A differential neighborhood model for automated driving is established. By integrating the Maximum Volume Inscribed Ellipse method into the differential neighborhood search model, the maximum differential neighborhood at the current moment is obtained. An evaluation function encompassing longitudinal distance, lateral deviation, and safety margin is designed to dynamically select the optimal differential neighborhood for the next moment. Trajectory smoothness induced by the variable differential neighborhood search is optimized using a barrier function, and the switching stability index for the variable differential neighborhood search is derived using the average dwell-time method, ensuring controllable multi-convex-shape transitions. Experimental results demonstrate that, compared to the single-neighborhood search method, the proposed VDNS algorithm significantly improves the performance of convex space heuristic search in both dynamic and static environments, increasing the drivable convex space coverage by 20% and 7%, respectively. During two consecutive obstacle avoidance maneuvers, the convergence times for switching stability are controlled within 0.6 s and 0.4 s, with maximum velocity overshoots of only 1% and 2.94%. The results indicate that the VDNS algorithm effectively enhances trajectory generation quality while maintaining strong controllability in environments with both dynamic and static obstacles.