Variable differential neighborhood-based dynamic trajectory planning for automated vehicles

Aiming at the problems of low convex quality in single-neighborhood search, insufficient adaptability to dynamic obstacles, and poor controllability in multi-convex region switching for autonomous vehicle trajectory planning, this paper proposes a dynamic trajectory planning method based on Variable Differential Neighborhood Search (VDNS). The core objectives are to improve the coverage and quality of drivable convex space, enhance the smoothness of trajectory under neighborhood switching, and ensure the stability and convergence of multi-convex shape transition, so as to provide a safe, efficient and robust trajectory planning solution for autonomous driving in dynamic urban traffic scenarios.

Firstly, a differential neighborhood model integrating vehicle kinematics and real-time environmental perception is established. By embedding the Maximum Volume Inscribed Ellipse method into the differential neighborhood search framework, the maximum differential neighborhood at the current moment is generated, which provides a strict lower bound of safe convex polyhedron space and balances the quality and efficiency of neighborhood generation. Secondly, a comprehensive evaluation function considering longitudinal driving distance, lateral deviation and safety margin is constructed, and an adaptive weight adjustment mechanism based on scene risk and motion urgency is introduced to realize the dynamic optimization of the next moment differential neighborhood. Then, the logarithmic barrier function is adopted to transform the trajectory smoothness optimization with inequality constraints into an unconstrained quadratic programming problem, and the Newton iteration method is used to solve it, which suppresses trajectory oscillation and meets vehicle dynamics constraints. Finally, the average dwell-time method is applied to establish the switching stability index of variable differential neighborhood search. Each differential neighborhood is regarded as an independent subsystem, and the sufficient conditions for exponential convergence of the switched system are derived to guarantee the controllability of multi-convex shape transition.

The joint simulation based on PreScan, Simulink and CarSim shows that: 1) Compared with the single-neighborhood search (NS) algorithm and iterative regional inflation (IRIS) algorithm, the proposed VDNS algorithm improves the coverage of drivable convex space by 20% in dynamic obstacle environment and 7% in static obstacle environment, with significantly enhanced heuristic search performance. 2) In two consecutive obstacle avoidance maneuvers, the convergence time of neighborhood switching stability is controlled within 0.6 s and 0.4 s, and the maximum velocity overshoot is only 1.00% and 2.94%, showing strong switching stability. 3) The trajectory generated by VDNS is continuous and smooth without oscillation, which overcomes the shortage of poor smoothness in traditional IRIS algorithm. 4) With the increase of obstacle number, the single-step time complexity of VDNS is lower than that of IRIS, and the computational efficiency is higher in complex environments. 5) The adaptive weight mechanism achieves better balance among safety, efficiency and smoothness, which is superior to the fixed weight strategy in trajectory quality and obstacle avoidance performance.

The VDNS-based dynamic trajectory planning method effectively improves the convex quality of neighborhood search and the controllability of multi-convex region switching. It not only expands the drivable convex space and enhances the dynamic adaptability to obstacles, but also ensures the smoothness of trajectory and the stability of neighborhood switching. This method can be applied to urban dynamic traffic scenarios with static and dynamic obstacles, and provides a new technical approach for real-time, safe and reliable trajectory planning of autonomous vehicles.