General Optimal Trajectory Planning: Enabling Autonomous Vehicles with the Principle of Least Action

This study presents a general optimal trajectory planning (GOTP) framework for autonomous vehicles (AVs) that can effectively avoid obstacles and guide AVs to complete driving tasks safely and efficiently. Firstly, we employ the fifth-order Bezier curve to generate and smooth the reference path along the road centerline. Cartesian coordinates are then transformed to achieve the curvature continuity of the generated curve. Considering the road constraints and vehicle dynamics, limited polynomial candidate trajectories are generated and smoothed in a curvilinear coordinate system. Furthermore, in selecting the optimal trajectory, we develop a unified and auto-tune objective function based on the principle of least action by employing AVs to simulate drivers’ behavior and summarizing their manipulation characteristics of “seeking benefits and avoiding losses.” Finally, by integrating the idea of receding-horizon optimization, the proposed framework is achieved by considering dynamic multi-performance objectives and selecting trajectories that satisfy feasibility, optimality, and adaptability. Extensive simulations and experiments are performed, and the results demonstrate the framework's feasibility and effectiveness, which avoids both dynamic and static obstacles and applies to various scenarios with multi-source interactive traffic participants. Moreover, we prove that the proposed method can guarantee real-time planning and safety requirements compared to drivers’ manipulation.