Obstacle Avoidance Trajectory Planning for Autonomous Vehicles on Urban Roads Based on Gaussian Pseudo-Spectral Method

Abstract

Urban autonomous vehicles on city roads are subject to various constraints when changing lanes, and commonly used trajectory planning methods struggle to describe these conditions accurately and directly. Therefore, generating accurate and adaptable trajectories is crucial for safer and more efficient trajectory planning. This study proposes an optimal control model for local path planning that integrates dynamic vehicle constraints and boundary conditions into the optimization problem’s constraint set. Using the lane-changing scenario as a basis, this study establishes environmental and collision avoidance constraints during driving and develops a performance metric that optimizes both time and turning angle. The study employs the Gauss pseudo-spectral method to continuously discretize the state and control variables, converting the optimal control problem into a nonlinear programming problem. Using numerical solutions, variable control and state trajectories that satisfy multiple constraint conditions while optimizing the performance metric are generated. The study employs two weights in the experiment to evaluate the method’s performance, and the findings demonstrate that the proposed method guarantees safe obstacle avoidance, is stable, and is computationally efficient at various interpolation points compared to the Legendre pseudo-spectral method (LPM) and the Shooting method.

Keywords

• gauss pseudo-spectral method
• trajectory planning
• optimum control
• dual-index performance indicator function