A Linear Collision Avoidance Constraint Method for Automated Parking Trajectory Optimization Using Vehicle Geometric Analysis

Automated parking trajectory planning presents unique challenges due to confined spaces and complex obstacle distributions in urban environments. This paper formulates the parking trajectory planning as an optimization problem that minimizes path tracking errors and control efforts, where handling the non-convex nature of collision avoidance poses a key computational challenge. The proposed approach transforms these non-convex constraints into linear bounds through geometric analysis of the vehicle rectangular envelope. By leveraging the vehicle’s geometric characteristics, the method derives four-directional linear constraints at each timestep, ensuring collision-free motion while reducing optimization complexity. The approach is integrated into a two-stage planning framework, where Hybrid A* generates an initial path to guide the construction of linear constraint corridors for subsequent trajectory optimization. Experimental results across multiple parking scenarios demonstrate improved computational efficiency compared to conventional non-convex optimization approaches while maintaining satisfactory trajectory smoothness and safety.