As autonomous driving continues to advance, automated parking is becoming increasingly essential. However, significant challenges arise when implementing path velocity decomposition (PVD) trajectory planning for automated parking. The primary challenge is ensuring rapid and precise collision-free trajectory planning, which is often in conflict. The secondary challenge involves maintaining sufficient control feasibility of the planned trajectory, particularly at gear shifting points (GSP). This paper proposes a PVD-based rapid iterative trajectory planning (RITP) method to solve the above challenges. The proposed method effectively balances the necessity for time efficiency and precise collision avoidance through a novel collision avoidance framework. Moreover, it enhances the overall control feasibility of the planned trajectory by incorporating the vehicle kinematics model and including terminal smoothing constraints (TSC) at GSP during path planning. Specifically, the proposed method leverages differential flatness to ensure the planned path adheres to the vehicle kinematic model. Additionally, it utilizes TSC to maintain curvature continuity at GSP, thereby enhancing the control feasibility of the overall trajectory. The simulation results demonstrate superior time efficiency and tracking errors compared to model-integrated and other iteration-based trajectory planning methods. In the real-world experiment, the proposed method was implemented and validated on a ROS-based vehicle, demonstrating the applicability of the RITP method for real vehicles.

Generating overtaking trajectories in high-speed scenarios presents significant challenges and is typically addressed through hierarchical planning methods. However, this method has two primary drawbacks. First, heuristic algorithms can only provide a single initial solution, which may lead to local optima and consequently diminish the quality of the solution. Second, the time efficiency of trajectory refinement based on numerical optimization is insufficient. To overcome these limitations, this paper proposes an overtaking trajectory planning framework based on spatio-temporal topology and reachable set analysis (SROP), to improve trajectory quality and time efficiency. Specifically, this paper introduces topological classes to describe trajectories representing different overtaking behaviors, which support the spatio-temporal topological search method employed by the upper-layer planner to identify diverse initial paths. This approach helps prevent getting stuck in local optima, enhancing the overall solution quality by considering multiple initial solutions from distinct topologies. Moreover, the reachable set method is integrated into the lower-layer planner for parallel trajectory evaluation. This method enhances planning efficiency by decoupling vehicle model constraints from the optimization process, enabling parallel computation while ensuring control feasibility. Simulation results show that the proposed method improves the smoothness of generated trajectories by 66.8% compared to state-of-the-art methods, highlighting its effectiveness in enhancing trajectory quality. Additionally, this method reduces computation time by 62.9%, demonstrating its efficiency.