An Overtaking Trajectory Planning Framework Based on Spatio-temporal Topology and Reachable Set Analysis Ensuring Time Efficiency

TL;DR

Topological classes are introduced 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 to improve trajectory quality and time efficiency.

Abstract

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.

Figures (23)

• Figure 1: The overall architecture of the overtaking trajectory planning framework
• Figure 2: Illustration of overtaking trajectory generation in the $s$-$l$-$t$ configuration space
• Figure 3: Illustration of overtaking trajectory generation on the plane
• Figure 5: Road search graph in spatio-temporal space.
• Figure 6: The search space on raod at $t=t_n$.

Theorems & Definitions (1)

• Definition 1: High Control Feasibility Trajectory