Generating overtaking trajectories in high-speed scenarios is typically addressed through hierarchical planning, which often suffers from local optima due to single initial solutions and low computational efficiency during numerical optimization. To overcome these limitations, this paper proposes a Spatio-temporal topology and Reachable set analysis enhanced Overtaking trajectory Planning framework (SROP). Specifically, by introducing topological classes to represent distinct overtaking behaviors, the upper-layer planner performs a spatio-temporal search to extract diverse initial paths, effectively preventing local optima. Subsequently, a lower-layer planner conducts parallel trajectory evaluation using reachable sets, which decouples vehicle kinematic constraints from the optimization process to ensure feasibility and significantly accelerate computation. Numerical experiments demonstrate that SROP improves trajectory smoothness by 66.8% and reduces computation time by 62.9% compared to state-of-the-art methods. Furthermore, by seamlessly integrating the method into the F1TENTH autonomous racing simulation platform, a 100-lap sensitivity analysis demonstrates high overtaking success rates in challenging scenarios, thereby validating its practical utility, real-time efficiency, and robustness.

翻译：在高速场景下生成超车轨迹通常采用分层规划方法，但该方法常因单一初始解陷入局部最优，且数值优化过程中计算效率低下。为克服这些局限性，本文提出一种基于时空拓扑与可达集分析增强的超车轨迹规划框架（SROP）。具体而言，通过引入拓扑类来表征不同的超车行为，上层规划器执行时空搜索以提取多样化的初始路径，有效避免了局部最优。随后，下层规划器利用可达集进行并行轨迹评估，将车辆运动学约束从优化过程中解耦以确保可行性，并显著加速计算。数值实验表明，与最先进方法相比，SROP将轨迹平滑度提升66.8%，计算时间减少62.9%。此外，通过将该方法无缝集成至F1TENTH自主赛车仿真平台，在100圈的灵敏度分析中验证了其在复杂场景下极高的超车成功率，从而证实了其实用性、实时效率与鲁棒性。