This paper presents an efficient algorithm, naming Centralized Searching and Decentralized Optimization (CSDO), to find feasible solution for large-scale Multi-Vehicle Trajectory Planning (MVTP) problem. Due to the intractable growth of non-convex constraints with the number of agents, exploring various homotopy classes that imply different convex domains, is crucial for finding a feasible solution. However, existing methods struggle to explore various homotopy classes efficiently due to combining it with time-consuming precise trajectory solution finding. CSDO, addresses this limitation by separating them into different levels and integrating an efficient Multi-Agent Path Finding (MAPF) algorithm to search homotopy classes. It first searches for a coarse initial guess using a large search step, identifying a specific homotopy class. Subsequent decentralized Quadratic Programming (QP) refinement processes this guess, resolving minor collisions efficiently. Experimental results demonstrate that CSDO outperforms existing MVTP algorithms in large-scale, high-density scenarios, achieving up to 95% success rate in 50m $\times$ 50m random scenarios around one second. Source codes are released in https://github.com/YangSVM/CSDOTrajectoryPlanning.

翻译：本文提出一种高效算法，命名为集中式搜索与分布式优化（CSDO），用于求解大规模多车辆轨迹规划（MVTP）问题的可行解。由于非凸约束随智能体数量呈难处理性增长，探索蕴含不同凸域的各类同伦类对于寻找可行解至关重要。然而，现有方法因将同伦类探索与耗时的精确轨迹求解相耦合，难以高效探索多种同伦类。CSDO通过将其分离至不同层级并集成高效的多智能体路径查找（MAPF）算法来搜索同伦类，从而克服此局限。该方法首先采用大搜索步长搜索粗略初始猜测，以确定特定同伦类；随后通过分布式二次规划（QP）细化过程处理该猜测，高效消除微小碰撞。实验结果表明，CSDO在大规模高密度场景中优于现有MVTP算法，在50m×50m随机场景中约一秒内达成高达95%的成功率。源代码发布于https://github.com/YangSVM/CSDOTrajectoryPlanning。