解决凸集图中起始与目标区域断连问题，让机器人规划重获可行路径。
GCS-Bridging: Restoring Connectivity of Disconnected Convex Sets for Graph-of-Convex-Sets Motion Planning
- 通过无碰撞路径连接断开的凸集，再膨胀恢复连通性。
- 在多种算法和场景下恢复连通性成功率高达99.8%。
- 适用于实际机器人平台，验证了方法在真实环境中的有效性。
基于凸集图（GCS）的轨迹优化将配置空间中的无碰撞区域表示为一组有限的凸集，并直接在此基础上进行无碰撞轨迹规划，显著简化了规划过程。然而，现有GCS方法通常假设凸区域间具备足够连通性，未显式处理起点与目标区域属于初始GCS地图不同连通分量的情况。为此，本文提出GCS-Bridging，通过生成无碰撞点路径连接断开的凸集，并随后进行凸集膨胀，从而恢复原本不可行的GCS规划问题的可行性。在多个IRIS相关算法和场景下的大量仿真表明，GCS-Bridging在初始GCS地图中成功恢复了起始到目标的连通性，成功率高达99.8%。此外，在单臂Franka平台的真实世界场景中，针对初始断连的起始与目标区域进行的硬件实验，验证了该方法在实际运动规划中的有效性。项目主页：https://zhouxk1997.github.io/GCS_Bridging/
原文摘要 · Abstract (English)
Graph-of-Convex-Sets (GCS)-based trajectory optimization represents collision-free regions in configuration space as a finite collection of convex sets and directly performs collision-free trajectory planning over these sets, substantially simplifying the planning process. However, existing GCS-based trajectory planning methods generally assume sufficient connectivity among the convex regions and do not explicitly address cases in which the start and goal regions belong to different connected components of the initial GCS map. To address this limitation, we propose GCS-Bridging, which reconnects disconnected convex regions through collision-free point paths followed by convex region inflation, thereby recovering the feasibility of otherwise disconnected GCS planning problems. Extensive simulations across multiple IRIS-related algorithms and scenarios demonstrate that GCS-Bridging restores missing start-to-goal connectivity in the initial GCS map with a 99.8% success rate. In addition, a hardware experiment on a single-arm Franka platform in a real-world scenario with initially disconnected start and goal regions validates the effectiveness of the proposed method in practical motion planning. Project website: https://zhouxk1997.github.io/GCS_Bridging/
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