In this paper, we propose a new method called Clustering Topological PRM (CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered environments. Finding such distinct paths, e.g., going around an obstacle from a different side, is useful in many applications. Among others, using multiple distinct paths is necessary for optimization-based trajectory planners where found trajectories are restricted to only a single homotopy class of a given path. Distinct paths can also be used to guide sampling-based motion planning and thus increase the effectiveness of planning in environments with narrow passages. Graph-based representation called roadmap is a common representation for path planning and also for finding multiple distinct paths. However, challenging environments with multiple narrow passages require a densely sampled roadmap to capture the connectivity of the environment. Searching such a dense roadmap for multiple paths is computationally too expensive. Therefore, the majority of existing methods construct only a sparse roadmap which, however, struggles to find all distinct paths in challenging environments. To this end, we propose the CTopPRM which creates a sparse graph by clustering an initially sampled dense roadmap. Such a reduced roadmap allows fast identification of homotopically distinct paths captured in the dense roadmap. We show, that compared to the existing methods the CTopPRM improves the probability of finding all distinct paths by almost 20% in tested environments, during same run-time. The source code of our method is released as an open-source package.

翻译：本文提出了一种名为聚类拓扑PRM（CTopPRM）的新方法，用于在三维杂乱环境中寻找多条同伦不同的路径。寻找此类不同路径（例如从不同侧面绕过障碍物）在许多应用中具有实用价值。尤其对于基于优化的轨迹规划器而言，由于所得轨迹仅局限于给定路径的单一同伦类，必须使用多条不同路径。此外，不同路径还可用于引导基于采样的运动规划，从而提高窄通道环境中的规划有效性。基于图表示的路径图是路径规划及寻找多条不同路径的常见表示方式。然而，具有多个窄通道的挑战性环境需要密集采样路径图以捕捉环境连通性，而在如此稠密图中搜索多条路径的计算代价过高。因此，现有方法大多仅构建稀疏路径图，但此类稀疏图在复杂环境中难以发现所有不同路径。为此，我们提出CTopPRM方法，通过对初始采样的稠密路径图进行聚类来生成稀疏图。这种降维后的路径图能够快速识别稠密图中包含的同伦不同路径。实验表明，与现有方法相比，CTopPRM在相同运行时间内将测试环境中发现所有不同路径的概率提升了近20%。本文方法源代码已作为开源包发布。