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：本文提出了一种称为聚类拓扑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（例如从不同侧绕过障碍物）在许多应用中非常有用。其中，在基于优化的轨迹规划中，由于所得轨迹仅受限于给定路径的单一同伦类，因此使用多条不同路径是必要的。同时，不同路径还可用于引导基于采样的运动规划，从而提高在狭窄通道环境中规划的有效性。称为路标图的图结构表示是路径规划以及寻找多条不同路径的常用方法。然而，具有多个狭窄通道的复杂环境需要密集采样的路标图来捕捉环境的连通性。在如此密集的路标图上搜索多条路径在计算上成本过高。因此，现有方法大多仅构建稀疏路标图，但此类稀疏路标图难以在复杂环境中找到所有不同路径。为解决这一问题，我们提出CTopPRM，通过对初始采样的密集路标图进行聚类来创建稀疏图。这种精简的路标图能够快速识别密集路标图中捕获的同伦不同路径。实验表明，与现有方法相比，CTopPRM在相同运行时间内，能将测试环境中找到所有不同路径的概率提高近20%。我们方法的源代码已作为开源包发布。