Many robotics applications benefit from being able to compute multiple locally optimal paths in a given configuration space. Examples include path planning for of tethered robots with cable-length constraints, systems involving cables, multi-robot topological exploration & coverage, and, congestion reduction for mobile robots navigation without inter-robot coordination. Existing paradigm is to use topological path planning methods that can provide optimal paths from distinct topological classes available in the underlying configuration space. However, these methods usually require non-trivial and non-universal geometrical constructions, which are prohibitively complex or expensive in 3 or higher dimensional configuration spaces with complex topology. Furthermore, topological methods are unable to distinguish between locally optimal paths that belong to the same topological class but are distinct because of genus-zero obstacles in 3D or due to high-cost or high-curvature regions. In this paper we propose an universal and generalized approach to multiple, locally-optimal path planning using the concept of a novel neighborhood-augmented graph, search-based planning in which can compute paths that are topo-geometrically distinct. This approach can find desired number of locally optimal paths in a wider variety of configuration spaces without requiring any complex pre-processing or geometric constructions. Unlike the existing topological methods, resulting optimal paths are not restricted to distinct topological classes, thus making the algorithm applicable to many other problems where locally optimal and geometrically distinct paths are of interest. We demonstrate the use of our algorithm to planning for shortest traversible paths for a tethered robot in 3D with cable-length constraint, and validate the results in simulations and real robot experimentation.

翻译：众多机器人应用受益于在给定配置空间中计算多条局部最优路径的能力。例如，具有缆绳长度约束的系绳机器人路径规划、涉及缆绳的系统、多机器人拓扑探索与覆盖，以及无需机器人间协调的移动机器人导航中的拥堵减少。现有范式采用拓扑路径规划方法，这些方法能够从底层配置空间中可用的不同拓扑类别中提供最优路径。然而，这些方法通常需要非平凡且非通用的几何构造，这在具有复杂拓扑的三维或更高维配置空间中过于复杂或昂贵。此外，拓扑方法无法区分属于同一拓扑类别但因三维中的零亏格障碍物或高成本、高曲率区域而不同的局部最优路径。在本文中，我们提出了一种通用且泛化的多局部最优路径规划方法，该方法基于新颖的邻域增强图概念，在此图上的搜索规划能够计算出拓扑几何不同的路径。该方法无需任何复杂的预处理或几何构造，即可在更广泛的配置空间中找到所需数量的局部最优路径。与现有拓扑方法不同，所得最优路径不局限于不同的拓扑类别，从而使该算法适用于许多其他关注局部最优且几何不同路径的问题。我们展示了该算法在缆绳长度约束下三维系绳机器人的最短可行路径规划中的应用，并通过仿真和实际机器人实验验证了结果。