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 multi-class path planning using the concept of a novel neighborhood-augmented graph, search-based planning in which can compute paths in distinct topo-geometric classes. 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. For the demonstration of an application of the proposed approach, we implement our algorithm to planning for shortest traversible paths for a tethered robot with cable-length constraint navigating in 3D and validate it in simulations & experiments.

翻译：许多机器人应用受益于能够在给定构型空间中计算多条局部最优路径，例如具有缆绳长度约束的缆绳约束机器人路径规划、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缓解。现有范式采用拓扑路径规划方法，可从底层构型空间中不同拓扑类别中获得最优路径。然而，这些方法通常需要复杂且非通用的几何构造，在具有复杂拓扑的三维或更高维构型空间中实施时极为复杂或成本高昂。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。本文提出一种通用化的多类别路径规划方法，基于新型邻域增强图概念，通过搜索可计算不同拓扑几何类别中的路径。该方法能够在更广泛的构型空间中获取所需数量的局部最优路径，无需任何复杂预处理或几何构造。与现有拓扑方法不同，所得最优路径不局限于不同拓扑类别，从而使得算法可适用于许多其他关注局部最优且几何相异路径的问题。为演示所提方法的应用，我们将算法实现于三维空间中受缆绳长度约束的缆绳约束机器人最短可通行路径规划，并通过仿真与实验进行验证。