Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better approximations of the continuous search space, but makes the search for a solution more computationally costly. A coarser resolution might allow the algorithms to find solutions quickly at the expense of quality. For large state spaces, it can be beneficial to search for solutions across multiple resolutions even though defining the discretisations is challenging. The recently proposed algorithm Multi-Resolution A* (MRA*) searches over multiple resolutions. It traverses large areas of obstacle-free space and escapes local minima at a coarse resolution. It can also navigate so-called narrow passageways at a finer resolution. In this work, we develop AMRA*, an anytime version of MRA*. AMRA* tries to find a solution quickly using the coarse resolution as much as possible. It then refines the solution by relying on the fine resolution to discover better paths that may not have been available at the coarse resolution. In addition to being anytime, AMRA* can also leverage information sharing between multiple heuristics. We prove that AMRA* is complete and optimal (in-the-limit of time) with respect to the finest resolution. We show its performance on 2D grid navigation and 4D kinodynamic planning problems.

翻译：基于启发式搜索的运动规划算法通常通过离散化搜索空间来解决最短路径问题，其性能与离散化精度密切相关。细粒度离散化能够更好地逼近连续搜索空间，但会增加求解的计算成本；粗粒度离散化可快速求得解，却以牺牲解质量为代价。对于大规模状态空间，跨分辨率搜索具有显著优势，但离散化定义本身存在挑战。最新提出的多分辨率A*（MRA*）算法通过跨分辨率搜索，既能以粗分辨率穿越大面积无障碍空间并逃离局部极小值，也能以细分辨率导航狭窄通道。本文提出AMRA*——MRA*的任意时刻版本。AMRA*优先利用粗分辨率快速获取初始解，随后借助细分辨率发现粗分辨率无法获得的更优路径以精细化解。除具备任意时刻特性外，AMRA*还能实现多种启发式之间的信息共享。我们证明了AMRA*在最细分辨率下的完备性与（时间极限意义上的）最优性，并在二维栅格导航和四维动力学规划问题中验证了其性能。