We present a fast algorithm for the design of smooth paths (or trajectories) that are constrained to lie in a collection of axis-aligned boxes. We consider the case where the number of these safe boxes is large, and basic preprocessing of them (such as finding their intersections) can be done offline. At runtime we quickly generate a smooth path between given initial and terminal positions. Our algorithm designs trajectories that are guaranteed to be safe at all times, and it detects infeasibility whenever such a trajectory does not exist. Our algorithm is based on two subproblems that we can solve very efficiently: finding a shortest path in a weighted graph, and solving (multiple) convex optimal control problems. We demonstrate the proposed path planner on large-scale numerical examples, and we provide an efficient open-source software implementation, fastpathplanning.

翻译：我们提出了一种快速算法，用于设计约束在轴对齐箱体集合中的平滑路径（或轨迹）。我们考虑安全箱体数量较大且基本预处理（例如寻找它们的交集）可离线完成的情况。在运行时，我们快速生成给定初始位置与终止位置之间的平滑路径。我们的算法设计的轨迹可保证始终安全，且当此类轨迹不存在时能够检测到不可行性。该算法基于两个可高效求解的子问题：在加权图中寻找最短路径，以及求解（多个）凸最优控制问题。我们通过大规模数值示例展示了所提出的路径规划器，并提供了高效的开源软件实现fastpathplanning。