Incremental Multi-Scale Search Algorithm for Dynamic Path Planning With Low Worst-Case Complexity

Path-planning (equivalently, path-finding) problems are fundamental in many applications, such as transportation, VLSI design, robot navigation, and many more. In this paper, we consider dynamic shortest path-planning problems on a graph with a single endpoint pair and with potentially changing edge weights over time. Several algorithms exist in the literature that solve this problem, notably among them the Lifelong Planning algorithm. The algorithm is an incremental search algorithm that replans the path when there are changes in the environment. In numerical experiments, however, it was observed that the performance of is sensitive in the number of vertex expansions required to update the graph when an edge weight value changes or when a vertex is added or deleted. Although, in most cases, the classical requires a relatively small number of updates, in some other cases the amount of work required by the to find the optimal path can be overwhelming. To address this issue, in this paper, we propose an extension of the baseline algorithm, by making efficient use of a multiscale representation of the environment. This multiscale representation allows one to quickly localize the changed edges, and subsequently update the priority queue efficiently. This incremental multiscale ( for short) algorithm leads to an improvement both in terms of robustness and computational complexity-in the worst case-when compared to the classical . Numerical experiments validate the aforementioned claims.