The concept of path homotopy has received widely attention in the field of path planning in recent years. However, as far as we know, there is no method that fast and efficiently determines the congruence between paths and can be used directly to guide the path planning process. In this article, a topological encoder based on convex dissection for a two-dimensional bounded Euclidean space is developed, which can efficiently encode all homotopy path classes between any two points. Thereafter, the optimal path planning task is thus consisted of two steps: (i) search for the homotopy path class that may contain the optimal path, and (ii) obtain the shortest homotopy path in this class. Furthermore, an optimal path planning algorithm called RWCDT (Random Walk based on Convex Division Topology), is proposed. RWCDT uses a constrained random walk search algorithm to search for different homotopy path classes and applies an iterative compression algorithm to obtain the shortest path in each class. Through a series of experiments, it was determined that the performance of the proposed algorithm is comparable with state-of-the-art path planning algorithms. Hence, the application significance of the developed homotopy path class encoder in the field of path planning was verified.

翻译：近年来，路径同伦概念在路径规划领域受到广泛关注。然而，据我们所知，目前尚无一种能快速高效判定路径间同伦关系、并可直接用于指导路径规划过程的方法。本文针对二维有界欧氏空间，提出了一种基于凸剖分的拓扑编码器，能够高效编码任意两点间的所有同伦路径类。据此，最优路径规划任务可分为两步：(i)搜索可能包含最优路径的同伦路径类；(ii)在该类中获取最短同伦路径。进一步地，提出了一种名为RWCDT（基于凸剖分拓扑的随机游走）的最优路径规划算法。该算法采用约束随机游走搜索算法搜索不同同伦路径类，并应用迭代压缩算法获取每类中的最短路径。通过系列实验表明，所提算法性能与当代最优路径规划算法相当，从而验证了所开发同伦路径类编码器在路径规划领域的应用价值。