Homotopy Path Class Encoder Based on Convex Dissection Topology

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.