# A Homotopy Invariant Based on Convex Dissection Topology and a Distance Optimal Path Planning Algorithm

arXiv: https://arxiv.org/abs/2302.13026 · HTML: https://mlsanity.com/paper/2302.13026/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2023.

## Built on by (most cited first, 2 of 2)

- [Safe and Interpretable Multimodal Path Planning for Multi-Agent Cooperation](https://mlsanity.com/paper/2602.19304/) (2026)
- [The active visual sensing methods for robotic welding: review, tutorial and prospect](https://mlsanity.com/paper/2405.00685/) (2024)

## Abstract (arXiv)

The concept of path homotopy has received widely attention in the field of path planning in recent years. In this article, a homotopy invariant 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 consists 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 CDT-RRT* (Rapidly-exploring Random Tree Star based on Convex Division Topology) is proposed. We designed an efficient sampling formula for CDT-RRT*, which gives it a tendency to actively explore unknown homotopy classes, and incorporated the principles of the Elastic Band 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 invariant in the field of path planning was verified.