Approximate Topological Optimization using Multi-Mode Estimation for Robot Motion Planning

TL;DR

This paper introduces an approximate multimodal optimization algorithm for robot motion planning that identifies all local optimal paths with asymptotic guarantees, leveraging Morse theory and sparse roadmaps.

Contribution

It presents a novel multi-mode estimation algorithm that combines sparse roadmaps with existing optimization methods to find all local optima in path planning.

Findings

Algorithm asymptotically converges to all modes

Initial results show promising topological insights

Integrates Morse theory with path optimization

Abstract

In this extended abstract, we report on ongoing work towards an approximate multimodal optimization algorithm with asymptotic guarantees. Multimodal optimization is the problem of finding all local optimal solutions (modes) to a path optimization problem. This is important to compress path databases, as contingencies for replanning and as source of symbolic representations. Following ideas from Morse theory, we define modes as paths invariant under optimization of a cost functional. We develop a multi-mode estimation algorithm which approximately finds all modes of a given motion optimization problem and asymptotically converges. This is made possible by integrating sparse roadmaps with an existing single-mode optimization algorithm. Initial evaluation results show the multi-mode estimation algorithm as a promising direction to study path spaces from a topological point of view.