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

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.

arXiv comment5 pages, Extended Abstract for RSS Workshop on Geometry and Topology in Robotics

References in corpus (6)

• Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference
• The Topology ToolKit
• Long-Horizon Multi-Robot Rearrangement Planning for Construction Assembly
• Local Optima Networks: A New Model of Combinatorial Fitness Landscapes
• Newton methods for k-order Markov Constrained Motion Problems
• Implicit Multiagent Coordination at Unsignalized Intersections via Multimodal Inference Enabled by Topological Braids