Approximate Topological Optimization using Multi-Mode Estimation for Robot Motion Planning
This work addresses multimodal optimization for robot motion planning, offering a topological approach to path spaces, but it is incremental as it builds on existing single-mode optimization methods.
The paper tackled the problem of finding all local optimal solutions (modes) in robot motion planning to compress path databases and provide replanning contingencies, developing a multi-mode estimation algorithm that asymptotically converges and shows promising initial results.
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.