Customize Harmonic Potential Fields via Hybrid Optimization over Homotopic Paths

TL;DR

This paper introduces a hybrid optimization method to customize harmonic potential fields for robot navigation, allowing control over path topologies in complex environments while maintaining safety and convergence.

Contribution

It presents a novel approach to find and optimize homotopy classes of paths in harmonic potentials using diffeomorphic transformations and hybrid optimization techniques.

Findings

Successfully generates paths with desired topological properties in complex environments.

Maintains safety and convergence guarantees of harmonic potentials.

Demonstrates effectiveness through extensive simulations and hardware experiments.

Abstract

Safe navigation within a workspace is a fundamental skill for autonomous robots to accomplish more complex tasks. Harmonic potentials are artificial potential fields that are analytical, globally convergent and provably free of local minima. Thus, it has been widely used for generating safe and reliable robot navigation control policies. However, most existing methods do not allow customization of the harmonic potential fields nor the resulting paths, particularly regarding their topological properties. In this paper, we propose a novel method that automatically finds homotopy classes of paths that can be generated by valid harmonic potential fields. The considered complex workspaces can be as general as forest worlds consisting of numerous overlapping star-obstacles. The method is based on a hybrid optimization algorithm that searches over homotopy classes, selects the structure of each tree-of-stars within the forest, and optimizes over the continuous weight parameters for each purged tree via the projected gradient descent. The key insight is to transform the forest world to the unbounded point world via proper diffeomorphic transformations. It not only facilitates a simpler design of the multi-directional D-signature between non-homotopic paths, but also retain the safety and convergence properties. Extensive simulations and hardware experiments are conducted for non-trivial scenarios, where the navigation potentials are customized for desired homotopic properties. Project page: https://shuaikang-wang.github.io/CustFields.