Ergodic Trajectory Optimization on Generalized Domains Using Maximum Mean Discrepancy

TL;DR

This paper introduces a generalized ergodic trajectory optimization method using maximum mean discrepancy, enabling coverage path planning across diverse domains without domain-specific knowledge, and demonstrating improved computational scalability.

Contribution

It extends ergodic trajectory optimization to general domains using kernel MMD, removing the need for domain-specific utility maps and basis functions.

Findings

Successfully generates coverage trajectories on various domains

Shows improved computational scaling over existing methods

Handles differential kinematics constraints and Lie groups

Abstract

We present a novel formulation of ergodic trajectory optimization that can be specified over general domains using kernel maximum mean discrepancy. Ergodic trajectory optimization is an effective approach that generates coverage paths for problems related to robotic inspection, information gathering problems, and search and rescue. These optimization schemes compel the robot to spend time in a region proportional to the expected utility of visiting that region. Current methods for ergodic trajectory optimization rely on domain-specific knowledge, e.g., a defined utility map, and well-defined spatial basis functions to produce ergodic trajectories. Here, we present a generalization of ergodic trajectory optimization based on maximum mean discrepancy that requires only samples from the search domain. We demonstrate the ability of our approach to produce coverage trajectories on a variety of problem domains including robotic inspection of objects with differential kinematics constraints and on Lie groups without having access to domain specific knowledge. Furthermore, we show favorable computational scaling compared to existing state-of-the-art methods for ergodic trajectory optimization with a trade-off between domain specific knowledge and computational scaling, thus extending the versatility of ergodic coverage on a wider application domain.