Measure Preserving Flows for Ergodic Search in Convoluted Environments

TL;DR

This paper introduces a novel ergodic search method using measure-preserving flows and Laplace-Beltrami eigenfunctions to improve autonomous robot search in complex, obstacle-rich environments, ensuring collision-free multi-agent trajectories.

Contribution

It proposes a modified ergodic metric incorporating map geometry and obstacle data, along with measure-preserving vector fields for obstacle avoidance and multi-agent collision-free path planning.

Findings

Effective in complex environments with obstacles

Generates feasible, collision-free trajectories

Outperforms prior ergodic search methods

Abstract

Autonomous robotic search has important applications in robotics, such as the search for signs of life after a disaster. When \emph{a priori} information is available, for example in the form of a distribution, a planner can use that distribution to guide the search. Ergodic search is one method that uses the information distribution to generate a trajectory that minimizes the ergodic metric, in that it encourages the robot to spend more time in regions with high information and proportionally less time in the remaining regions. Unfortunately, prior works in ergodic search do not perform well in complex environments with obstacles such as a building's interior or a maze. To address this, our work presents a modified ergodic metric using the Laplace-Beltrami eigenfunctions to capture map geometry and obstacle locations within the ergodic metric. Further, we introduce an approach to generate trajectories that minimize the ergodic metric while guaranteeing obstacle avoidance using measure-preserving vector fields. Finally, we leverage the divergence-free nature of these vector fields to generate collision-free trajectories for multiple agents. We demonstrate our approach via simulations with single and multi-agent systems on maps representing interior hallways and long corridors with non-uniform information distribution. In particular, we illustrate the generation of feasible trajectories in complex environments where prior methods fail.