Volumetric Ergodic Control

TL;DR

This paper introduces a volumetric ergodic control method that enhances coverage efficiency for robots interacting with volumetric environments, maintaining guarantees and supporting real-time applications.

Contribution

It extends ergodic control to volumetric representations, improving coverage efficiency while preserving theoretical guarantees and supporting diverse robot models.

Findings

Improves coverage efficiency by over 2x compared to standard ergodic control.

Maintains 100% task completion rate across various experiments.

Supports real-time control with minimal computational overhead.

Abstract

Ergodic control synthesizes optimal coverage behaviors over spatial distributions for nonlinear systems. However, existing formulations model the robot as a non-volumetric point, whereas in practice a robot interacts with the environment through its body and sensors with physical volume. In this work, we introduce a new ergodic control formulation that optimizes spatial coverage using a volumetric state representation. Our method preserves the asymptotic coverage guarantees of ergodic control, adds minimal computational overhead for real-time control, and supports arbitrary sample-based volumetric models. We evaluate our method across search and manipulation tasks -- with multiple robot dynamics and end-effector geometries or sensor models -- and show that it improves coverage efficiency by more than a factor of two while maintaining a 100% task completion rate across all experiments, outperforming the standard ergodic control method. Finally, we demonstrate the effectiveness of our method on a robot arm performing mechanical erasing tasks. Project website: https://murpheylab.github.io/vec/