Asymptotically Optimal Ergodic Coverage on Generalized Motion Fields

TL;DR

This paper introduces a flow-adaptive ergodic coverage method for autonomous exploration in dynamic, deforming environments, providing formal guarantees and effective data collection in challenging settings.

Contribution

It formulates adaptive exploration as an ergodic coverage problem that accounts for evolving domains and flow dynamics, extending previous work with a new flow-adaptive ergodic metric.

Findings

Method generalizes to diverse spatiotemporal processes including oceanography and animal movement.

Experiments demonstrate effective ergodic coverage in flow-restricted, non-convex environments.

Physical robot experiments validate coverage guarantees in real-world scenarios.

Abstract

Autonomous robotic exploration in remote and extreme environments allows scientists to model complex transport phenomena and collective behaviors described by continuously deforming flow fields. Although these environments are naturally modeled as time-varying domains, most adaptive exploration methods assume static environments and fail to provide adequate coverage or satisfy any formal guarantees. This is especially the case in oceanography where autonomous underwater systems (UxS) have highly restrictive compute and payload requirements that necessitate path planning methods that yield robust data collection strategies in open-loop and underactuated settings. In this work, to address the aforementioned issues, we propose to formulate adaptive search as an ergodic coverage problem and investigate certifying coverage in the ergodic sense over evolving domains with flow-induced dynamics. We expand upon recent work demonstrating maximum mean discrepancy (MMD) as a functional ergodic metric, and derive a flow-adaptive formulation that explicitly accounts for domain evolution within the coverage objective. We show that this approach preserves ergodic coverage guarantees in ambient flows and enables effective exploration in under-actuated, and even open-loop planning settings by integrating environment dynamics. Experiments validate that our method generalizes to diverse spatiotemporal processes including ocean exploration, and tracking human and cattle movement. Physical experiments on aerial and legged robotic platforms validate our ability to obtain ergodic coverage in non-convex, flow-restricted environments while respecting robot dynamics.