Asymptotically Optimal Ergodic Coverage on Generalized Motion Fields

2026-05-13

AI Summary

This work addresses the lack of theoretical guarantees for autonomous exploration in time-varying flow fields by proposing an ergodic coverage method that explicitly incorporates environmental dynamics. It extends the Maximum Mean Discrepancy (MMD) ergodic metric to evolving domains, formulating a coverage objective function that embeds flow field dynamics. The approach achieves asymptotically optimal coverage under open-loop and underactuated constraints. By integrating MMD-based ergodic control, flow-adaptive path planning, and non-convex dynamic environment optimization, the method demonstrates effectiveness in applications such as oceanic surveying and tracking of human or animal movements. Real-world experiments with aerial and legged robots successfully validate its capability to achieve efficient ergodic coverage in non-convex, dynamic flow environments.

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.

Problem

• ergodic coverage
• time-varying domains
• autonomous exploration
• flow-induced dynamics
• underactuated systems

Innovation

• ergodic coverage
• maximum mean discrepancy
• flow-adaptive planning
• time-varying domains
• autonomous exploration