Asymptotically Optimal Ergodic Coverage on Generalized Motion Fields
Authors: Christian Hughes, Yilang Liu, Yanis Lahrach, Julia Engdahl, Houston Warren, Darrick Lee, Fabio Ramos, Travis Miles, +1 more
Organizations: Yale University · Université Catholique de Louvain · Rutgers University · University of Sydney · University of Edinburgh
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.
In this work, we address the problem of multi-robot adaptive coverage, where teams of robots perform dynamic sampling by continuously adjusting their positions to collect data in an environment. This task can be challenging, particularly when robots must be efficiently allocated to new sampling locations over time. Ergodic search methods optimize robot trajectories by ensuring that the robots' time-averaged spatial distribution aligns with the spatial distribution of environmental information. While these methods promote effective exploration provided a target distribution, they often fail to account for unknown prior distributions of the environment. To overcome this limitation, we propose an adaptive coverage strategy that utilizes real-time feedback from an environmental model to adjust robot sampling behavior in response to unknown conditions. Our approach enhances traditional ergodic trajectory optimization by constructing a target spatial information distribution based on parametric models of the environment, which are updated online. This strategy assumes that the environment is either static or changes slowly compared to the robot's motion. Our framework allows robots to dynamically prioritize regions of high interest, improving coverage efficiency, synthesizing effective control policies for individual agents, and optimizing resource use in settings with unknown prior distributions. We validate our approach through simulations, demonstrating its effectiveness in enhancing coverage and resource allocation.
Designing continuous trajectories whose time-averaged occupancy provably matches a prescribed spatial density (the \emph{ergodic coverage} problem) is central to UAV-assisted data collection and sensing, robotic exploration, and mobile monitoring. For flying agents in particular, this challenge is acute: trajectories must balance coverage fidelity against tight energy budgets, no-fly zones, and acceleration limits. Existing methods either re-optimize each trajectory online (with cost growing in the horizon and re-running for every target, agent, and realization) or rely on bespoke analytical constructions that must be re-derived for each new constraint. We propose a \emph{epushforward} framework that decouples ergodicity from density matching: an analytic latent trajectory provides exact uniform ergodicity on a simple annular domain, and a single map, learned offline by optimal-transport conditional flow matching, transports this latent occupancy onto the prescribed target density. The composed trajectory is then asymptotically ergodic with respect to the learned pushforward distribution, with deviation from the target controlled by the flow-matching training loss. Once trained for a given target density and constraint set, the map serves an unbounded number of trajectories and a multi-agent fleet without per-agent retraining, and many differentiable operational constraints (no-fly zones, acceleration ceilings, or fairness penalties) enter as additive soft penalties in the training loss without re-deriving the design. We prove three results (an acceleration-energy bound, an O(1/K) ergodic convergence rate in the number of trajectory cycles K, and an approximation-error bound) that combine into an end-to-end coverage bound estimable from CFM training diagnostics (certified given an architectural Lipschitz bound on vθ).
Ehsan Aghazadeh, Masoud Malekzadeh, Ahmad Ghasemi +1
Autonomous robotic systems are increasingly deployed for mapping, monitoring, and inspection in complex and unstructured environments. However, most existing path planning approaches remain domain-specific (i.e., in the air, on land, or at sea), limiting their scalability and cross-platform applicability. This article presents OmniPlanner, a unified planning framework for autonomous exploration and inspection across aerial, ground, and underwater robots. The method integrates volumetric exploration and viewpoint-based inspection, alongside target reach behaviors within a single modular architecture, complemented by a platform abstraction layer that captures morphology-specific sensing, traversability and motion constraints. This enables the same planning strategy to generalize across distinct mobility domains with minimal retuning. The framework is validated through extensive simulation studies and field deployments in underground mines, industrial facilities, forests, submarine bunkers, and structured outdoor environments. Across these diverse scenarios, OmniPlanner demonstrates robust performance, consistent cross-domain generalization, and improved exploration and inspection efficiency compared to representative state-of-the-art baselines. Videos presenting the OmniPlanner framework and demonstrating its field deployments across aerial, ground, and underwater robots are available at https://ntnu-arl.github.io/omniplanner, and the source code is publicly available at https://github.com/ntnu-arl/gbplanner_ros/tree/gbplanner3.