Multi-Robot Gaussian Process Estimation and Coverage: A Deterministic Sequencing Algorithm and Regret Analysis

TL;DR

This paper introduces a deterministic sequencing algorithm for multi-robot coverage of unknown sensory fields modeled as Gaussian Processes, balancing exploration and exploitation with regret analysis and empirical validation.

Contribution

It proposes the DSLC algorithm that adaptively schedules learning and coverage, providing theoretical regret bounds and demonstrating effectiveness through wildfire coverage simulations.

Findings

DSLC effectively balances exploration and exploitation.

Theoretical upper bounds on coverage regret are established.

Empirical results show successful wildfire coverage simulation.

Abstract

We study the problem of distributed multi-robot coverage over an unknown, nonuniform sensory field. Modeling the sensory field as a realization of a Gaussian Process and using Bayesian techniques, we devise a policy which aims to balance the tradeoff between learning the sensory function and covering the environment. We propose an adaptive coverage algorithm called Deterministic Sequencing of Learning and Coverage (DSLC) that schedules learning and coverage epochs such that its emphasis gradually shifts from exploration to exploitation while never fully ceasing to learn. Using a novel definition of coverage regret which characterizes overall coverage performance of a multi-robot team over a time horizon $T$, we analyze DSLC to provide an upper bound on expected cumulative coverage regret. Finally, we illustrate the empirical performance of the algorithm through simulations of the coverage task over an unknown distribution of wildfires.