Multi-Robot Foremost Coverage of Time-Varying Graphs

Abstract

In this paper we demonstrate the application of time-varying graphs (TVGs) for modeling and analyzing multi-robot foremost coverage in dynamic environments. In particular, we consider the multi-robot, multi-depot Dynamic Map Visitation Problem (DMVP), in which a team of robots must visit a collection of critical locations as quickly as possible, in an environment that may change rapidly and unpredictably during navigation. We analyze DMVP in the context of the $\mathcal {R} \supset \mathcal {B} \supset \mathcal {P}$ TVG hierarchy. We present exact offline algorithms for $k$ robots on edge-recurrent TVGs ($\mathcal {R}$) over a range of topologies motivated by border coverage: an $O(Tn)$ algorithm on a path and an $O(T\frac{n^2}{k})$ algorithm on a cycle (where $T$ is a time bound that is linear in the input size), as well as polynomial and fixed parameter tractable solutions for more general notions of border coverage. We also present algorithms for the case of two robots on a tree (and outline generalizations to $k$ robots), including an $O(n^5)$ exact algorithm for the case of edge-periodic TVGs ($\mathcal {P}$) with period 2, and a tight poly-time approximation for time-bounded edge-recurrent TVGs ($\mathcal {B}$). Finally, we present a linear-time $\frac{12 \varDelta }{5}$-approximation for two robots on general graphs in $\mathcal {B}$ with edge-recurrence bound $\varDelta$.