Approximate Environment Decompositions for Robot Coverage Planning using Submodular Set Cover

TL;DR

This paper presents a novel method for decomposing 2D environments into overlapping sectors for robot coverage planning, leveraging submodular set cover theory to provide approximation guarantees and improve upon existing methods.

Contribution

The paper introduces a new environment decomposition approach using submodular set cover with approximation guarantees, allowing for overlapping sectors and flexible coverage orientations.

Findings

Provides an approximation guarantee for the number of sectors

Outperforms existing coverage planning methods on real-world maps

Enables flexible, overlapping sector decompositions

Abstract

In this paper, we investigate the problem of decomposing 2D environments for robot coverage planning. Coverage path planning (CPP) involves computing a cost-minimizing path for a robot equipped with a coverage or sensing tool so that the tool visits all points in the environment. CPP is an NP-Hard problem, so existing approaches simplify the problem by decomposing the environment into the minimum number of sectors. Sectors are sub-regions of the environment that can each be covered using a lawnmower path (i.e., along parallel straight-line paths) oriented at an angle. However, traditional methods either limit the coverage orientations to be axis-parallel (horizontal/vertical) or provide no guarantees on the number of sectors in the decomposition. We introduce an approach to decompose the environment into possibly overlapping rectangular sectors. We provide an approximation guarantee on the number of sectors computed using our approach for a given environment. We do this by leveraging the submodular property of the sector coverage function, which enables us to formulate the decomposition problem as a submodular set cover (SSC) problem with well-known approximation guarantees for the greedy algorithm. Our approach improves upon existing coverage planning methods, as demonstrated through an evaluation using maps of complex real-world environments.