Approximate Environment Decompositions for Robot Coverage Planning using Submodular Set Cover
Megnath Ramesh, Frank Imeson, Baris Fidan, Stephen L. Smith
TL;DR
The paper addresses efficient coverage path planning (CPP) for 2D environments by decomposing the area into rectangular sectors and solving sector selection as a Submodular Set Cover (SSC) problem. A greedy sector-decomposition approach exploits the submodularity of the sector-coverage function to obtain approximation guarantees, while a sector-touring stage uses a GTSP formulation to stitch sector-covering paths into a complete CPP. Key contributions include formulating sector decomposition as SSC, proving the submodularity of the area-coverage function, providing a theoretical bound on the resulting CPP length, and demonstrating real-world improvements over state-of-the-art baselines on complex maps. The method yields fewer sectors and lower coverage-path costs by allowing non-axis-aligned, overlapping sectors and by merging neighboring sectors, offering practical advantages for robots with versatile sensing or coverage tools. Overall, the work advances CPP by combining principled combinatorial optimization with geometric sector identification to reduce over-decomposition and improve path efficiency.
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.