Optimal Partitioning of Non-Convex Environments for Minimum Turn Coverage Planning

Abstract

In this letter, we tackle the problem of planning an optimal coverage path for a robot operating indoors. Many existing approaches attempt to discourage turns in the path by covering the environment along the least number of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">coverage lines</i> , i.e., straight-line paths. This is because turning not only slows down the robot but also negatively affects the quality of coverage, e.g., tools like cameras and cleaning attachments commonly have poor performance around turns. The problem of minimizing coverage lines however is typically solved using heuristics that do not guarantee optimality. In this work, we propose a turn-minimizing coverage planning method that computes the optimal number of axis-parallel (horizontal/vertical) coverage lines for the environment in polynomial time. We do this by formulating a linear program (LP) that optimally partitions the environment into axis-parallel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ranks</i> (non-intersecting rectangles of width equal to the tool width). We then generate coverage paths for a set of real-world indoor environments and compare the results with state-of-the-art coverage approaches.