Optimal line-sweep-based decompositions for coverage algorithms

Robotic coverage is the problem of moving a sensor or actuator over all points in given region. Ultimately, we want a coverage path that minimizes some cost such as time. We take the approach of decomposing the coverage region into subregions, selecting a sequence of those subregions, and then generating a path that covers each subregion in turn. We focus on generating decompositions based upon the planar line sweep. After a general overview of the coverage problem, we describe how our assumptions lead to the optimality criterion of minimizing the sum of subregion altitudes (which are measured relative to the sweep direction assigned to that subregion). For a line-sweep decomposition, the sweep direction is the same for all subregions. We describe how to find the optimal sweep direction for convex polygonal worlds. We then introduce the minimal sum of altitudes (MSA) decomposition in which we may assign a different sweep direction to each subregion. This decomposition is better for generating an optimal coverage path. We describe a method based on multiple line sweeps and dynamic programming to generate the MSA decomposition.