Complete sensor-based coverage with extended-range detectors: a hierarchical decomposition in terms of critical points and Voronoi diagrams

Sensor-based coverage uses sensor information to determine a path that passes a detector over all points in an unknown space. Our prior work in coverage prescribed a path for a circular robot of radius r to pass over all points in unknown spaces; in this case we set the detector range δ to be equal to the robot\´s radius, r. Our prior work in Voronoi diagrams prescribed a path for a circular robot with infinite detector range (δ=∞) to pass its detector over all points in an unknown bounded space. This work combines these, results to consider "efficient" coverage with a finite-range detector with r<δ<∞. We define a new hierarchical decomposition with two types of cells: VAST and NARROW. In the VAST-cells, we treat the circular detector like a robot and re-use our critical point based coverage algorithm. In the NARROW-cells, since the obstacles are within the detector range, we effectively have an infinite-range detector, so the robot simply follows the Voronoi diagram. This paper proves that this approach ensures complete coverage with extended-range detectors, which includes a switching procedure from VAST to NARROW-cells