Probably approximately correct coverage for robots with uncertainty

The classical problem of robot coverage is to plan a path that brings a point on the robot within a fixed distance of every point in the free space. In the presence of significant uncertainty in sensing and actuation, it may no longer be possible to guarantee that the robot covers all of the free space all the time, and so it becomes unclear what problem we are trying to solve. We will restore clarity by adopting a "probably approximately correct" measure of performance that captures the probability 1-ε of covering a fraction 1-δ of the free space. The problem of coverage for a robot with uncertainty is then to plan a feedback policy that achieves a given value of ε and δ. Just as solutions to the classical problem are judged by the resulting path length, solutions to our problem are judged by the required execution time. We will show the practical utility of our performance measure by applying it to several examples in simulation.