Geometrical interpretation on the coverage problems for a mobile agent

This paper addresses the problem of fully covering an a priori known environment with fixed obstacles by a mobile agent. The blind region (i.e., the region hidden by the obstacles from the viewpoint of the agent) is described geometrically via both an exact and an over-approximation procedure. It is shown that the structure of this region depends on the hyperplane arrangement originating from the obstacles. This is further used to provide an mixed integer programming construction which allows to test if the feasible space is (or is not) fully covered by the agent(s). These novel results are examined over illustrative examples.