A coverage algorithm for a class of non-convex regions

The paper describes a framework for solving the coverage problem for a class of non-convex domains. In [1] we have shown how a diffeomorphism can be used to transform a non-convex coverage problem to a convex one to which the Lloyd's algorithm [2] can be applied. In this paper we show how a diffeomorphism can be constructed for convex regions with obstacles in its interior, so that the solution of the transformed problem yields the solution of the original non-convex problem. As part of this investigation we also identify stationary points of the Lloyd's algorithm in non-convex domains. We provide the formal analysis of the approach and demonstrate its effectiveness through simulations.