Performing coverage on nonconvex domains

We present a framework for extending coverage algorithms from convex to nonconvex domains. We are particularly interested in coverage in the presence of obstacles, that is domains that contain holes. We identify a class of connected regions in ℝ² than can be mapped through a diffeomorphism to an almost convex region in ℝ² - a convex region from which a finite (possibly empty) set of points has been subtracted. The transformation allows us to solve the coverage problem using the approach of Cortés et al. [1], and obtain the solution of the original problem through inverse transformation. We provide a formal analysis of the approach and demonstrate its effectiveness through simulations. We conclude the paper with a discussion on possible extensions of the work that we are currently undertaking.