The goal of coverage path planning is to determine a path that passes a detector over all points in an environment. This work prescribes a provably complete coverage path planner for robots in unknown spaces. We achieve coverage using Morse decompositions which are exact cellular. decompositions whose cells are defined in terms of critical points of Morse functions. Generically, two critical points define a cell. We encode the topology of the Morse decomposition using a graph that has nodes corresponding to the critical points and edges representing the cells defined by pairs of critical points. The robot simultaneously covers the space while incrementally constructing this graph. To achieve this, the robot must sense all the critical points. Therefore, we first introduce a critical point sensing method that uses range sensors. Then we present a provably complete algorithm which guarantees that the robot will encounter all the critical points, thereby constructing the full graph, i.e., achieving complete coverage. We also validate our approach by performing experiments on a mobile robot equipped with a sonar ring.
