A provably complete exploration strategy by constructing Voronoi diagrams

We present novel exploration algorithms and a control law that enables the construction of Voronoi diagrams over unknown areas using a single vehicle equipped with range sensors. The control law uses range measurements to make the vehicle track Voronoi edges between obstacles. The exploration algorithms make decisions at vertices in the Voronoi diagram to expand the explored area until a complete Voronoi diagram is constructed in finite time. Our exploration algorithms are provably complete, and the convergence of the control law is guaranteed. Simulations and experimental results are provided to demonstrate the effectiveness of both the control law and the exploration algorithms.