Exploration path generation for multiple mobile robots using reaction-diffusion equation on a graph

In this paper, we present a method to generate exploration path for multiple mobile robots in a restricted working area. In exploration mission by mobile robots, the goal is to minimize the overall exploration time and ensure a thorough exploration. The key problem to be solved is to generate effective exploration paths so that mobile robots share their exploration regions in a working area. During the exploration, in situations in which new obstacles are detected on the paths or some observation points are not reachable by a mobile robot, the generated paths will not permit a thorough exploration. New paths that can ensure thorough exploration must accasionally be re-planned. The method proposed here should re-plan paths with low computational cost. The proposed method is realized by the combination of (a) deployment of the observation points in a working area using a reaction-diffusion equation on a graph, and (b) clustering the observation points to generate exploration paths that have a uniform path length for each mobile robot. Using reaction-diffusion equation on a graph in an observation point deployment will decentralize the computation of each observation point position. The efficiency and robustness of the proposed method are evaluated in simulations and in real exploration missions by two mobile robots in indoor environments.