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In this paper we deal with the problem of covering an environment using a group of mobile robots with nonholonomic kinematic and dynamic constraints. In comparison with standard coverage control procedures, we develop a combined controller for Voronoi-based coverage approach in which kinematic and dynamic constraints of the actual mobile sensing robots are incorporated in the controller design. The stability of the entire systems is guaranteed using Lyapunov stability analysis. Furthermore, a collision avoidance component is incorporated in the kinematic controller in order to guarantee a collision free coverage of the area. Numerical simulations are provided approving the effectiveness of the proposed method through several experimental scenarios.