Collision-free formation and heading consensus of nonholonomic robots as a pose regulation problem

This paper presents a novel, decentralized control algorithm to address the problem of controlling of multiple, network connected, nonholonomic mobile robots to achieve a collision-free formation and heading consensus simultaneously. Our approach transforms the formation and heading consensus problem to a pose regulation problem. The pose is derived by a virtual graph, which is an isomorphic mapping of the graph of the network connected systems. If the system is holonomic, traditional consensus on the virtual graph can stabilize the real system to the desired formation. In the case of nonholonomic systems, such as mobile robots, each robot's pose then is regulated to the known consensus pose by a novel smooth and continuous control law. The control law also induces the real robot systems to achieve not only the desired formation but also heading consensus. We prove the proposed control schemes are globally asymptotically stable. Theoretical analysis, several simulations, and experiments have been conducted to verify the effectiveness of the proposed approach.