On the Topologies Conforming Singular Perturbation in Formation Control of Nonholonomic Robots

Abstract

Formation control of a group of robots finds application in generating different geometric patterns and shapes, and also in locking known static or moving objects. This paper mainly explores different topologies which can be used for the formation of single group of wheeled mobile robots with nonholonomic constraints along with the existing ones. These topologies represents the connectivity constraint relationship among the robots. Each of these topologies or transformations separates the group into a reference vector (e.g. a centroid or a leader) and other shape variables, thus separating the overall dynamics into reference dynamics and shape dynamics. The gains of the controllers of these two dynamics are such chosen that the overall dynamics becomes a singularly perturbed system. Thus two dynamics converge at different time, shape vector dynamics being the faster than the reference dynamics. Negative gradient of a potential based function has been appended to the controller to ensure collision avoidance among the robots. Simulation results has been provided to demonstrate the effectiveness of the proposed controller.