Multi Time Scale Behaviour of The Formation of Multiple Groups of Nonholonomic Wheeled Mobile Robots

Different geometric patterns and shapes are generated using groups of agents, and this needs formation control. In this paper, Centroid Based Transformation (CBT), has been applied to decompose the combined dynamics of nonholonomic Wheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shape dynamics, and the dynamics of the centroid. The intra group shape dynamics can further be partitioned into the shape dynamics of each group, giving the notion of multiple group. Thus separate controllers have been designed for each subsystem. The gains of the controllers are such chosen that the overall system becomes singularly perturbed system, and different subsystems converge to their desired values at different times. Then multi-time scale convergence analysis has been carried out in this paper. Negative gradient of a potential based function has been added to the controller to ensure collision avoidance among the robots. Simulation results have been provided to demonstrate the effectiveness of the proposed controller.