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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 nonholonomicWheeled Mobile Robots (WMRs) into three subsystems: intra and inter group shapedynamics, and the dynamics of the centroid. The intra group shape dynamics canfurther be partitioned into the shape dynamics of each group, giving the notionof multiple group. Thus separate controllers have been designed for eachsubsystem. The gains of the controllers are such chosen that the overall systembecomes singularly perturbed system, and different subsystems converge to theirdesired values at different times. Then multi-time scale convergence analysishas been carried out in this paper. Negative gradient of a potential basedfunction has been added to the controller to ensure collision avoidance amongthe robots. Simulation results have been provided to demonstrate theeffectiveness of the proposed controller.

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