Formation control of multiple groups of robots

Formation of multiple groups of agents is an important issue to generate different geometric patterns and shapes. In this paper, a centroid based transformation (CBT), that captures the constraint relationship among agents, has been introduced for multiple groups of agents, and it decomposes the combined dynamics of double integrator systems into intra group shape dynamics, inter group shape dynamics, and the dynamics of the centroid. Upon application of the transformation, a modular architecture is formed, which gives the flexibility to design separate control laws for intra group, inter group shape variables, and the tracking control of the centroid. A new control law has been proposed such that the overall error dynamics becomes singularly perturbed system. Three time scale convergence of the error dynamics, has been achieved by selecting suitable controller gains, and also order of the system is significantly reduced after the convergence of the intra and inter group shape variables. Negative gradient of a potential based function has been appended to the controller to ensure collision avoidance among the agents. Simulation results has been provided to demonstrate the effectiveness of the proposed controller.