Three time scale behaviour analysis of the Leader Follower formation of multiple groups of nonholonomic robots

Formation control of multiple groups of agents finds application in generating different geometric patterns and shapes for wide area navigation, and also in locking known static or moving objects. Our previous work [30] entails defining a topology to capture the constraint relationship among multiple groups of robots by means of Centroid Based Transformation (CBT). The calculation of centroid requires information of all the robots of all the groups. In an attempt to reduce the communication overhead, we define a Leader Follower based topology, here in this paper, and introduce Leader Follower Based Transformation (LFT) for multiple groups of robots. LFT decomposes the collective dynamics of nonholonomic wheeled mobile robots into intra and inter group shape variables, and overall leader of the group. This hierarchy gives the flexibility to design separate control laws for intra group, inter group shape variables, and the tracking control of the leader. 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 added to the controller to ensure collision avoidance among the agents. Simulation results has been provided to demonstrate the effectiveness of the proposed controller.