Hybrid Consensus-Based Control of Nonholonomic Mobile Robot Formation

This paper addresses the hybrid consensus-based formation keeping problem for nonholonomic mobile robots in the presence of a novel time-varying, composite, nonlinear velocity-tracking error system. First, continuous-time regulation and consensus-based formation controllers are developed for a group of wheeled mobile robots. These controllers are then used to create a hybrid automaton, which drives the robots to their goal positions while maintaining a specified formation.In order to avoid the hard switches between regulation and formation keeping controllers, a novel blended velocity tracking error approach is proposed in this work to create nonlinear, time-varying velocity error dynamics. Therefore, the hybrid controller consists of two discrete modes, each with continuous dynamics, and the novel blended velocity tracking error approach provides a smooth transition between each mode. The controller in the regulation mode drives the robot to a goal position while the formation keeping controller ensures that the robots achieve a specified geometric formation prior to reaching their goal-position. Time-varying Lyapunov functions are used to rigorously demonstrate that the formation errors converge to a small bounded region around the origin and the size of the bound can be adjusted by using the switching conditions. Convergence to goal position while in formation is also demonstrated in the same Lyapunov analysis illustrating that the robots are converging to their goal positions while operating in both regulation and formation keeping mode. Simulation results verify the theoretical conjectures