Hybrid consensus-based formation control of agents with second order dynamics

In this paper, a novel hybrid consensus based formation controller is designed for agents moving in the x-y plane to drive them to a goal point while maintaining a specified formation. The proposed hybrid automaton consists of two discrete states, each with continuous dynamics: a regulation state and a formation keeping state. The controller in the regulation state is designed to drive the agent to a goal position while the formation keeping controller ensures that the agents achieve a specified geometric formation prior to reaching their goalposition. The proposed controller creates hybrid dynamics from the interactions between the continuous and discrete states. The analysis and design of hybrid systems is generally more difficult than that of purely discrete or purely continuous systems since the discrete dynamics may affect the continuous evolution and vice versa. Therefore, the stability of the hybrid approach is proven by using multiple Lyapunov functions and also considers the switching conditions between the regulation and the formation states. The Lyapunov based approach demonstrates 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, and simulation results verify the theoretical conjectures.