A Discontinuous Consensus Algorithm with Neighbor Counting

A cooperative consensus algorithm is proposed for a group of double integrators. This algorithm is based on minimal relative information and does not use communication networks. Each agent counts the number of predecessor and successor neighbors. The difference of these numbers is used in the controller instead of any accurate range or position measurements. Non-smooth Lyapunov method is used to analyze the stability under the proposed consensus algorithm. Under certain conditions, the proposed protocol can ensure bounded control input, finite-time convergence, or fixed-time convergence. Simulation results illustrate the effectiveness of the proposed algorithm.