Asymptotic Leaderless Consensus Control of Nonholonomic Chained Systems

This paper designs a smooth time-invariant distributed static control law to solve the asymptotic distributed leaderless consensus control problem of nonholonomic chained systems over a communication graph. A novel Lyapunov function is firstly constructed, then a control law is constructed to ensure the Lyapunov function non-increasing. The Lyapunov method, the LaSalle invariance principle, the graph theory, technical lemmas and matrix computations are used to analyze the system stability, overcoming the difficulties caused by high dimension and nonholonomic constraint. The proposed control law is able to guarantee the state vector of the whole systems globally asymptotically converge to a common configuration, under undirected connected communication scenarios. A numerical simulation example is implemented to demonstrate the effectiveness of the control schemes.