Global K-exponential stabilization of nonholonomic chained systems by continuous feedback

Two global continuous feedback control laws were proposed to stabilize nonholonomic chained systems, namely, the continuous time-varying feedback control law and the dynamic time-invariant feedback control law. The first control law achieved continuity and asymptoticality by using an exponential decay term related to the initial state values, while the second achieved controllability, continuity and asymptoticality by setting the initial value of the introduced assistant state variable. The two control laws could guarantee that all the states converged to zero continuously and asymptotically at exponential rates, which overcame the short-comings that the previous control laws could not achieve continuity, asymptoticality and exponential rates at the same time. The proposed control laws are applied to the mobile robot and a four-dimension chained system. The simulation results show that the smoothness and convergence rates of the state/control trajectories are better than the previous works.