Smooth time-varying regulation of nonholonomic chained systems

The problem of regulating a nonholonomic system in chained form to an equilibrium state is addressed and solved by a smooth time-varying control law. The proposed scheme based on Lyapunov analysis can guarantee asymptotic stabilization and exponential stabilization, respectively, by simply changing a term in the controller expression. Therefore, the controller can be used for theoretical analysis and practical application. The additional novelty of the proposed approach is that the parameters in our controller have clear physical meanings and are easily implemented and tuned. Simulation results based on a numerical example and a tricycle-type mobile robot are presented to demonstrate the effectiveness of the developed method.