Gain Design of Quasi-Continuous Exponential Stabilizing Controller for a Nonholonomic Mobile Robot

The control of nonholonomic canonical form using an invariant manifold is investigated to apply to a mobile robot steered by two independent driving wheels. A quasi-continuous exponential stabilizing controller is designed by using another input pattern. Additionally, the control gain designing method is proposed for this controller. Modified error system of nonholonomic double integrator model is used as nonholonomic canonical form. Generally, the gain cannot be calculated due to the non-linear transform of system. Owing to complicated relation of several parameters, the controller behavior is inconstant by gain pattern. We propose a method of designing gain which uses desired settling time. An approximate equation to obtain designed gains is derived based on the evaluation function. The design method to determine gains of the assumed actual system is simulated. The effectiveness of the proposed method is confirmed by these simulations.