Abstract
A design methodology is presented for tracking control of a class of second-order nonholonomic systems. The method consists of three steps. In the first step we transform the system into an extended chained-form system. This extended chained-form system is in cascade form and we apply a linear feedback to the first subsystem. In the second step, the second subsystem is exponentially stabilized by applying a backstepping procedure. In the third and final step it is shown that the closed-loop tracking dynamics of the extended chained-form system are globally exponentially stable under a persistence of excitation condition on the reference trajectory. The control design methodology is applied to an underactuated planar manipulator with two translational and one rotational joint (PPR). The simulation results show a good performance of the tracking controller.
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