An Input Extension Control Method for A Class of Second-Order Nonholonomic Mechanical Systems with Drift

The exponential stabilization control of a class of second-order nonholonomic systems with drift is investigated. From the point of view of the general control model of the nonholonomic system with drift, based on the Lie bracket extension theorem and Lie algebra rank condition, a motion planning method with extending the input by power polynomial is proposed. An exponential stabilization control theorem based on the power polynomial extension technique is proved for the underactuated manipulators of which the number of actuated joints is not less than it of the passive joints. A 2R and 3R underactuated manipulators with passive last joint are simulated for proving the validity of the method