Control of underactuated mechanical systems: application to the planar 2R robot

We consider the problem of stabilizing a 2R robot which moves in the horizontal plane by using a single actuator at the base. This system is representative of the class of underactuated mechanical systems that are not controllable in the first approximation. The presence of a drift term in the dynamic equations makes the application of most existing control techniques impossible. The proposed stabilization method makes use of three basic tools, namely (i) partial feedback linearization of the dynamic equations, (ii) computation of a nilpotent approximation of the system, and (iii) iterative application of an open-loop control designed on the nilpotent system. Although the procedure is presented for the 2R robot case, it provides guidelines for devising a method of general applicability.

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