Semi-analytic finite horizon control of an underactuated manipulator

In this paper we propose a method to generate piecewise constant control within finite time horizon for a nonlinear system. Local (weak) controllability related to accessibility properties with piecewise constant control is analyzed and used directly for control purposes. More precisely, we concatenate flows of vector fields of the system to generate appropriate constant input values. The method is applied to an underactuated manipulator model which fails to meet the Brockett condition but possesses controllability properties which are also analyzed in this paper. Simulation results show the feasibility of this method.