Abstract
In this paper, we present a motion planning method for a certain class of underactuated manipulators, in which avoidance for singular points of the feedback linearization is achieved by the optimal control. Manipulators with a last joint which is unactuated and revolute are subject to second-order nonholonomic constraints. Applying the feedback linearization to them, the motion has been planned by employing a polynomial interpolation. However, there may exist singular points of the transformation in the planned trajectory. We design a performance index involving penalty terms that prevent the state of the system from singular points themselves or approaching to them. Numerical examples are given to show the validity of the proposed method.
