Control of mechanical systems with second-order nonholonomic constraints: underactuated manipulators

An analysis of underactuated manipulators from both the dynamic and the control points of view is presented. While the unactuated joints dynamic equation is recognized to be a nonholonomic constraint in the general case, necessary and sufficient conditions are given to identify special cases in which such a constraint is integrable. In contrast to most examples in the literature, the unactuated joints dynamics is an instance of a second-order nonholonomic constraint. it is shown that smooth feedback stabilization to a single equilibrium point is not possible, and a feedback scheme providing stabilization to a manifold of equilibrium positions is proposed