Free-joint manipulators: motion control under second-order nonholonomic constraints

The control problem for robot manipulators having some unactuated joints is addressed. The nonholonomic nature of the constraint expressing the dynamics of the free joints is recognized in the general case, and conditions are derived to identify special cases in which such a constraint is integrable. In contrast to most examples in the literature, the free-joint dynamics is an instance of second-order nonholonomic constraint. It is shown that smooth feedback stabilization to a single equilibrium point is not possible. A feedback scheme achieving stabilization to a manifold of equilibrium positions is proposed. Its correctness is established theoretically as well as confirmed by simulation results