A consideration on dynamic constraint of planar manipulators with free-joints

It is known that the manipulators with free-joints are typical mechanical systems dominated by second-order nonholonomic constraints. This paper points out that only the second-order nonholonomic constraint at the first free-joint of the manipulator is integrable to first-order constraint, and that the integrated constraint has linear form of generalized velocities. This constraint implies that a planar manipulator whose first joint is replaced to a free-joint driven by a reaction wheel can be controlled using the same control strategy as that used for the original manipulator. Integrability of the resulting first-order constraint is also discussed for different planar manipulators with free-joints, and the usefulness of the first-order nonholo-nomic constraint is demonstrated numerically in a path-planning problem for a manipulator with two free-joints.