Control of 2R Free-Joint Manipulators via the Averaging Method

A manipulator with free joints is a class of underactuated mechanisms. Control of such systems is one of major topics in robotics and control engineering. In this paper, we apply the averaging method to manipulators connected by free joints and describe their behaviors in response to periodic inputs. We analyze 2R free-joint manipulators and show that the systems have invariant manifolds de ned by an energy-like conserved quantity. We also develop two control methods via feedback modulation of the input amplitude to reach a desired invariant manifold. Second-order averaging is executed to obtain better approximation and a termination control method at the destination is formulated based on the analysis. The e ectiveness of the method is veri ed by simulations and experiments.