Analysis and Control of Underactuated Mechanisms via the Averaging Method

Control of underactuated mechanisms is one of major research topics in control engineering and robotics. A manipulator with free joints is one of such the systems and its control is di cult via ordinary nonlinear control methods. In this paper, we discuss control of free-joint manipulators whose rst joint is only actuated and the others are free joints. We apply the averaging method to analysis of their behaviors in response to periodic motion of the rst joint. We reveal an invariability of the averaged motion independent of the input-amplitude. We identify time-invariant manifolds of 2R and 3R free-joint manipulators and de ne the Hamiltonians of their averaged system. We propose a control method by amplitudemodulation to feedback the Hamiltonian. The method enables us to position the both joints of 2R free-joint manipulator. The e ectiveness of the method is veri ed by computer simulations.