Abstract: A new model of elastic one-legged hopping robot is proposed. The hopping robot is constructed by two actuated arms and an elastic passive telescopic leg. Motion control of the one-legged robot such as stance balance, lift-off and hopping stably depends on the dynamics coupling of the system. The mechanism model of the robot and the variable constraints property of it are analyzed. It is shown that the robot is a nonholonomic system, which is second order in stance phase, first order in flight phase. A motion control algorithm is proposed for hopping control in vertical direction based on nonlinear transformation of inputs for this kind of underactuted nonholonomic dynamic system. The whole state variables are controlled by considering the orientation of the leg, the vibration of the linear spring, and the momentum of the robot system in horizontal direction. Some simulations test the feasibility of the control method numerically. The research results are helpful for investigating the techniques to save energy of the elastic underactuated mechanical system by utilizing the vibration of compliant components, thus the research can be used for reference in designing other new elastic underactuated mechanical systems and their application in space field.

Key words: Control, Dynamics, Elasticity, Hopping robot, Underactuation