Dynamics synthesis and control for a hopping robot with articulated leg

To investigate the design and the applications of elastic underactuated mechanisms for improving the energy efficiency of dynamic mechanical systems, the dynamics and control of a one-legged hopping robot with articulated leg is studied in this paper. To ensure the controllability of the elastic underactuated mechanism, a dynamics synthesis method is proposed for designing the underactuated mechanism so that the dynamics of the system can be transformed into the strict feedback normal form. To improve the energy efficiency of the one-legged locomotion system, an optimal motion planning method is presented to optimize the trajectories of the robot joints. A nonlinear controller is proposed to stabilize the hopping robot to its balance configuration in stance phase, and a switched linear controller is proposed to stabilize the continuous hopping movement. The stability of the presented controllers is analyzed in theory and verified by some numerical simulations.