Compensation of nonlinear dynamics for energy/phase control of hopping robot

Hopping height control is one of the difficult problems in legged control. Many kinds of research employ a leg spring for the supplement of energy, and model the robot as a spring-mass model. Feedback linearization enables to cancel the nonlinear terms theoretically. However, it is difficult to identify the nonlinear terms including the parameters precisely in the real world. This paper nominalizes the robot dynamics as the desired spring-mass system applying a disturbance observer. In order to realize the desired characteristics of the spring and the mass, the disturbance including the nonlinear terms is rejected firstly by a disturbance observer. To make the mass in the workspace as constant, the nominal inertia of the disturbance observer in the joint space is varied. Next, by adding the desired virtual elastic force, the robot dynamics is nominalized as the desired spring-mass system. Based on the nominalized spring-mass dynamics, hopping-height control using energy/phase control is implemented. While energy control is often used for hopping height control, the energy/phase control enables the hopping-height control and the spring-mass oscillation simultaneously. Constant hopping-height and stepwise hopping height are realized experimentally through the proposed control method. The simulations in the case of the ideal dynamics are also conducted for comparison.