Stance control of the SLIP hopper with adjustable stiffness of leg spring

In this paper, a stance control strategy of the Spring Loaded Inverted Pendulum (SLIP) hopper with adjustable stiffness of leg spring is proposed. Due to the lack of a closed form analytic solution of SLIP dynamics, a novel perturbation method is developed to obtain the approximate analytic solution of the SLIP dynamics in stance phase, based on which the apex return map is also established. To compensate the energy variation between the current apex state and the desired apex state, a stiffness adjustment of leg spring in stance phase is presented. The deadbeat controller of the angle of attack is designed to track the regulated apex height and horizontal velocity in a single stride. Moreover, we illustrate through simulations that the SLIP hopper applied the proposed stance controller reveals high tracking accuracy and rapidly converges to regulated apex state. This work will benefit in both structure and adaptive controller design of legged bio-inspired robot.