Research on the Analyticity of SLIP Model Based on Perturbation Theory and Locomotion Control

An approximate analytical solution of SLIP (spring loaded inverted pendulum) model dynamics in stance phase is proposed based on perturbation theory, aiming at resolving the lack of analytical method to deal with SLIP model dynamics. The Poincare map of apex height in flight phase is established through which the entire dynamics of SLIP model is derived analytically. The error analysis results indicate that the prediction of apex height with approximate solution possesses high approximation precision. Aiming at the locomotion control of SLIP hopper, the deadbeat controller for apex height of SLIP system is designed based on the inverse Poincare map. The tracking simulation of desired step signal is implemented to show that the algorithm proposed in this paper not only can track the desired trajectory but also inhibits overshoot effectively. Furthermore, the equivalence of apex velocity control and height control is verified through analyzing the experiment curve of horizontal velocity of the center of mass, which extends the application range of the algorithm.