Perturbation-based approximate analytic solutions to an articulated SLIP model for legged robots

The classical spring-loaded inverted pendulum (SLIP) model only takes the axial force along the equivalent leg into account without considering the tangential force. This disadvantage limits its potential when it is served as a template for legged locomotion of animals and robots that both have the tangential forces along their legs, even though it is a simple model. To handle the problem, firstly, an articulated/generalized spring-loaded inverted pendulum (ASLIP) model is proposed. Both axial and tangential force along the equivalent leg are considered in the proposed model. Secondly, the analytical approximate solution for the proposed model is addressed through perturbation method. Finally, comparative simulations show that the proposed model can achieve better prediction accuracy than the classical model. It means that the prediction accuracy of approximations depends on not only the methods of analytical approximate solutions, but also the established model. This research provides a more accurate method to predict the movement trajectory of legged locomotion and a more appropriate model representation for the control of legged locomotion.