A.U. Kilic and D.J. Braun, A Novel Approximation for the Spring Loaded Inverted Pendulum Model of Locomotion, Detroit, MI, USA, pp. 4315-4321, 2023.
The Spring-Loaded Inverted Pendulum (SLIP) is a heuristic model of robot locomotion. SLIP is commonly used to predict center-of-mass motion and derive simple control laws for stable locomotion. However, the SLIP model is not integrable, which means that no closed-form relation can be derived to understand how the design and control parameters of the SLIP model affect stable locomotion. There exist a number of different analytical approximations to the SLIP model when considering small and symmetric step lengths. In this paper, we present a novel approximation to the SLIP model without relying on a small symmetric step length assumption. The model was found to accurately predict the stability of the SLIP model for large and asymmetric steps alike and was used to design a novel analytical stiffness control strategy that stabilizes the SLIP model in a couple of steps.