Spring loaded inverted pendulum running: A plant model.
William J. Schwind, Daniel E. Koditschek · Deep Blue (University of Michigan) · 1998
The spring loaded inverted pendulum (SLIP) has emerged as the right template for studying dynamic locomotion, whether in robots or animals. The SLIP template, which is nothing more than a mass on a spring (a simple pogo stick), has not only accurately modeled the most successful running robots built to date, but also has proven a good descriptive model for the center of mass trajectories for runners as diverse as humans, horses, cockroaches and crabs. The conceptual simplicity of this model, however, hides its analytical complexity. Until now, one consequence of this complexity has been the absence of an appropriate plant model. In this work the appropriate plant is not found in the SLIP's continuous dynamics, but rather a discrete manifestation of those dynamics. Unfortunately, the development of such a plant model is hindered by the non-integrability of the SLIP stance dynamics. This has prevented the SLIP template from being leveraged to greater advantage in both robotics and biomechanics research. The work presented in this dissertation provides a means to remove some of the analytical difficulties encountered in the pursuit of a SLIP plant model. In particular, novel approximation strategies that rely on an extension of the Mean Value Theorem for Integrals and Picard-style iterates are used to integrate the stance dynamics, resulting in a set of plant models, the iterates, which grow in both accuracy and complexity in a controlled manner. An initial application of a plant model generated in this manner is the identification of SLIP spring laws in human running. The accuracy of the fits obtained in the initial study presented in this dissertation suggest that the SLIP template is more than just a useful metaphor for human running--it may be a literal control target.