Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping
Author
Saranlı U.
Arslan, Ö.
Ankaralı, M. M.
Morgül, Ö.
Date
2010Source Title
Nonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems
Print ISSN
0924-090X
Publisher
Springer Netherlands
Volume
62
Issue
4
Pages
729 - 742
Language
English
Type
ArticleItem Usage Stats
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Abstract
This paper introduces an accurate yet analytically simple approximation to the stance dynamics of the Spring-Loaded Inverted Pendulum (SLIP) model in the presence of non-negligible damping and non-symmetric stance trajectories. Since the SLIP model has long been established as an accurate descriptive model for running behaviors, its careful analysis is instrumental in the design of successful locomotion controllers. Unfortunately, none of the existing analytic methods in the literature explicitly take damping into account, resulting in degraded predictive accuracy when they are used for dissipative runners. We show that the methods we propose not only yield average predictive errors below 2% in the presence of significant damping, but also outperform existing alternatives to approximate the trajectories of a lossless model. Finally, we exploit both the predictive performance and analytic simplicity of our approximations in the design of a gait-level running controller, demonstrating their practical utility and performance benefits. © 2010 Springer Science+Business Media B.V.
Keywords
Analytic approximationsDamping
Gait control
Hybrid dynamical systems
Legged locomotion
Spring-loaded inverted pendulum
Analytic approximation
Controllers
Dynamical systems
Pendulums
Position control
Trajectories
Damping