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      Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping

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      Author
      Saranlı U.
      Arslan, Ö.
      Ankaralı, M. M.
      Morgül, Ö.
      Date
      2010
      Source 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
      Article
      Item Usage Stats
      138
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      263
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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 approximations
      Damping
      Gait control
      Hybrid dynamical systems
      Legged locomotion
      Spring-loaded inverted pendulum
      Analytic approximation
      Controllers
      Dynamical systems
      Pendulums
      Position control
      Trajectories
      Damping
      Permalink
      http://hdl.handle.net/11693/22100
      Published Version (Please cite this version)
      http://dx.doi.org/10.1007/s11071-010-9757-8
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      • Department of Computer Engineering 1421
      • Department of Electrical and Electronics Engineering 3636
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