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Stability Analysis of Clock-driven Rigid-Body SLIP Model for RHex

The International Journal of Robotics Research, 2004

R. Altendorfer*, D. E. Koditschek*, P. Holmes‡
*: Department of Electrical Engineering and Computer Science, University of Michigan
‡: Department of Mechanical and Aerospace Engineering, Princeton University

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Abstract
      We apply the stability analysis for hybrid legged locomotion systems, introduced in our companion paper in this issue, to a new simple clock-driven SLIP model inspired by the robot RHex. We adopt in stance phase the three-degrees-of-freedom (3DoF) spring loaded inverted pendulum (SLIP) model introduced in our companion paper to capture RHex’s pitching dynamics in the sagittal plane. The coordinating influence of RHex’s open-loop clock controller is subsumed into a leg placement strategy derived from a bipedal abstraction of RHex. The “symmetric” factorization analysis introduced in our companion paper yields a necessary condition for gait stability expressed in closed form, which can be imposed directly on the clock parameter space. This represents the first reported analytical insight into how a dynamical runner might be stabilized by a completely feed forward rhythmic limb coordination pattern. Correspondence in steady-state gait location and stability characteristics with an appropriately tuned 24DoF model of RHex provides numerical evidence that the 3DoF SLIP model offers a descriptive explanation for the robot’s empirical running behavior.
BibTeX Entry
@article{journals/ijrr/AltendorferKH04a,
  author = {Richard Altendorfer and Daniel E. Koditschek and Philip Holmes},
  interhash = {29e503021effa2f113623447615661d6},
  intrahash = {af8e5bfa960a267b4c535b52edf60db2},
  journal = {I. J. Robotic Res.},
  number = {10-11},
  pages = {1001-1012},
  title = {Stability Analysis of a Clock-Driven Rigid-Body SLIP Model for RHex.},
  url = {http://dblp.uni-trier.de/db/journals/ijrr/ijrr23.html#AltendorferKH04a},
  volume = 23,
  year = 2004,
  keywords = {dblp},
  ee = {http://ijr.sagepub.com/cgi/content/abstract/23/10-11/1001},
  added-at = {2006-09-08T00:00:00.000+0200},
  description = {dblp},
  biburl = {http://www.bibsonomy.org/bibtex/2af8e5bfa960a267b4c535b52edf60db2/dblp},
  date = {2006-09-08}
}

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