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Constrained accelerations for controlled geometric reduction: Sagittal-plane decoupling for bipedal locomotion

2010

Conference Paper

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Energy-shaping control methods have produced strong theoretical results for asymptotically stable 3D bipedal dynamic walking in the literature. In particular, geometric controlled reduction exploits robot symmetries to control momentum conservation laws that decouple the sagittal-plane dynamics, which are easier to stabilize. However, the associated control laws require high-dimensional matrix inverses multiplied with complicated energy-shaping terms, often making these control theories difficult to apply to highly-redundant humanoid robots. This paper presents a first step towards the application of energy-shaping methods on real robots by casting controlled reduction into a framework of constrained accelerations for inverse dynamics control. By representing momentum conservation laws as constraints in acceleration space, we construct a general expression for desired joint accelerations that render the constraint surface invariant. By appropriately choosing an orthogonal projection, we show that the unconstrained (reduced) dynamics are decoupled from the constrained dynamics. Any acceleration-based controller can then be used to stabilize this planar subsystem, including passivity-based methods. The resulting control law is surprisingly simple and represents a practical way to employ control theoretic stability results in robotic platforms. Simulated walking of a 3D compass-gait biped show correspondence between the new and original controllers, and simulated motions of a 16-DOF humanoid demonstrate the applicability of this method.

Author(s): Gregg, R. D. and Righetti, L. and Buchli, J. and Schaal, S.
Book Title: Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on
Pages: 1-7
Year: 2010
Month: December
Day: 6-8

Department(s): Autonomous Motion, Movement Generation and Control
Bibtex Type: Conference Paper (inproceedings)

Cross Ref: p10421
Note: clmc
URL: http://www-clmc.usc.edu/publications/G/gregg-Humanoids2010.pdf

BibTex

@inproceedings{Gregg_HRIIC_2010,
  title = {Constrained accelerations for controlled geometric reduction: Sagittal-plane decoupling for bipedal locomotion},
  author = {Gregg, R. D. and Righetti, L. and Buchli, J. and Schaal, S.},
  booktitle = {Humanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on},
  pages = {1-7},
  month = dec,
  year = {2010},
  note = {clmc},
  crossref = {p10421},
  url = {http://www-clmc.usc.edu/publications/G/gregg-Humanoids2010.pdf},
  month_numeric = {12}
}