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Reference TypeConference Proceedings
Author(s)Gregg, R. D.;Righetti, L.;Buchli, J.;Schaal, S.
Year2010
TitleConstrained accelerations for controlled geometric reduction: Sagittal-plane decoupling for bipedal locomotion
Journal/Conference/Book TitleHumanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on
Keywordsasymptotic stability humanoid robots legged locomotion matrix inversion matrix multiplication robot dynamics 16-DOF humanoid 3D compass-gait biped acceleration-based controller asymptotically stable 3D bipedal dynamic walking bipedal locomotion
AbstractEnergy-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.
Pages1-7
Date6-8 Dec. 2010
Alternate Journal/TitleHumanoid Robots (Humanoids), 2010 10th IEEE-RAS International Conference on
Short TitleConstrained accelerations for controlled geometric reduction: Sagittal-plane decoupling for bipedal locomotion
URL(s) http://www-clmc.usc.edu/publications/G/gregg-Humanoids2010.pdf

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