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Stabilization of periodic orbits for planar walking with noninstantaneous double-support phase

Hamed, K. A ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1109/TSMCA.2011.2169246
  3. Abstract:
  4. This paper presents an analytical approach to design a continuous time-invariant two-level control scheme for asymptotic stabilization of a desired period-one trajectory for a hybrid model describing walking by a planar biped robot with noninstantaneous double-support phase and point feet. It is assumed that the hybrid model consists of both single- and double-support phases. The design method is based on the concept of hybrid zero dynamics. At the first level, parameterized continuous within-stride controllers, including single- and double-support-phase controllers, are employed. These controllers create a family of 2-D finite-time attractive and invariant submanifolds on which the dynamics of the mechanical system is restricted. Moreover, since the mechanical system during the double-support phase is overactuated, the feedback law during this phase is designed to be minimum norm on the desired periodic orbit. At the second level, parameters of the within-stride controllers are updated by an event-based update law to achieve hybrid invariance, which results in a reduced-order hybrid model for walking. By these means, stability properties of the periodic orbit can be analyzed and modified by a restricted Poincaré return map. Finally, a numerical example for the proposed control scheme is presented
  5. Keywords:
  6. Event-based controller ; Motion planning algorithm ; Poincare return map ; Bipedal robot ; Double-support phase ; Event-based ; Hybrid zero dynamics ; Motion planning algorithms ; Return map ; Two-level control ; Asymptotic stability ; Biped locomotion ; Level control ; Mechanical engineering ; Mechanics ; Time varying systems ; Chaos theory
  7. Source: IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans ; Volume 42, Issue 3 , 2012 , Pages 685-706 ; 10834427 (ISSN)
  8. URL: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6062421&url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F3468%2F4359265%2F06062421.pdf%3Farnumber%3D6062421