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Observer-Based Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Underactuated Bipedal Walking

Akbari Hamed, Kaveh and Ames, Aaron D. and Gregg, Robert D. (2018) Observer-Based Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Underactuated Bipedal Walking. In: 2018 Annual American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 1438-1445. ISBN 978-1-5386-5428-6. https://resolver.caltech.edu/CaltechAUTHORS:20190205-081031030

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Abstract

This paper presents a systematic approach to design observer-based output feedback controllers for hybrid dynamical systems arising from bipedal walking. We consider a class of parameterized observer-based output feedback controllers for local exponential stabilization of hybrid periodic orbits. The properties of the Poincaré map are investigated to show that the Jacobian linearization of the Poincaré map takes a triangular form. This demonstrates the nonlinear separation principle for periodic orbits. In particular, the exponential stabilization of hybrid periodic orbits under dynamic output feedback control can be achieved by solving separate eigenvalue placement problems for the nonlinear state feedback and the observer. The paper then solves the state feedback and observer design problems by employing an iterative algorithm based on a sequence of optimization problems involving bilinear and linear matrix inequalities. The theoretical results are confirmed by designing a nonlinear observer-based output feedback controller for underactuated walking of a 3D humanoid model with 18 state variables, 54 state feedback parameters, and 271 observer parameters.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.23919/ACC.2018.8431607DOIArticle
ORCID:
AuthorORCID
Akbari Hamed, Kaveh0000-0001-9597-1691
Ames, Aaron D.0000-0003-0848-3177
Gregg, Robert D.0000-0002-0729-2857
Additional Information:© 2018 AACC. This material is based upon work supported by the National Science Foundation under Grant Number 1637704. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NSF. R. D. Gregg holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund.
Funders:
Funding AgencyGrant Number
NSFCMMI-1637704
Burroughs Wellcome FundUNSPECIFIED
Record Number:CaltechAUTHORS:20190205-081031030
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190205-081031030
Official Citation:K. A. Hamed, A. D. Ames and R. D. Gregg, "Observer-Based Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Underactuated Bipedal Walking," 2018 Annual American Control Conference (ACC), Milwaukee, WI, 2018, pp. 1438-1445. doi: 10.23919/ACC.2018.8431607
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92650
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 19:42
Last Modified:03 Oct 2019 20:46

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