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Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion

Akbari Hamed, Kaveh and Gregg, Robert D. and Ames, Aaron D. (2018) Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion. In: 2018 Annual American Control Conference (ACC). IEEE , Piscataway, NJ, pp. 2210-2217. ISBN 978-1-5386-5428-6.

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Models of bipedal walking are hybrid with continuous-time phases representing the Lagrangian stance dynamics and discrete-time transitions representing the impact of the swing leg with the walking surface. The design of continuous-time feedback controllers that exponentially stabilize periodic gaits for hybrid models of underactuated 3D bipedal walking is a significant challenge. We recently introduced a method based on an iterative sequence of optimization problems involving bilinear matrix inequalities (BMIs) to systematically design stabilizing continuous-time controllers for single domain hybrid models of underactuated bipedal robots with point feet. This paper addresses the exponential stabilization problem for multi-contact walking gaits with nontrivial feet. A family of parameterized continuous-time controllers is proposed for different phases of the walking cycle. The BMI algorithm is extended to the multi-domain hybrid models of anthropomorphic 3D walking locomotion to look for stabilizing controller parameters. The Poincaré map is addressed and a new set of sufficient conditions is presented that guarantees the convergence of the BMI algorithm to a stabilizing set of controller parameters at a finite number of iterations. The power of the algorithm is ultimately demonstrated through the design of stabilizing virtual constraint controllers for dynamic walking of a 3D humanoid model with 28 state variables and 275 controller parameters.

Item Type:Book Section
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URLURL TypeDescription
Akbari Hamed, Kaveh0000-0001-9597-1691
Gregg, Robert D.0000-0002-0729-2857
Ames, Aaron D.0000-0003-0848-3177
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.
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Burroughs Wellcome FundUNSPECIFIED
Record Number:CaltechAUTHORS:20190205-075309563
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Official Citation:K. A. Hamed, R. D. Gregg and A. D. Ames, "Exponentially Stabilizing Controllers for Multi-Contact 3D Bipedal Locomotion," 2018 Annual American Control Conference (ACC), Milwaukee, WI, 2018, pp. 2210-2217. doi: 10.23919/ACC.2018.8431799
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92649
Deposited By: Tony Diaz
Deposited On:05 Feb 2019 18:34
Last Modified:16 Nov 2021 03:52

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