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Dynamic Humanoid Locomotion: A Scalable Formulation for HZD Gait Optimization

Hereid, Ayonga and Hubicki, Christian M. and Cousineau, Eric A. and Ames, Aaron D. (2018) Dynamic Humanoid Locomotion: A Scalable Formulation for HZD Gait Optimization. IEEE Transactions on Robotics, 34 (2). pp. 370-387. ISSN 1552-3098. doi:10.1109/TRO.2017.2783371.

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Hybrid zero dynamics (HZD) has emerged as a popular framework for dynamic walking but has significant implementation difficulties when applied to the high degrees of freedom humanoids. The primary impediment is the process of gait design—it is difficult for optimizers to converge on a viable set of virtual constraints defining a gait. This paper presents a methodology that allows for fast and reliable generation of dynamic robotic walking gaits through the HZD framework, even in the presence of underactuation. Specifically, we describe an optimization formulation that builds upon the novel combination of HZD and direct collocation methods. Furthermore, achieving a scalable implementation required developing a defect-variable substitution formulation to simplify expressions, which ultimately allows us to generate compact analytic Jacobians of the constraints. We experimentally validate our methodology on an underactuated humanoid, DURUS, a spring-legged machine designed to facilitate energy-economical walking. We show that the optimization approach, in concert with the HZD framework, yields dynamic and stable walking gaits in hardware with a total electrical cost of transport of 1.33.

Item Type:Article
Related URLs:
URLURL TypeDescription
Hereid, Ayonga0000-0002-4156-2013
Hubicki, Christian M.0000-0002-2092-3772
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2018 IEEE. Manuscript received January 15, 2017; revised September 6, 2017; accepted November 6, 2017. Date of publication January 17, 2018; date of current version April 12, 2018. This paper was recommended for publication by Associate Editor P.-B. Wieber and Editor A. Kheddar upon evaluation of the reviewers’ comments. This work supported by in part by DARPA under Grant D15AP00006 and in part by NSF Grant CPS-1239055 and Grant NRI-1526519.
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)D15AP00006
Subject Keywords:Humanoid robots, hybrid zero dynamics, legged locomotion, motion planning
Issue or Number:2
Record Number:CaltechAUTHORS:20180118-141115865
Persistent URL:
Official Citation:A. Hereid, C. M. Hubicki, E. A. Cousineau and A. D. Ames, "Dynamic Humanoid Locomotion: A Scalable Formulation for HZD Gait Optimization," in IEEE Transactions on Robotics, vol. 34, no. 2, pp. 370-387, April 2018. doi: 10.1109/TRO.2017.2783371. URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84393
Deposited By: Ruth Sustaita
Deposited On:18 Jan 2018 22:29
Last Modified:15 Nov 2021 20:19

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