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Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking

Akbari Hamed, Kaveh and Ames, Aaron D. (2020) Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking. IEEE Transactions on Control Systems Technology, 28 (6). pp. 2689-2696. ISSN 1063-6536. doi:10.1109/tcst.2019.2947874.

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This brief addresses zero dynamics associated with relative degree one and two nonholonomic outputs for exponential stabilization of given periodic orbits for hybrid models of bipedal locomotion. Zero dynamics manifolds are constructed to contain the orbit while being invariant under both the continuous- and discrete-time dynamics. The associated restriction dynamics are termed the hybrid zero dynamics (HZD). Prior results on the HZD have mainly relied on input–output linearization of holonomic outputs and are referred to as holonomic HZD (H-HZD). This brief presents reduced-order expressions for the HZD associated with nonholonomic output functions referred to as nonholonomic HZD (NH-HZD). This brief systematically synthesizes NH-HZD controllers to stabilize periodic orbits based on a reduced-order stability analysis. A comprehensive study of H-HZD and NH-HZD is presented. It is shown that NH-HZD can stabilize a broader range of walking gaits that are not stabilizable through traditional H-HZD. The power of the analytical results is finally illustrated on a hybrid model of a bipedal robot through numerical simulations.

Item Type:Article
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Akbari Hamed, Kaveh0000-0001-9597-1691
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2019 IEEE. Manuscript received May 4, 2019; revised August 30, 2019; accepted October 9, 2019. Date of publication October 28, 2019; date of current version October 9, 2020. Manuscript received in final form October 10, 2019. The work of K. A. Hamed was supported by the National Science Foundation (NSF) under Grant 1854898, Grant 1906727, Grant 1923216, and Grant 1924617. The work of A. D. Ames was supported in part by NSF under Grant 1544332, Grant 1724457, Grant 1724464, Grant 1923239, and Grant 1924526, and in part by Disney Research LA. Recommended by Associate Editor M. Maggiore.
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Subject Keywords:Hybrid zero dynamics (HZD), nonholonomic outputs, periodic orbits, underactuated bipedal robots
Issue or Number:6
Record Number:CaltechAUTHORS:20191031-124926682
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Official Citation:K. Akbari Hamed and A. D. Ames, "Nonholonomic Hybrid Zero Dynamics for the Stabilization of Periodic Orbits: Application to Underactuated Robotic Walking," in IEEE Transactions on Control Systems Technology, vol. 28, no. 6, pp. 2689-2696, Nov. 2020, doi: 10.1109/TCST.2019.2947874.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99586
Deposited By: George Porter
Deposited On:31 Oct 2019 20:40
Last Modified:16 Nov 2021 17:47

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