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Coupled Control Lyapunov Functions for Interconnected Systems, With Application to Quadrupedal Locomotion

Ma, Wen-Loong and Csomay-Shanklin, Noel and Kolathaya, Shishir and Hamed, Kaveh Akbari and Ames, Aaron D. (2021) Coupled Control Lyapunov Functions for Interconnected Systems, With Application to Quadrupedal Locomotion. IEEE Robotics and Automation Letters, 6 (2). pp. 3761-3768. ISSN 2377-3766. doi:10.1109/LRA.2021.3065174.

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This letter addresses the problem of formally guaranteeing the stability of interconnected systems with local controllers with a view toward stabilizing quadrupeds viewed as coupled bipeds. In particular, we present a novel framework that views general rigid-body systems as a collection of lower-dimensional systems that are coupled via reaction forces. Stabilizing the corresponding coupled control system can thus be addressed by stabilizing each subsystem coupled through the passive dynamics. The main results of the letter are stability conditions that guarantee convergence for each control subsystem by formulating coupled control Lyapunov functions (CCLFs) using the notion of input-to-state stability (ISS). This theoretical result is illustrated via a simple cart-pole example, where exponential stability is obtained. Next, building on previous results where an 18-DOF quadrupedal robot is decomposed into two interconnected bipedal systems for efficient periodic gait generation, we design model-free quadratic programs (QPs) using the CCLFs to stabilize the continuous dynamics and thus achieve experimental walking and simulated hopping and running on the Vision 60 quadrupedal robot.

Item Type:Article
Related URLs:
URLURL TypeDescription
Ma, Wen-Loong0000-0002-0115-5632
Csomay-Shanklin, Noel0000-0002-2361-1694
Kolathaya, Shishir0000-0001-8689-2318
Hamed, Kaveh Akbari0000-0001-9597-1691
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2021 IEEE. Manuscript received October 15, 2020 and February 5, 2021; accepted February 15, 2021. Date of publication March 11, 2021; date of current version March 30, 2021. This letter was recommended for publication by Associate Editor M. Hutter and Editor A. Kheddar upon evaluation of the reviewers’ comments. This work was supported by NSF under Grant 1724464. The work of Kaveh Akbari Hamed was supported by NSF under Grants 1923216 and 1924617.
Funding AgencyGrant Number
Subject Keywords:Legged robots, motion control, optimization and optimal control
Issue or Number:2
Record Number:CaltechAUTHORS:20210421-085752484
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Official Citation:W. -L. Ma, N. Csomay-Shanklin, S. Kolathaya, K. A. Hamed and A. D. Ames, "Coupled Control Lyapunov Functions for Interconnected Systems, With Application to Quadrupedal Locomotion," in IEEE Robotics and Automation Letters, vol. 6, no. 2, pp. 3761-3768, April 2021, doi: 10.1109/LRA.2021.3065174
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108777
Deposited By: Tony Diaz
Deposited On:21 Apr 2021 21:13
Last Modified:21 Apr 2021 21:13

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