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Control Policies for a Large Region of Attraction for Dynamically Balancing Legged Robots: A Sampling-Based Approach

Published online by Cambridge University Press:  05 May 2020

Pranav A. Bhounsule Open the ORCID record for Pranav A. Bhounsule [Opens in a new window] ,
Ali Zamani ,
Jeremy Krause ,
Steven Farra  and
Jason Pusey
Pranav A. Bhounsule*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: pranav@uic.edu, alizamani.mecheng@gmail.com, robotics68@gmail.com
Ali Zamani
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: pranav@uic.edu, alizamani.mecheng@gmail.com, robotics68@gmail.com
Jeremy Krause
Affiliation:
Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 842 W Taylor St, Chicago, IL60607, USA. E-mails: pranav@uic.edu, alizamani.mecheng@gmail.com, robotics68@gmail.com
Steven Farra
Affiliation:
Department of Mechanical Engineering, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX78249, USA. E-mail: zvo618@my.utsa.edu
Jason Pusey
Affiliation:
Vehicle Technology Directorate, U.S. Army Research Laboratory, Aberdeen Proving Grounds, Aberdeen, MD21001, USA. E-mail: jason.l.pusey.civ@mail.mil
*
*Corresponding author. E-mail: pranav@uic.edu
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Summary

The popular approach of assuming a control policy and then finding the largest region of attraction (ROA) (e.g., sum-of-squares optimization) may lead to conservative estimates of the ROA, especially for highly nonlinear systems. We present a sampling-based approach that starts by assuming an ROA and then finds the necessary control policy by performing trajectory optimization on sampled initial conditions. Our method works with black-box models, produces a relatively large ROA, and ensures exponential convergence of the initial conditions to the periodic motion. We demonstrate the approach on a model of hopping and include extensive verification and robustness checks.

Keywords

Region of attractionOrbital Lyapunov functionPoincaré mapPeriodic motionDynamically balancing legged robotsDeep learning neural nets
Type
Articles
Information
Robotica , Volume 39 , Issue 1 , January 2021 , pp. 107 - 122
Copyright
Copyright © Cambridge University Press 2020

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