Local Koopman Operators for Data-Driven Control of Robotic Systems

Giorgos Mamakoukas; Maria Castaño; Xiaobo Tan; Todd Murphey

doi:10.15607/RSS.2019.XV.054

Local Koopman Operators for Data-Driven Control of Robotic Systems

Giorgos Mamakoukas, Maria Castaño, Xiaobo Tan, Todd Murphey

Mechanical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

72 Scopus citations

Abstract

This paper presents a data-driven methodology for linear embedding of nonlinear systems. Utilizing structural knowledge of general nonlinear dynamics, the authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics. With the linear representation, the nonlinear system is then controlled with an LQR feedback policy, the gains of which need to be calculated only once. As a result, the approach enables fast control synthesis. We demonstrate the efficacy of the approach with simulations and experimental results on the modeling and control of a tail-actuated robotic fish and show that the proposed policy is comparable to backstepping control. To the best of our knowledge, this is the first experimental validation of Koopman-based LQR control.

Original language	English (US)
Title of host publication	Robotics
Subtitle of host publication	Science and Systems XV
Editors	Antonio Bicchi, Hadas Kress-Gazit, Seth Hutchinson
Publisher	MIT Press Journals
ISBN (Print)	9780992374754
DOIs	https://doi.org/10.15607/RSS.2019.XV.054
State	Published - 2019
Event	15th Robotics: Science and Systems, RSS 2019 - Freiburg im Breisgau, Germany Duration: Jun 22 2019 → Jun 26 2019

Publication series

Name	Robotics: Science and Systems
ISSN (Electronic)	2330-765X

Conference

Conference	15th Robotics: Science and Systems, RSS 2019
Country/Territory	Germany
City	Freiburg im Breisgau
Period	6/22/19 → 6/26/19

Funding

This material is based upon work supported by the National Science Foundation (IIS-1717951, IIS-1715714, DGE1424871). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

ASJC Scopus subject areas

Artificial Intelligence
Control and Systems Engineering
Electrical and Electronic Engineering

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10.15607/RSS.2019.XV.054

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title = "Local Koopman Operators for Data-Driven Control of Robotic Systems",

abstract = "This paper presents a data-driven methodology for linear embedding of nonlinear systems. Utilizing structural knowledge of general nonlinear dynamics, the authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics. With the linear representation, the nonlinear system is then controlled with an LQR feedback policy, the gains of which need to be calculated only once. As a result, the approach enables fast control synthesis. We demonstrate the efficacy of the approach with simulations and experimental results on the modeling and control of a tail-actuated robotic fish and show that the proposed policy is comparable to backstepping control. To the best of our knowledge, this is the first experimental validation of Koopman-based LQR control.",

author = "Giorgos Mamakoukas and Maria Casta{\~n}o and Xiaobo Tan and Todd Murphey",

year = "2019",

doi = "10.15607/RSS.2019.XV.054",

language = "English (US)",

isbn = "9780992374754",

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Mamakoukas, G, Castaño, M, Tan, X & Murphey, T 2019, Local Koopman Operators for Data-Driven Control of Robotic Systems. in A Bicchi, H Kress-Gazit & S Hutchinson (eds), Robotics: Science and Systems XV. Robotics: Science and Systems, MIT Press Journals, 15th Robotics: Science and Systems, RSS 2019, Freiburg im Breisgau, Germany, 6/22/19. https://doi.org/10.15607/RSS.2019.XV.054

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T1 - Local Koopman Operators for Data-Driven Control of Robotic Systems

AU - Mamakoukas, Giorgos

AU - Castaño, Maria

AU - Tan, Xiaobo

AU - Murphey, Todd

PY - 2019

Y1 - 2019

N2 - This paper presents a data-driven methodology for linear embedding of nonlinear systems. Utilizing structural knowledge of general nonlinear dynamics, the authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics. With the linear representation, the nonlinear system is then controlled with an LQR feedback policy, the gains of which need to be calculated only once. As a result, the approach enables fast control synthesis. We demonstrate the efficacy of the approach with simulations and experimental results on the modeling and control of a tail-actuated robotic fish and show that the proposed policy is comparable to backstepping control. To the best of our knowledge, this is the first experimental validation of Koopman-based LQR control.

AB - This paper presents a data-driven methodology for linear embedding of nonlinear systems. Utilizing structural knowledge of general nonlinear dynamics, the authors exploit the Koopman operator to develop a systematic, data-driven approach for constructing a linear representation in terms of higher order derivatives of the underlying nonlinear dynamics. With the linear representation, the nonlinear system is then controlled with an LQR feedback policy, the gains of which need to be calculated only once. As a result, the approach enables fast control synthesis. We demonstrate the efficacy of the approach with simulations and experimental results on the modeling and control of a tail-actuated robotic fish and show that the proposed policy is comparable to backstepping control. To the best of our knowledge, this is the first experimental validation of Koopman-based LQR control.

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T3 - Robotics: Science and Systems

BT - Robotics

A2 - Bicchi, Antonio

A2 - Kress-Gazit, Hadas

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PB - MIT Press Journals

T2 - 15th Robotics: Science and Systems, RSS 2019

Y2 - 22 June 2019 through 26 June 2019

ER -

Local Koopman Operators for Data-Driven Control of Robotic Systems

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