A nonlinear optimal control approach for the spherical robot

Gerasimos Rigatos; Krishna Busawon; Jorge Pomares; Patrice Wira; Masoud Abbaszadeh

doi:10.1109/IECON.2018.8591405

A nonlinear optimal control approach for the spherical robot

Gerasimos Rigatos^*, Krishna Busawon, Jorge Pomares, Patrice Wira, Masoud Abbaszadeh

^*Corresponding author for this work

Mathematics, Physics and Electrical Engineering

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

3 Citations (Scopus)

Abstract

A nonlinear H-infinity (optimal) control approach is developed for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system's state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the system's Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller's feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.

Original language	English
Title of host publication	Proceedings
Subtitle of host publication	IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society
Place of Publication	Piscataway
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2496-2501
Number of pages	6
ISBN (Electronic)	9781509066841
ISBN (Print)	9781509066858
DOIs	https://doi.org/10.1109/IECON.2018.8591405
Publication status	Published - 31 Dec 2018
Event	44th Annual Conference of the IEEE Industrial Electronics Society, IECON 2018 - Washington, United States Duration: 20 Oct 2018 → 23 Oct 2018

Conference

Conference	44th Annual Conference of the IEEE Industrial Electronics Society, IECON 2018
Country/Territory	United States
City	Washington
Period	20/10/18 → 23/10/18

Access to Document

10.1109/IECON.2018.8591405

Cite this

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title = "A nonlinear optimal control approach for the spherical robot",

abstract = "A nonlinear H-infinity (optimal) control approach is developed for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system's state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the system's Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller's feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.",

author = "Gerasimos Rigatos and Krishna Busawon and Jorge Pomares and Patrice Wira and Masoud Abbaszadeh",

year = "2018",

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language = "English",

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pages = "2496--2501",

booktitle = "Proceedings",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

address = "United States",

note = "44th Annual Conference of the IEEE Industrial Electronics Society, IECON 2018 ; Conference date: 20-10-2018 Through 23-10-2018",

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Rigatos, G, Busawon, K, Pomares, J, Wira, P & Abbaszadeh, M 2018, A nonlinear optimal control approach for the spherical robot. in Proceedings: IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society. Institute of Electrical and Electronics Engineers Inc., Piscataway, pp. 2496-2501, 44th Annual Conference of the IEEE Industrial Electronics Society, IECON 2018, Washington, United States, 20/10/18. https://doi.org/10.1109/IECON.2018.8591405

A nonlinear optimal control approach for the spherical robot. / Rigatos, Gerasimos; Busawon, Krishna; Pomares, Jorge et al.
Proceedings: IECON 2018 - 44th Annual Conference of the IEEE Industrial Electronics Society. Piscataway: Institute of Electrical and Electronics Engineers Inc., 2018. p. 2496-2501.

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

TY - GEN

T1 - A nonlinear optimal control approach for the spherical robot

AU - Rigatos, Gerasimos

AU - Busawon, Krishna

AU - Pomares, Jorge

AU - Wira, Patrice

AU - Abbaszadeh, Masoud

PY - 2018/12/31

Y1 - 2018/12/31

N2 - A nonlinear H-infinity (optimal) control approach is developed for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system's state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the system's Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller's feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.

AB - A nonlinear H-infinity (optimal) control approach is developed for the problem of the control of the spherical rolling robot. The solution of such a control problem is a nontrivial case due to underactuation and strong nonlinearities in the system's state-space description. The dynamic model of the robot undergoes approximate linearization around a temporary operating point which is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the computation of the system's Jacobian matrices. For the linearized dynamics of the spherical robot an H-infinity controller is designed. To compute the controller's feedback gains an algebraic Riccati equation in solved at each iteration of the control algorithm. The global asymptotic stability properties of the control method are proven through Lyapunov analysis. Finally, for the implementation of sensorless control for the spherical rolling robot, the H-infinity Kalman Filter is used as a robust state estimator.

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DO - 10.1109/IECON.2018.8591405

M3 - Conference contribution

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SN - 9781509066858

SP - 2496

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BT - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

CY - Piscataway

T2 - 44th Annual Conference of the IEEE Industrial Electronics Society, IECON 2018

Y2 - 20 October 2018 through 23 October 2018

ER -

A nonlinear optimal control approach for the spherical robot

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