Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach

Pirooz Vakili; Hanieh Mirzaei; Shahrooz Zarbafian; Ioannis Ch Paschalidis; Dima Kozakov; Sandor Vajda

doi:10.1109/CDC.2014.7040301

Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach

Pirooz Vakili
, Hanieh Mirzaei
, Shahrooz Zarbafian
, Ioannis Ch Paschalidis
, Dima Kozakov
, Sandor Vajda

Applied Mathematics and Statistics

Boston University

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

1 Scopus citations

Abstract

In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

Original language	English
Title of host publication	53rd IEEE Conference on Decision and Control,CDC 2014
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5825-5830
Number of pages	6
Edition	February
ISBN (Electronic)	9781479977468
DOIs	https://doi.org/10.1109/CDC.2014.7040301
State	Published - 2014
Event	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 - Los Angeles, United States Duration: Dec 15 2014 → Dec 17 2014

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Number	February
Volume	2015-February
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014
Country/Territory	United States
City	Los Angeles
Period	12/15/14 → 12/17/14

Access to Document

10.1109/CDC.2014.7040301

Cite this

Vakili, P., Mirzaei, H., Zarbafian, S., Paschalidis, I. C., Kozakov, D., & Vajda, S. (2014). Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach. In 53rd IEEE Conference on Decision and Control,CDC 2014 (February ed., pp. 5825-5830). Article 7040301 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2014.7040301

Vakili, Pirooz ; Mirzaei, Hanieh ; Zarbafian, Shahrooz et al. / Optimization on the space of rigid and flexible motions : An alternative manifold optimization approach. 53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. pp. 5825-5830 (Proceedings of the IEEE Conference on Decision and Control; February).

@inproceedings{c7dff7289bcf4f80b5e300938f1e724c,

title = "Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach",

abstract = "In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.",

author = "Pirooz Vakili and Hanieh Mirzaei and Shahrooz Zarbafian and Paschalidis, \{Ioannis Ch\} and Dima Kozakov and Sandor Vajda",

note = "Publisher Copyright: {\textcopyright} 2014 IEEE.; 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014 ; Conference date: 15-12-2014 Through 17-12-2014",

year = "2014",

doi = "10.1109/CDC.2014.7040301",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

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

number = "February",

pages = "5825--5830",

booktitle = "53rd IEEE Conference on Decision and Control,CDC 2014",

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Vakili, P, Mirzaei, H, Zarbafian, S, Paschalidis, IC, Kozakov, D & Vajda, S 2014, Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach. in 53rd IEEE Conference on Decision and Control,CDC 2014. February edn, 7040301, Proceedings of the IEEE Conference on Decision and Control, no. February, vol. 2015-February, Institute of Electrical and Electronics Engineers Inc., pp. 5825-5830, 2014 53rd IEEE Annual Conference on Decision and Control, CDC 2014, Los Angeles, United States, 12/15/14. https://doi.org/10.1109/CDC.2014.7040301

Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach. / Vakili, Pirooz; Mirzaei, Hanieh; Zarbafian, Shahrooz et al.
53rd IEEE Conference on Decision and Control,CDC 2014. February. ed. Institute of Electrical and Electronics Engineers Inc., 2014. p. 5825-5830 7040301 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2015-February, No. February).

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

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AU - Paschalidis, Ioannis Ch

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AB - In this paper we consider the problem of minimization of a cost function that depends on the location and poses of one or more rigid bodies, or bodies that consist of rigid parts hinged together. We present a unified setting for formulating this problem as an optimization on an appropriately defined manifold for which efficient manifold optimizations can be developed. This setting is based on a Lie group representation of the rigid movements of a body that is different from what is commonly used for this purpose. We illustrate this approach by using the steepest descent algorithm on the manifold of the search space and specify conditions for its convergence.

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M3 - Conference contribution

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Vakili P, Mirzaei H, Zarbafian S, Paschalidis IC, Kozakov D, Vajda S. Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach. In 53rd IEEE Conference on Decision and Control,CDC 2014. February ed. Institute of Electrical and Electronics Engineers Inc. 2014. p. 5825-5830. 7040301. (Proceedings of the IEEE Conference on Decision and Control; February). doi: 10.1109/CDC.2014.7040301

Optimization on the space of rigid and flexible motions: An alternative manifold optimization approach

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