Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study

Robert Mahony; Tarek Hamel; Jochen Trumpf; Christian Lageman

doi:10.1109/CDC.2009.5399821

Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study

Robert Mahony^*, Tarek Hamel, Jochen Trumpf, Christian Lageman

^*Corresponding author for this work

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

48 Citations (Scopus)

Abstract

This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixed-frame measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly on the vector measurements, allowing a mix of both inertial and body-fixed measurements.We provide a comprehensive stability analysis of the observer error dynamics. We show that even with a single vector measurement it is often possible to recover asymptotically stable observer error dynamics.

Original language	English
Title of host publication	Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6407-6412
Number of pages	6
ISBN (Print)	9781424438716
DOIs	https://doi.org/10.1109/CDC.2009.5399821
Publication status	Published - 2009
Event	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 - Shanghai, China Duration: 15 Dec 2009 → 18 Dec 2009

Publication series

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

Conference

Conference	48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009
Country/Territory	China
City	Shanghai
Period	15/12/09 → 18/12/09

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10.1109/CDC.2009.5399821

Cite this

Mahony, R., Hamel, T., Trumpf, J., & Lageman, C. (2009). Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 (pp. 6407-6412). Article 5399821 (Proceedings of the IEEE Conference on Decision and Control). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2009.5399821

Mahony, Robert ; Hamel, Tarek ; Trumpf, Jochen et al. / Nonlinear attitude observers on SO(3) for complementary and compatible measurements : A theoretical study. Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. pp. 6407-6412 (Proceedings of the IEEE Conference on Decision and Control).

@inproceedings{cb625fe9579941ed9a06b35ec5722ecb,

title = "Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study",

abstract = "This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixed-frame measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly on the vector measurements, allowing a mix of both inertial and body-fixed measurements.We provide a comprehensive stability analysis of the observer error dynamics. We show that even with a single vector measurement it is often possible to recover asymptotically stable observer error dynamics.",

author = "Robert Mahony and Tarek Hamel and Jochen Trumpf and Christian Lageman",

year = "2009",

doi = "10.1109/CDC.2009.5399821",

language = "English",

isbn = "9781424438716",

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

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

pages = "6407--6412",

booktitle = "Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009",

address = "United States",

note = "48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009 ; Conference date: 15-12-2009 Through 18-12-2009",

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Mahony, R, Hamel, T, Trumpf, J & Lageman, C 2009, Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study. in Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009., 5399821, Proceedings of the IEEE Conference on Decision and Control, Institute of Electrical and Electronics Engineers Inc., pp. 6407-6412, 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009, Shanghai, China, 15/12/09. https://doi.org/10.1109/CDC.2009.5399821

Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study. / Mahony, Robert; Hamel, Tarek; Trumpf, Jochen et al.
Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc., 2009. p. 6407-6412 5399821 (Proceedings of the IEEE Conference on Decision and Control).

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

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T1 - Nonlinear attitude observers on SO(3) for complementary and compatible measurements

T2 - 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

AU - Mahony, Robert

AU - Hamel, Tarek

AU - Trumpf, Jochen

AU - Lageman, Christian

PY - 2009

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N2 - This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixed-frame measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly on the vector measurements, allowing a mix of both inertial and body-fixed measurements.We provide a comprehensive stability analysis of the observer error dynamics. We show that even with a single vector measurement it is often possible to recover asymptotically stable observer error dynamics.

AB - This paper considers the question of designing an attitude observer exploiting the structure of the Special Orthogonal Group SO(3) for both inertial and body-fixed-frame measurements. We consider measurements from a minimal sensor suite, typically a rate gyroscope along with several measurements of inertial and/or body-fixed vector directions. We propose fully nonlinear pose observers based directly on the vector measurements, allowing a mix of both inertial and body-fixed measurements.We provide a comprehensive stability analysis of the observer error dynamics. We show that even with a single vector measurement it is often possible to recover asymptotically stable observer error dynamics.

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DO - 10.1109/CDC.2009.5399821

M3 - Conference contribution

SN - 9781424438716

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BT - Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009

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Mahony R, Hamel T, Trumpf J, Lageman C. Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study. In Proceedings of the 48th IEEE Conference on Decision and Control held jointly with 2009 28th Chinese Control Conference, CDC/CCC 2009. Institute of Electrical and Electronics Engineers Inc. 2009. p. 6407-6412. 5399821. (Proceedings of the IEEE Conference on Decision and Control). doi: 10.1109/CDC.2009.5399821

Nonlinear attitude observers on SO(3) for complementary and compatible measurements: A theoretical study

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