Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle

Maziar Izadi, Amit Sanyal, Rakesh R. Warier

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Stable estimation of rigid body motion states from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d' Alembert principle from variational mechanics. From body-fixed sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation errors and an artificial potential function of pose (attitude and position) estimation errors. An additional dissipation term that is linear in the velocity estimation errors is introduced, and the Lagrange-d' Alembert principle is applied to the Lagrangian with this dissipation. This estimation framework is shown to be almost globally asymptotically stable in the state space of rigid body motions. It is discretized for computer implementation using the discrete Lagrange-d' Alembert principle, as a first order Lie group variational integrator. In the presence of bounded measurement noise from sensors, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states. Ongoing and future work will explore finite-time stable extensions of this framework for nonlinear observer design, with applications to rigid body and multi-body systems.

Original languageEnglish (US)
Title of host publication2018 IEEE Conference on Decision and Control, CDC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1270-1275
Number of pages6
ISBN (Electronic)9781538613955
DOIs
StatePublished - Jan 18 2019
Event57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States
Duration: Dec 17 2018Dec 19 2018

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2018-December
ISSN (Print)0743-1546

Conference

Conference57th IEEE Conference on Decision and Control, CDC 2018
CountryUnited States
CityMiami
Period12/17/1812/19/18

Fingerprint

Pose Estimation
Estimation Error
Lagrange
Error analysis
Rigid Body Motion
Dissipation
Variational Integrators
Nonlinear Observer
Lie groups
Sensor
Observer Design
Multibody Systems
Globally Asymptotically Stable
Sensors
Term
Potential Function
Kinetic energy
Rigid Body
Mechanics
Dynamic models

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Izadi, M., Sanyal, A., & Warier, R. R. (2019). Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 1270-1275). [8619341] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619341

Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle. / Izadi, Maziar; Sanyal, Amit; Warier, Rakesh R.

2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. p. 1270-1275 8619341 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Izadi, M, Sanyal, A & Warier, RR 2019, Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619341, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 1270-1275, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 12/17/18. https://doi.org/10.1109/CDC.2018.8619341
Izadi M, Sanyal A, Warier RR. Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle. In 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc. 2019. p. 1270-1275. 8619341. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2018.8619341
Izadi, Maziar ; Sanyal, Amit ; Warier, Rakesh R. / Variational Attitude and Pose Estimation Using the Lagrange-d' Alembert Principle. 2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2019. pp. 1270-1275 (Proceedings of the IEEE Conference on Decision and Control).
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