Rigid body motion estimation based on the Lagrange-d'Alembert principle

Maziar Izadi, Amit Sanyal, Ernest Barany, Sasi P. Viswanathan

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

10 Scopus citations

Abstract

Stable estimation of rigid body pose and velocities from noisy measurements, without any knowledge of the dynamics model, is treated using the Lagrange-d'Alembert principle from variational mechanics. With body-fixed optical and inertial sensor measurements, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in velocity estimation error and the sum of two artificial potential functions; one obtained from a generalization of Wahba's function for attitude estimation and another which is quadratic in the position estimate error. An additional dissipation term that is linear in the velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. This estimation scheme is discretized using discrete variational mechanics. The presented pose estimator requires optical measurements of at least three inertially fixed landmarks or beacons in order to estimate instantaneous pose. The discrete estimation scheme can also estimate velocities from such optical measurements. In the presence of bounded measurement noise in the vector measurements, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.

Original languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3699-3704
Number of pages6
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

ASJC Scopus subject areas

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

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  • Cite this

    Izadi, M., Sanyal, A., Barany, E., & Viswanathan, S. P. (2015). Rigid body motion estimation based on the Lagrange-d'Alembert principle. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 3699-3704). [7402793] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402793