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

Maziar Izadi, Amit Sanyal

Research output: Contribution to journalArticle

38 Citations (Scopus)

Abstract

Estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the Lagrange-d'Alembert principle from variational mechanics. It is shown that Wahba's cost function for attitude determination from two or more non-collinear vector measurements can be generalized and represented as a Morse function of the attitude estimation error on the Lie group of rigid body rotations. With body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba's function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. These estimation schemes are discretized for computer implementation using discrete variational mechanics. A first order Lie group variational integrator is obtained as a discrete-time implementation. In the presence of bounded measurement noise, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.

Original languageEnglish (US)
Pages (from-to)2570-2577
Number of pages8
JournalAutomatica
Volume50
Issue number10
DOIs
StatePublished - Oct 1 2014
Externally publishedYes

Fingerprint

Angular velocity
Error analysis
Lie groups
Mechanics
State estimation
Kinetic energy
Cost functions
Dynamic models
Sensors
Computer simulation

Keywords

  • Attitude estimation
  • Lagrange-d'Alembert principle
  • Lie group variational integrator

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

Rigid body attitude estimation based on the Lagrange-d'Alembert principle. / Izadi, Maziar; Sanyal, Amit.

In: Automatica, Vol. 50, No. 10, 01.10.2014, p. 2570-2577.

Research output: Contribution to journalArticle

@article{b0346fe3e71f4898ae80254602ace58d,
title = "Rigid body attitude estimation based on the Lagrange-d'Alembert principle",
abstract = "Estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the Lagrange-d'Alembert principle from variational mechanics. It is shown that Wahba's cost function for attitude determination from two or more non-collinear vector measurements can be generalized and represented as a Morse function of the attitude estimation error on the Lie group of rigid body rotations. With body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba's function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. These estimation schemes are discretized for computer implementation using discrete variational mechanics. A first order Lie group variational integrator is obtained as a discrete-time implementation. In the presence of bounded measurement noise, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.",
keywords = "Attitude estimation, Lagrange-d'Alembert principle, Lie group variational integrator",
author = "Maziar Izadi and Amit Sanyal",
year = "2014",
month = "10",
day = "1",
doi = "10.1016/j.automatica.2014.08.010",
language = "English (US)",
volume = "50",
pages = "2570--2577",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier",
number = "10",

}

TY - JOUR

T1 - Rigid body attitude estimation based on the Lagrange-d'Alembert principle

AU - Izadi, Maziar

AU - Sanyal, Amit

PY - 2014/10/1

Y1 - 2014/10/1

N2 - Estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the Lagrange-d'Alembert principle from variational mechanics. It is shown that Wahba's cost function for attitude determination from two or more non-collinear vector measurements can be generalized and represented as a Morse function of the attitude estimation error on the Lie group of rigid body rotations. With body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba's function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. These estimation schemes are discretized for computer implementation using discrete variational mechanics. A first order Lie group variational integrator is obtained as a discrete-time implementation. In the presence of bounded measurement noise, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.

AB - Estimation of rigid body attitude and angular velocity without any knowledge of the attitude dynamics model is treated using the Lagrange-d'Alembert principle from variational mechanics. It is shown that Wahba's cost function for attitude determination from two or more non-collinear vector measurements can be generalized and represented as a Morse function of the attitude estimation error on the Lie group of rigid body rotations. With body-fixed sensor measurements of direction vectors and angular velocity, a Lagrangian is obtained as the difference between a kinetic energy-like term that is quadratic in the angular velocity estimation error and an artificial potential obtained from Wahba's function. An additional dissipation term that depends on the angular velocity estimation error is introduced, and the Lagrange-d'Alembert principle is applied to the Lagrangian with this dissipation. A Lyapunov analysis shows that the state estimation scheme so obtained provides stable asymptotic convergence of state estimates to actual states in the absence of measurement noise, with an almost global domain of attraction. These estimation schemes are discretized for computer implementation using discrete variational mechanics. A first order Lie group variational integrator is obtained as a discrete-time implementation. In the presence of bounded measurement noise, numerical simulations show that the estimated states converge to a bounded neighborhood of the actual states.

KW - Attitude estimation

KW - Lagrange-d'Alembert principle

KW - Lie group variational integrator

UR - http://www.scopus.com/inward/record.url?scp=85027957418&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85027957418&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2014.08.010

DO - 10.1016/j.automatica.2014.08.010

M3 - Article

AN - SCOPUS:85027957418

VL - 50

SP - 2570

EP - 2577

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 10

ER -