### 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 vision 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. 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. This estimation scheme is discretized for computer implementation using discrete variational mechanics, as a first order Lie group variational integrator. The discrete estimation scheme can also estimate velocities from such onboard sensor measurements. Moreover, all states can be estimated during time periods when measurements of only two inertial vectors, the angular velocity vector, and one feature point position vector are available in body frame. 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 true states.

Original language | English (US) |
---|---|

Pages (from-to) | 78-88 |

Number of pages | 11 |

Journal | Automatica |

Volume | 71 |

DOIs | |

State | Published - Sep 1 2016 |

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### Keywords

- Lagrange-d'Alembert principle
- Lie group variational integrator
- Pose estimation
- Variational estimator

### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

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

Research output: Contribution to journal › Article

*Automatica*, vol. 71, pp. 78-88. https://doi.org/10.1016/j.automatica.2016.04.028

}

TY - JOUR

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

AU - Izadi, Maziar

AU - Sanyal, Amit

PY - 2016/9/1

Y1 - 2016/9/1

N2 - 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 vision 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. 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. This estimation scheme is discretized for computer implementation using discrete variational mechanics, as a first order Lie group variational integrator. The discrete estimation scheme can also estimate velocities from such onboard sensor measurements. Moreover, all states can be estimated during time periods when measurements of only two inertial vectors, the angular velocity vector, and one feature point position vector are available in body frame. 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 true states.

AB - 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 vision 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. 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. This estimation scheme is discretized for computer implementation using discrete variational mechanics, as a first order Lie group variational integrator. The discrete estimation scheme can also estimate velocities from such onboard sensor measurements. Moreover, all states can be estimated during time periods when measurements of only two inertial vectors, the angular velocity vector, and one feature point position vector are available in body frame. 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 true states.

KW - Lagrange-d'Alembert principle

KW - Lie group variational integrator

KW - Pose estimation

KW - Variational estimator

UR - http://www.scopus.com/inward/record.url?scp=84974555850&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84974555850&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2016.04.028

DO - 10.1016/j.automatica.2016.04.028

M3 - Article

AN - SCOPUS:84974555850

VL - 71

SP - 78

EP - 88

JO - Automatica

JF - Automatica

SN - 0005-1098

ER -