Rigid Body Motion Estimation based on the Lagrange-d'Alembert Principle

TL;DR

This paper introduces a novel variational mechanics-based method for stable rigid body pose and velocity estimation from noisy measurements without requiring a dynamics model, applicable with optical and inertial sensors.

Contribution

It develops a new estimation scheme based on the Lagrange-d'Alembert principle that does not depend on the system's dynamics model and can estimate velocities from optical measurements.

Findings

Estimates converge to a bounded neighborhood of true states under noise.

Requires at least three inertial landmarks for pose estimation.

Discretized scheme effectively estimates pose and velocities from optical data.

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.