Stable Estimation of Rigid Body Motion using Geometric Mechanics

TL;DR

This paper introduces asymptotically stable, robust state estimation schemes for rigid body motion using geometric mechanics, ensuring nonlinear stability without dependence on sensor noise or external disturbances.

Contribution

It develops novel estimation schemes based on variational mechanics that do not require prior knowledge of the rigid body's dynamics.

Findings

Estimation schemes are robust to initial errors.

They do not need re-tuning for changing sensor noise.

The schemes guarantee nonlinear stability.

Abstract

In this work, asymptotically stable state estimation schemes are proposed for rigid body motion, using the framework of geometric mechanics. Rigorous stability analyses of the estimation schemes presented here guarantee the nonlinear stability of these schemes. The stability of these schemes does not depend on the characteristics of the sensor measurement noise or external disturbances. In addition, they are robust to initial errors in the state estimates and do not need to be re-tuned when sensor noise properties change. In the first part of this dissertation, estimation of rigid body states is considered, given the dynamics model of the rigid body. In the second part, an estimation scheme that does not require knowledge of the dynamics of the rigid body is derived, based on onboard sensor measurements obtained at an appropriate frequency. The frequency of such measurements must be suitably high to resolve the motion of the rigid body. These attitude and pose estimation schemes are obtained by applying the Lagrange-d'Alembert principle from variational mechanics, to a Lagrangian constructed from state estimation errors and a dissipative term linear in the velocity estimation errors.