Global Symplectic Uncertainty Propagation on SO(3)

TL;DR

This paper presents a novel global uncertainty propagation method for rigid body dynamics on SO(3), combining geometric numerical integration, harmonic analysis, and probabilistic techniques to accurately model uncertainties on the manifold.

Contribution

It introduces a global uncertainty propagation scheme that supports probability densities on the entire manifold, leveraging Lie group variational integrators for geometric fidelity.

Findings

The method preserves the geometric structure of uncertainties in Hamiltonian systems.

It enables global attitude estimation considering full probability distributions.

The approach outperforms local methods in capturing uncertainty on SO(3).

Abstract

This paper introduces a global uncertainty propagation scheme for rigid body dynamics, through a combination of numerical parametric uncertainty techniques, noncommutative harmonic analysis, and geometric numerical integration. This method is distinguished from prior approaches, as it allows one to consider probability densities that are global, and are not supported on only a single coordinate chart on the manifold. The use of Lie group variational integrators, that are symplectic and stay on the Lie group, as the underlying numerical propagator ensures that the advected probability densities respect the geometric properties of uncertainty propagation in Hamiltonian systems, which arise as consequence of the Gromov nonsqueezing theorem from symplectic geometry. We also describe how the global uncertainty propagation scheme can be applied to the problem of global attitude estimation.