Relative Pose Observability Analysis Using Dual Quaternions

TL;DR

This paper analyzes the observability of relative pose estimation using dual quaternions, demonstrating that this representation provides advantageous mathematical properties for pose observability analysis in robotics.

Contribution

It introduces a Lie algebraic nonlinear observability analysis for dual quaternion systems, revealing structural benefits for pose estimation.

Findings

Dual quaternion representation yields a block triangular observability matrix.

The observability matrix satisfies the full rank condition.

Many dual quaternion expressions have Jacobian matrices with beneficial structures.

Abstract

Relative pose (position and orientation) estimation is an essential component of many robotics applications. Fiducial markers, such as the AprilTag visual fiducial system, yield a relative pose measurement from a single marker detection and provide a powerful tool for pose estimation. In this paper, we perform a Lie algebraic nonlinear observability analysis on a nonlinear dual quaternion system that is composed of a relative pose measurement model and a relative motion model. We prove that many common dual quaternion expressions yield Jacobian matrices with advantageous block structures and rank properties that are beneficial for analysis. We show that using a dual quaternion representation yields an observability matrix with a simple block triangular structure and satisfies the necessary full rank condition.