Relative Pose Observability Analysis Using Dual Quaternions

2024-12-31

AI Summary

This work addresses the observability problem in robot relative pose estimation using dual-quaternion modeling. We formulate a nonlinear system integrating single-frame AprilTag measurements with a relative motion model, and conduct rigorous observability analysis within a Lie algebraic framework. For the first time, we prove that several dual-quaternion parameterizations yield Jacobian matrices with favorable block structure and full rank, thereby revealing that the observability matrix admits a compact block-triangular form and is strictly full-rank. This establishes verifiable sufficient conditions for the observability of relative pose systems, providing theoretical guarantees and a structured analytical tool for vision-tag-driven tightly coupled state estimators. The results significantly enhance both accuracy and robustness of pose estimation.

Technology Category

• Intelligent Robots: State Estimation
• Computer Vision: Biometrics, Face, Gesture & Pose
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• observability
• dual-quaternion
• robotic-positioning

Innovation

• Dual Quaternions
• Robot Position Estimation
• Observability Analysis