使用对偶四元数的相对位姿可观测性分析
Relative Pose Observability Analysis Using Dual Quaternions
AI总结：
本文利用对偶四元数表示相对位姿与运动模型，通过李代数非线性可观测性分析证明其 Jacobian 与可观测性矩阵具有有利块结构并满足满秩条件。
摘要：
相对位姿（位置和方向）估计是许多机器人应用的重要组成部分。基准标记，例如 AprilTag 视觉基准系统，能够通过单次标记检测产生相对位姿测量，并为位姿估计提供强大工具。本文针对一个由相对位姿测量模型和相对运动模型组成的非线性对偶四元数系统，进行了李代数非线性可观测性分析。我们证明，许多常见的对偶四元数表达式会产生具有有利块结构和秩性质的 Jacobian 矩阵，这些性质有助于分析。我们表明，使用对偶四元数表示可得到具有简单块三角结构的可观测性矩阵，并满足必要的满秩条件。
英文摘要：
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.
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