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Recursive Estimation of Rigid Body Motions

刚体运动的递归估计

基本信息

批准号：
325035548
负责人：
Professor Dr.-Ing. Uwe D. Hanebeck
金额：
--
依托单位：
Lehrstuhl für Intelligente Sensor-Aktor-Systeme (ISAS)
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2019-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/325035548?language=en
关键词：
Recursive Estimation Rigid Body Motions

项目摘要

In this proposal, we focus on algorithms for recursive estimation of rigid body motions. A rigid body motion consists of a translation and a rotation. The group of rigid body motions in three dimensions is called SE(3) and plays an important role in a variety of applications in robotics, aerospace, and computer vision. Consider for example the problem of accurate motion tracking of a moving object, say, a robotic arm, an airplane, or a head-mounted camera. All these problems necessitate estimation of the pose of the considered object, i.e., the rigid body motion of a reference coordinate frame to the body coordinate frame.For this purpose, we propose a new probability distribution on SE(3) that can be used to represent uncertain rigid body motions. Unlike most approaches in literature, the novel distribution is based on so-called unit dual quaternions, a generalization of unit quaternions to the case of rigid body motions. The novel distribution can be seen as a generalization of the hyperspherical Bingham distribution, which has been applied to estimation on the rotation group SO(3) based on unit quaternions. Similar to the Bingham density, the novel density is antipodally symmetric, i.e., x and -x always have the same probability density, which resolves the problem that unit dual quaternions q and -q represent the same rigid body motion.Based on this new probability density, we plan to develop recursive estimation algorithms that have several key advantages compared to state-of-the-art algorithms. First of all, we can represent all rigid body motions, whereas methods based on the corresponding Lie algebra typically cannot represent rotations by exactly 180 degrees. Second, there are no singularities and there is no need to switch between different parameterizations. Furthermore, we do not need to make any assumptions that the uncertainty is low, that rotations are small, or that the density describing the rigid body motions is approximately Gaussian. Due to these advantages, we expect that recursive estimation algorithms based on the new density will outperform state-of-the-art approaches that rely on Gaussian assumptions or locally linear approximations.

在这个建议中，我们专注于递归估计刚体运动的算法。刚体运动由平移和旋转组成。三维刚体运动组称为SE（3），在机器人、航空航天和计算机视觉的各种应用中起着重要作用。例如，考虑移动对象的精确运动跟踪问题，例如，机器人手臂，飞机或头戴式摄像机。所有这些问题都需要估计所考虑对象的姿态，即，本文提出了一种新的概率分布，它可以用来表示不确定的刚体运动.与文献中的大多数方法不同，这种新颖的分布基于所谓的单位对偶四元数，这是单位四元数对刚体运动情况的概括。新分布可以看作是超球Bingham分布的推广，超球Bingham分布已被应用于基于单位四元数的旋转群SO（3）的估计。类似于宾厄姆密度，新密度是对极对称的，即，x和-x总是具有相同的概率密度，这解决了单位对偶四元数q和-q表示相同的刚体运动的问题。基于这个新的概率密度，我们计划开发递归估计算法，该算法与最先进的算法相比具有几个关键优势。首先，我们可以表示所有刚体运动，而基于相应李代数的方法通常不能表示精确180度的旋转。第二，没有奇点，不需要在不同的参数化之间切换。此外，我们不需要假设不确定性很低，旋转很小，或者描述刚体运动的密度近似为高斯。由于这些优点，我们预计基于新密度的递归估计算法将优于依赖于高斯假设或局部线性近似的最先进方法。