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.

在这个提案中，我们重点关注刚体运动的递归估计算法。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发挥着重要作用。例如，考虑移动物体（例如机械臂、飞机或头戴式摄像机）的精确运动跟踪问题。所有这些问题都需要估计所考虑对象的位姿，即参考坐标系到身体坐标系的刚体运动。为此，我们提出了 SE(3) 上的新概率分布，可用于代表不确定的刚体运动。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，即单位四元数对刚体运动情况的推广。这种新颖的分布可以看作是超球面宾汉分布的推广，它已被应用于基于单位四元数的旋转群SO(3)的估计。与宾汉密度类似，新的密度是对映对称的，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代表相同刚体运动的问题。基于这个新的概率密度，我们计划开发递归估计算法，与最先进的算法相比，该算法具有几个关键优势。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无法表示精确 180 度的旋转。其次，不存在奇点，并且不需要在不同的参数化之间切换。此外，我们不需要做出任何不确定性低、旋转小或描述刚体运动的密度近似高斯的假设。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高斯假设或局部线性近似的最先进方法。

项目成果

期刊论文数量（7）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Nonlinear Progressive Filtering for SE(2) Estimation

DOI：
10.23919/icif.2018.8455231
发表时间：
2018-07
期刊：
2018 21st International Conference on Information Fusion (FUSION)
影响因子：
0
作者：
Kailai Li;G. Kurz;Lukas Bernreiter;U. Hanebeck
通讯作者：
Kailai Li;G. Kurz;Lukas Bernreiter;U. Hanebeck

Grid-Based Quaternion Filter for SO(3) Estimation

DOI：
10.23919/ecc51009.2020.9143723
发表时间：
2020-01-01
期刊：
2020 EUROPEAN CONTROL CONFERENCE (ECC 2020)
影响因子：
0
作者：
Li, Kailai;Pfaff, Florian;Hanebeck, Uwe D.
通讯作者：
Hanebeck, Uwe D.

Unscented Dual Quaternion Particle Filter for SE(3) Estimation

DOI：
10.1109/lcsys.2020.3005066
发表时间：
2021-04-01
期刊：
IEEE CONTROL SYSTEMS LETTERS
影响因子：
3
作者：
Li, Kailai;Pfaff, Florian;Hanebeck, Uwe D.
通讯作者：
Hanebeck, Uwe D.

Geometry-driven Deterministic Sampling for Nonlinear Bingham Filtering

DOI：
10.23919/ecc.2019.8796102
发表时间：
2019-01-01
期刊：
2019 18TH EUROPEAN CONTROL CONFERENCE (ECC)
影响因子：
0
作者：
Li, Kailai;Frisch, Daniel;Hanebeck, Uwe D.
通讯作者：
Hanebeck, Uwe D.

Geometry-Driven Stochastic Modeling of SE(3) States Based on Dual Quaternion Representation

DOI：
10.1109/icphys.2019.8780254
发表时间：
2019-01-01
期刊：
2019 IEEE INTERNATIONAL CONFERENCE ON INDUSTRIAL CYBER PHYSICAL SYSTEMS (ICPS 2019)
影响因子：
0
作者：
Li, Kailai;Pfaff, Florian;Hanebeck, Uwe D.
通讯作者：
Hanebeck, Uwe D.