Dual quaternion
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Quaternions and Rotation Sequences Open
In this paper we introduce and define the quaternion; we give a brief introduction to its properties and algebra, and we show, what appears to be, its primary application -the quaternion rotation operator.The quaternion rotation operator c…
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Quaternion kinematics for the error-state Kalman filter Open
This article is an exhaustive revision of concepts and formulas related to quaternions and rotations in 3D space, and their proper use in estimation engines such as the error-state Kalman filter. The paper includes an in-depth study of the…
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Dual Quaternion Knowledge Graph Embeddings Open
In this paper, we study the problem of learning representations of entities and relations in the knowledge graph for the link prediction task. Our idea is based on the observation that the vast majority of the related work only models the …
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A Method of Robot Base Frame Calibration by Using Dual Quaternion Algebra Open
When the robot is required to execute a certain task in the world coordinate system (WCS), it is necessary to find the coordinate transformation between the robot base coordinate system (RBCS) and WCS to enable the high precision motion pl…
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Improved quaternion-based integration scheme for rigid body motion Open
Rotation quaternions are frequently used for describing the orientation of non-spherical rigid bodies. Their compact representation by four numbers and disappearance of numerical problems, such as gimbal lock, are reasons for using them. W…
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Partial Lyapunov Strictification: Dual-Quaternion-Based Observer for 6-DOF Tracking Control Open
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Estimating SE(3) elements using a dual quaternion based linear Kalman filter Open
Many applications in robotics such as registration, object tracking, sensor calibration, etc. use Kalman filters to estimate a time invariant SE(3) element by locally linearizing a non-linear measurement model.Linearization-based filters t…
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Dual Quaternion Framework for Modeling of Spacecraft-Mounted Multibody Robotic Systems Open
This paper lays out a framework to model the kinematics and dynamics of a rigid spacecraft-mounted multibody robotic system. The framework is based on dual quaternion algebra, which combines rotational and translational information in a co…
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Spacecraft Robot Kinematics Using Dual Quaternions Open
In recent years, there has been a growing interest in servicing orbiting satellites. In most cases, in-orbit servicing relies on the use of spacecraft-mounted robotic manipulators to carry out complicated mission objectives. Dual quaternio…
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A dual quaternion algorithm of the Helmert transformation problem Open
Rigid transformation including rotation and translation can be elegantly represented by a unit dual quaternion. Thus, a non-differential model of the Helmert transformation (3D seven-parameter similarity transformation) is established base…
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Joint Stiffness Identification and Deformation Compensation of Serial Robots Based on Dual Quaternion Algebra Open
As the application of industrial robots is limited by low stiffness that causes low precision, a joint stiffness identification algorithm for serial robots is presented. In addition, a deformation compensation algorithm is proposed for the…
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The dual Euler-Rodrigues formula in various mathematical forms and their intrinsic relations Open
This paper examines the variations and derivations of the dual Euler-Rodrigues formula from various mathematical forms, including the matrix in 6 × 6, the dual matrix, Lie group SE(3) of the exponential map of the Lie algebra se(3), and th…
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Unit dual quaternion‐based pose optimisation for visual runway observations Open
This study addresses the pose estimation problem of an aircraft runway using visual observations in a landing approach scenario. The authors utilised the fact that the geodetic coordinates of most runways are known precisely with highly vi…
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Dual Quaternion Particle Filtering for Pose Estimation Open
This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodr…
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Helmert Transformation Problem. From Euler Angles Method to Quaternion Algebra Open
The three-dimensional coordinate’s transformation from one system to another, and more specifically, the Helmert transformation problem, is one of the most well-known transformations in the field of engineering. In this paper, its solution…
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Adaptive pose and inertial parameters estimation of free-floating tumbling space objects using dual vector quaternions Open
The robust parameter estimation of unknown space objects is essential to the on-orbit servicing missions. Based on the adaptive filtering techniques along with the dual quaternions modeling methods for pose estimation, this article propose…
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Quaternions as a solution to determining the angular kinematics of human movement Open
The three-dimensional description of rigid body kinematics is a key step in many studies in biomechanics. There are several options for describing rigid body orientation including Cardan angles, Euler angles, and quaternions; the utility o…
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Eigenvalues and Singular Values of Dual Quaternion Matrices Open
The poses of $m$ robotics in $n$ time points may be represented by an $m \times n$ dual quaternion matrix. In this paper, we study the spectral theory of dual quaternion matrices. We introduce right and left eigenvalues for square dual qua…
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Kinematic-Model-Free Orientation Control for Robot Manipulation Using Locally Weighted Dual Quaternions Open
Conventional control of robotic manipulators requires prior knowledge of their kinematic structure. Model-learning controllers have the advantage of being able to control robots without requiring a complete kinematic model and work well in…
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Inverse Kinematics with Dual-Quaternions, Exponential-Maps, and Joint Limits Open
We present a novel approach for solving articulated inverse kinematic problems (e.g., character structures) by means of an iterative dual-quaternion and exponentialmapping approach. As dual-quaternions are a break from the norm and offer a…
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The orthogonal planes split of quaternions and its relation to quaternion geometry of rotations Open
Recently the general orthogonal planes split with respect to any two pure unit quaternions f,g ∈ H, f2 = g2 = -1, including the case f = g, has proved extremely useful for the construction and geometric interpretation of general classes of…
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A Regularization-Patching Dual Quaternion Optimization Method for Solving the Hand-Eye Calibration Problem Open
The hand-eye calibration problem is an important application problem in robot research. Based on the 2-norm of dual quaternion vectors, we propose a new dual quaternion optimization method for the hand-eye calibration problem. The dual qua…
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Dual-Quaternion Analytic LQR Control Design for Spacecraft Proximity Operations Open
Proximity operations offer aggregate capability for a spacecraft operating in close proximity to another spacecraft, to perform on-orbit satellite servicing, or to a space object to perform debris removal. To utilize a spacecraft performin…
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Analytical Solution for Inverse Kinematics Using Dual Quaternions Open
This paper presents a new solution for inverse kinematics (IK) by using dual quaternions (DQ) as operators and combining them with the Paden-Kahan subproblem to determine the analytical solution. Kinematics under the structure of screw the…
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Coarse Alignment Technology on Moving base for SINS Based on the Improved Quaternion Filter Algorithm Open
Initial alignment of the strapdown inertial navigation system (SINS) is intended to determine the initial attitude matrix in a short time with certain accuracy. The alignment accuracy of the quaternion filter algorithm is remarkable, but t…
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Generalized commutative quaternions of the Fibonacci type Open
Quaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields. After the discovery of quaternions, modified quat…
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Dynamics of Mobile Manipulators Using Dual Quaternion Algebra Open
This article presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton–Euler formulation and uses twists and wrenches, which are pro…
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Grid-Based Quaternion Filter for SO(3) Estimation Open
A novel discrete Bayesian filtering scheme is proposed on the manifold of unit quaternions for rotation estimation. Existing quaternion filters rely on specific distributions (typically the Bingham distribution) to model the uncertainty in…
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Construction of dual-generalized complex Fibonacci and Lucas quaternions Open
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formu…
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Quaternion Attitude Control System of Highly Maneuverable Aircraft Open
In the era of rapid advancements in manned and unmanned aviation and robotics, there is a need for high-performance, robust attitude control of highly maneuverable fixed-wing aircraft, both manned and unmanned (UAVs). This paper presents a…