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IEEE Transactions on Robotics, ISSN 1552-3098, 10/2014, Volume 30, Issue 5, pp. 1037 - 1048
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 6/2015, Volume 25, Issue 2, pp. 403 - 414
In this study, we define the dual Fibonacci quaternion and the dual Lucas quaternion. We derive the relations between the dual Fibonacci and the dual Lucas... 
Mathematical Methods in Physics | dual Fibonacci quaternion | Theoretical, Mathematical and Computational Physics | Fibonacci quaternion | Applications of Mathematics | Physics, general | dual Lucas quaternion | Physics | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL
Journal Article
Journal of Intelligent & Robotic Systems, ISSN 0921-0296, 9/2017, Volume 87, Issue 3, pp. 643 - 660
Cluster space control is a method of multirobot formation keeping that considers a group of robots to be a single entity, defining state variables to represent... 
Engineering | Dual quaternions | Control, Robotics, Mechatronics | Multirobot | Artificial Intelligence (incl. Robotics) | Formation control | Mechanical Engineering | UAV | Mobile robots | Multicopters | Electrical Engineering | ATTITUDE | ROBOTICS | ARCHITECTURE | GENERATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Robots | Robotics | Clusters | Multiple robots | Singularities | Quaternions | Redundancy
Journal Article
ACM Transactions on Graphics (TOG), ISSN 0730-0301, 10/2008, Volume 27, Issue 4, pp. 1 - 23
Skinning of skeletally deformable models is extensively used for real-time animation of characters, creatures and similar objects. The standard solution,... 
linear combinations | rigid transformations | Skinning | transformation blending | dual quaternions | Transformation blending | Dual quaternions | Rigid transformations | Linear combinations | SPACE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | ANIMATION | SPLINES | DEFORMATION
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 6/2016, Volume 26, Issue 2, pp. 553 - 571
Journal Article
Robotics and Autonomous Systems, ISSN 0921-8890, 03/2016, Volume 77, pp. 15 - 24
Journal Article
IEEE Transactions on Control Systems Technology, ISSN 1063-6536, 11/2019, Volume 27, Issue 6, pp. 2453 - 2469
Journal Article
Robotics and Autonomous Systems, ISSN 0921-8890, 03/2016, Volume 77, pp. 66 - 73
This paper exploits screw theory expressed via unit dual quaternion representation and its algebra to formulate both the forward (position+velocity) kinematics... 
Control | Robot arm | Dual quaternion | Kinematics | ROBOTICS | AUTOMATION & CONTROL SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Models | Robots | Algebra | Quaternions | Robot control | Screws | Mathematical models | Representations | Engineering Sciences | Automatic
Journal Article
International Journal of Geometric Methods in Modern Physics, ISSN 0219-8878, 06/2012, Volume 9, Issue 4, pp. 1250035 - 1250021
Four-dimensional A(4) polytopes and their dual polytopes have been constructed as the orbits of the Coxeter-Weyl group W(A(4)) where the group elements and the... 
dual polytopes | Coxeter groups | W(A | 4D-polytopes | quaternions | W(A) | SUBGROUPS | PHYSICS, MATHEMATICAL | Polytopes | Construction | Quaternions | Projection | Orbits | Subgroups | Three dimensional
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 6/2016, Volume 26, Issue 2, pp. 873 - 884
Dual Fibonacci quaternions are first defined by [5]. In fact, these quaternions must be called as dual coefficient Fibonacci quaternions. In this paper, dual... 
Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Fibonacci quaternion | Applications of Mathematics | Physics, general | Dual Fibonacci quaternion | Dual Lucas quaternion | Physics | MATHEMATICS, APPLIED | NUMBERS | PHYSICS, MATHEMATICAL
Journal Article
Industrial Robot: the international journal of robotics research and application, ISSN 0143-991X, 03/2019, Volume 46, Issue 2, pp. 247 - 258
Purpose The purpose of this paper is to propose an error model for serial robot kinematic calibration based on dual quaternions. Design/methodology/approach... 
Industrial Robotics | MODEL | PARAMETERS | IDENTIFICATION | ENGINEERING, INDUSTRIAL | Robotics | Dual quaternion | Kinematic-parameter identification | ACCURACY | Error analysis | Tracking | Computer simulation | Calibration | Parameter identification | Accuracy | Algebra | Researchers | Algorithms | Quaternions | Kinematics | Lie groups | Position measurement | Mathematical models | Kinematic equations | Number theory | Robots | Methods
Journal Article
Advances in Applied Clifford Algebras, ISSN 0188-7009, 3/2016, Volume 26, Issue 1, pp. 399 - 416
The slice Lebesgue measure is introduced in this article in the theory of slice regular functions, which replaces the role of Lebesgue measure in the theory of... 
32A26 | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Lipschitz space | 30G35 | Slice regular function | Applications of Mathematics | Physics, general | Dual space | Physics | Bloch space | MATHEMATICS, APPLIED | REGULAR FUNCTIONS | PHYSICS, MATHEMATICAL
Journal Article
Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 18, pp. 5567 - 5579
The Jacobsthal quaternions defined by Szynal-Liana and Wloch [35]. In this paper, we defined some properties of Jacobsthal quaternions. Also, we investigated... 
Jacobsthal quaternion | Jacobsthal-Lucas number | Jacobsthal number | Jacobsthal-Lucas quaternion | POLYNOMIALS | MATHEMATICS | MATHEMATICS, APPLIED | COMPLEX FIBONACCI NUMBERS | DUAL QUATERNIONS
Journal Article
Optimal Control Applications and Methods, ISSN 0143-2087, 07/2018, Volume 39, Issue 4, pp. 1371 - 1392
Summary This paper proposes 2 distributed optimization algorithms for the estimation of spatial rigid motion using multiple image sensors in a connected... 
dual quaternion | distributed estimation | spatial rigid motion | Newton method | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CONSENSUS | AUTOMATION & CONTROL SYSTEMS | Mathematical optimization | Analysis | Sensors | Algorithms | Filtration | Quaternions | Computer simulation | Decomposition | Extended Kalman filter | Optimization | Convergence
Journal Article
Advances in Mechanical Engineering, ISSN 1687-8132, 1/2019, Volume 11, Issue 1, p. 168781401882311
The dual quaternion is the simplest and most effective mathematical tool to describe the translational and rotational motion of a general rigid body. Its... 
screw vector | dual quaternion | rigid body | measurement | Position and attitude updating | ALGORITHM | RELATIVE MOTION | ENGINEERING, MECHANICAL | SPACECRAFT | POSITION | THERMODYNAMICS | TRACKING | ROTATION VECTOR | Rigid structures | Algorithms | Quaternions | Computer simulation | Mathematical analysis | Rigid-body dynamics | Attitudes | Rotation
Journal Article
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