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Showing 1 to 20 of 40 for “"Quaternions"”.
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On the Theory of Quaternions
Ordered triplets serve to describe space geometrically just as ordered pairs serve to describe the plane. A multiplication can be defined on pairs consistent with the complex numbers. However, as this paper will show, one cannot define a multiplication on triplets which is consistent with the …
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Dual Quaternions for Gravity Recovery Missions
… filter by extending the results to dual quaternions, which allows the filter to provide quasi-optimal relative pose estimations. The utility of this filter is attributed to the fact the filter will estimate the relative attitude or pose between two frames provided the measurements of any …
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On Quaternions and Activity Classification Across Sensor Domains
Activity classification based on sensor data is a challenging task. Many studies have focused on two main methods to enable activity classification; namely sensor level classification and body-model level classification. This study aims to enable activity classification across sensor domains by …
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Exploiting quaternions to support expressive interactive character motion
… Euler angle representation. We show how to use quaternions and their exponential mappings to create distance metrics on character poses, perform simple statistical analysis of joint motion limits and blend multiple poses together. We demonstrate these joint primitives on three techniques which …
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Vertical Take-Off and Landing Control via Dual-Quaternions and Sliding Mode
… Through representing rigid body motion with dual-quaternions, translation and rotation can be represented in a single compact form that is free of singularities and provides the shortest path interpolation compared to any other formulation. These rigid bodies will be shown to follow a desired …
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Optimized Thruster Allocation Utilizing Dual Quaternions for the Asteroid Sample Return Mission (OSIRIS-REx)
… system. Due to the coupled nature of dual quaternions, a newly developed thruster distribution matrix is implemented to take both the coupled command body forces and torques and transform them into the individual thruster frames. The developed method is based on a min-max optimization that …
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Extension of some theorems of complex functional analysis to linear spaces over the quaternions and Cayley numbers
… spaces over the division rings of the real Quaternions and the real Cayley algebra. The basic structure of Banach spaces over these division rings and the rings of bounded operators on these spaces is developed. Examples of finite and infinite dimensional spaces over these division rings are …
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Spectral Properties of Quaternionic Unit Gain Cycles
The quaternions are a non-commutative division ring that extends the complex numbers. A gain graph is a simple graph together with a gain function that assigns a value from an arbitrary group to each edge of the graph. We can define certain concepts on these graphs such as adjacency and Laplacian …
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MODEL-BASED 3-D VISION
… a set of fuzzy-weighted quantities called fuzzy quaternions. The database of the models is generated by first creating the octree representation of the 3-D objects based on three orthogonal views of the objects and employing the volume intersection method. Subsequently, by using the multi-level …
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Applications of the Pauli algebra and other geometric algebras.
Relationships among the complex numbers, quaternions, and the Pauli algebra are developed by presenting them as geometrical (Clifford) algebras. Rotations are examined using both quaternions and the Pauli algebra, and in particular, algorithms that are used in three-dimensional simulations and …
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Nonlinear Control for Dual Quaternion Systems
… <p>A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group <em>SE</em> (3). An eight …
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Color Face Recognition using Quaternionic Gabor Filters
… color by the use of hypercomplex numbers called quaternions. Two software implementations have been written of the new method and the analogous method for use on monochromatic images. Test results show that the new method is superior in accuracy to the analogous monochrome method. Although color …
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Rigid Body Constrained Motion Optimization and Control on Lie Groups and Their Tangent Bundles
… special orthogonal group SO(3) and the space of quaternions H, are commonly used to represent attitude. When considering rigid body pose, that is spacecraft position and attitude, the special Euclidean group SE(3) and the space of dual quaternions DH are frequently utilized. All these groups are …
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Linear Colour Image Processing in Hypercomplex Algebra guided by Genetic Algorithms
… are mapped as projective vectors in form of full quaternions using homogeneous coordinates instead of Euclidean vectors as pure quaternions using Cartesian coordinates. The use of projective geometry provides a much richer set of geometric operations in the colour space compared to the Euclidean …
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Precision navigation for aerospace applications
… the process with a small angle linearization of quaternions. Simulations are run using real flight data. A bench top hardware prototype is tested. Results show good performance and give a variety of insights into the design of navigation systems. Special attention is given to convergence and the …
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Integral geometry, Hamiltonian dynamics, and Markov Chain Monte Carlo
… geometry of the Hopf fibration is encoded by the quaternions; we investigate the extent to which the elegant properties of this encoding are preserved when one replaces quaternions with general [beta] > 0 ghosts.
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Predicting continuous hand pose from wearable EMG sensor data using transformer-based deep-learning models
… and 84-dimensional finger-bone orientation quaternions in a hand-centered frame. Compared with a Long Short-Term Memory (LSTM)-based model, the Transformer-based model reduced whole-hand median prediction error from 3.6° to 3.3° for a joint angle model and from 17.4° to 15.1° for a bone …
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