Approaching dual quaternions from matrix algebra
Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and interpolated. Unfortunately, the combination of quaternions and dual numbers seem quite abstract and somewhat arbitrary when approached for t...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/24543 |
| Acceso en línea: | https://hdl.handle.net/2117/24543 https://dx.doi.org/10.1109/TRO.2014.2341312 |
| Access Level: | acceso abierto |
| Palabra clave: | Approximation theory Robots -- Kinematics Matrices Spatial kinematics Quaternions Biquaternions Double quaternions Dual quaternions Cayley factorization Aproximació, Teoria de l' Robots -- Cinemàtica Matrius (Matemàtica) Àrees temàtiques de la UPC::Informàtica::Robòtica |
| Sumario: | Dual quaternions give a neat and succinct way to encapsulate both translations and rotations into a unified representation that can easily be concatenated and interpolated. Unfortunately, the combination of quaternions and dual numbers seem quite abstract and somewhat arbitrary when approached for the first time. Actually, the use of quaternions or dual numbers separately are already seen as a break in mainstream robot kinematics, which is based on homogeneous transformations. This paper shows how dual quaternions arise in a natural way when approximating 3D homogeneous transformations by 4D rotation matrices. This results in a seamless presentation of rigid-body transformations based on matrices and dual quaternions which permits building intuition about the use of quaternions and their generalizations. |
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