Este trabajo presenta una nueva solución compacta basada en cuaterniones duales para el desarrollo de la cinemática de manipuladores robóticos. Se plantea el desarrollo de una herramienta en forma completa para poder observar claramente su correlación con el método de las matrices de transformación homogénea derivadas a partir de los parámetros de Denavit-Hartenberg. Se proponen herramientas para simplificar el uso de los cuaterniones duales para la obtención del modelo cinemático de mecanismos de cadena abierta definiendo la regla de la cadena aplicada a estos. Finalmente se ilustra su aplicación a un par de casos de estudio.
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Laboratoire de recherche en imagerie et orthopédie, département de génie de la production automatisée" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:4 [ 0 => "R. Aissaoui" 1 => "H. Mecheri" 2 => "N. Hagemeister" 3 => "J.A. de Guise" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Libro" => array:3 [ "fecha" => "1996" "editorial" => "École de Technologie Supérieure" "editorialLocalizacion" => "Montréal, (Québec), Canada" ] ] ] ] ] ] 1 => array:3 [ "identificador" => "bib0010" "etiqueta" => "Akyar, 2008" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Dual Quaternions in Spatial Kinematics in an Algebraic Sense" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "B. Akyar" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:7 [ "issn" => "13000098" "tituloSerie" => "Turkish Journal of Mathematics" "fecha" => "2008" "volumen" => "32" "numero" => "2" "paginaInicial" => "373" "paginaFinal" => "391" ] ] ] ] ] ] 2 => array:3 [ "identificador" => "bib0015" "etiqueta" => "Althoefer, 1996" "referencia" => array:1 [ 0 => array:1 [ "referenciaCompleta" => "Althoefer, K. (1996), Neuro-Fuzzy Motion Planning for Robotic Manipulators. PhD Thesis, Department of Electric of Electronic and Electrical Engineering. King's College London, University of London, London, UK." ] ] ] 3 => array:3 [ "identificador" => "bib0020" "etiqueta" => "Aracil et al., 2006" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Robots Paralelos: Máquinas con un Pasado para una Robótica del Futuro" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:4 [ 0 => "R. Aracil" 1 => "R.J. Saltarén" 2 => "J.M. Sabater" 3 => "O. Reinoso" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:7 [ "issn" => "16977912" "tituloSerie" => "Revista iberoamericana de automática e informática industrial (RIAI)" "fecha" => "2006" "volumen" => "3" "numero" => "1" "paginaInicial" => "16" "paginaFinal" => "28" ] ] ] ] ] ] 4 => array:3 [ "identificador" => "bib0025" "etiqueta" => "Berthold, 1987" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Closed-Form Solution of Absolute Orientation Using Unit Quaternions" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "K.P.H. Berthold" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "issn" => "07403232" "tituloSerie" => "Journal of the Optical Society of America" "fecha" => "1987" "volumen" => "4" "paginaInicial" => "629" "paginaFinal" => "642" ] ] ] ] ] ] 5 => array:3 [ "identificador" => "bib0030" "etiqueta" => "Cayley, 1889" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "On The Application of Quaternion to the Theory of Rotation" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "A. Cayley" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:5 [ "tituloSerie" => "The Collected Mathematical Papers, Cambridge at the University Press" "fecha" => "1889" "volumen" => "1" "paginaInicial" => "405" "paginaFinal" => "409" ] ] ] ] ] ] 6 => array:3 [ "identificador" => "bib0035" "etiqueta" => "Daniilidis y Bayro-Corrochano, 1996" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "The Dual Quaternion Approach to Hand-eye Calibration" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "K. Daniilidis" 1 => "E. Bayro-Corrochano" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:5 [ "tituloSerie" => "Proceedings of the 13th International Conference on Pattern Recognition" "fecha" => "1996" "volumen" => "1" "paginaInicial" => "318" "paginaFinal" => "322" ] ] ] ] ] ] 7 => array:3 [ "identificador" => "bib0040" "etiqueta" => "Denavit y Hartenberg, 1955" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "A Kinematic Notation for Lower-Pair Mechanics based on Matrices" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "J. Denavit" 1 => "R.S. Hartenberg" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "ASME, Journal Applied Mechanics" "fecha" => "1955" "volumen" => "22" "numero" => "2" "paginaInicial" => "215" "paginaFinal" => "221" ] ] ] ] ] ] 8 => array:3 [ "identificador" => "bib0045" "etiqueta" => "Funda, 1988" "referencia" => array:1 [ 0 => array:1 [ "referenciaCompleta" => "Funda, J. (1988), A Computational Analysis Of Line- Oriented Screw Transformations In Robotics. Department of Computer and Information Science, School of Engineering and Applied Science, University of Pennsylvania." ] ] ] 9 => array:3 [ "identificador" => "bib0050" "etiqueta" => "Funda et al., 1990" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "On Homogeneuos Transforms, Quaternions, and Computational Efficiency" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "J. Funda" 1 => "R.H. Taylor" 2 => "R.P. Paul" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "IEEE Transactions on Robotics and Automation" "fecha" => "1990" "volumen" => "6" "numero" => "3" "paginaInicial" => "382" "paginaFinal" => "388" ] ] ] ] ] ] 10 => array:3 [ "identificador" => "bib0055" "etiqueta" => "Hamilton, 1853" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Lecture on Quaternions" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "W.R. Hamilton" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Libro" => array:2 [ "fecha" => "1853" "editorial" => "The Halls of Trinity College" ] ] ] ] ] ] 11 => array:3 [ "identificador" => "bib0060" "etiqueta" => "Hart et al., 1994" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Visualizing Quaternion Rotation" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "J.C. Hart" 1 => "G.K. Francis" 2 => "L.H. Kauffman" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "ACM Transactions on Graphics" "fecha" => "1994" "volumen" => "13" "numero" => "3" "paginaInicial" => "256" "paginaFinal" => "276" ] ] ] ] ] ] 12 => array:3 [ "identificador" => "bib0065" "etiqueta" => "Husty et al., 2007" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "A New and Efficient Algorithm for the Inverse Kinematics of a General Serial 6R Manipulator" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "M.L. Husty" 1 => "F.M. Purner" 2 => "H.-P. Schrocker" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "Mechanism and machine theory" "fecha" => "2007" "volumen" => "42" "numero" => "1" "paginaInicial" => "66" "paginaFinal" => "81" ] ] ] ] ] ] 13 => array:3 [ "identificador" => "bib0070" "etiqueta" => "Kula y Yayli, 2006" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Dual Split Quaternions and Screw Motions in Minkowski 3- Space" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "L. Kula" 1 => "Y. Yayli" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:4 [ "tituloSerie" => "Iranian Journal of Science & Technology, Transaction A" "fecha" => "2006" "volumen" => "30" "numero" => "A3" ] ] ] ] ] ] 14 => array:3 [ "identificador" => "bib0075" "etiqueta" => "Merchán-Cruz, 2005" "referencia" => array:1 [ 0 => array:1 [ "referenciaCompleta" => "Merchán-Cruz, E.A. (2005), Soft-Computing Techniques in the Trajectory Planning of Trajectory Planning of Robot Manipulators Sharing a Common Workspace. <span class="elsevierStyleItalic">Ph.D. Thesis, Department of Automatic Control and Systems Engineering, The U. Sheffield, UK</span>." ] ] ] 15 => array:3 [ "identificador" => "bib0080" "etiqueta" => "Pennestrì y Valentini, 2009" "referencia" => array:1 [ 0 => array:1 [ "referenciaCompleta" => "Pennestrì, E. & Valentini, P. P. (2009), Dual Quaternions as a Tool for Rigid Body Motion Analysis: A Tutorial with an Application to Biomechanics. MULTIBODY DYNAMICS 2009, ECCOMAS Thematic Conference, doi:10.1.1.157.3845." ] ] ] 16 => array:3 [ "identificador" => "bib0085" "etiqueta" => "Perez y McCarthy, 2004" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Dual Quaternion Synthesis of a Parallel 2-TPR Robot" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "A. Perez" 1 => "J.M. McCarthy" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "LibroEditado" => array:4 [ "titulo" => "Proceedings of the WORKSHOP on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators" "paginaInicial" => "1" "paginaFinal" => "9" "serieFecha" => "2004" ] ] ] ] ] ] 17 => array:3 [ "identificador" => "bib0090" "etiqueta" => "Ramírez-Gordillo et al., 2009" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Trajectory Generation of Robot Manipulator using an Artificial Potential Function and Genetic Algorithms" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:5 [ 0 => "J. Ramírez-Gordillo" 1 => "J.J. Muñoz-César" 2 => "A. Gómez-Terán" 3 => "A. Valencia-Lazcano" 4 => "A.L. Soria-Moya" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:5 [ "tituloSerie" => "Applied Mechanics and Materials: Electromechanical and Systems Engineering" "fecha" => "2009" "volumen" => "15" "paginaInicial" => "73" "paginaFinal" => "78" ] ] ] ] ] ] 18 => array:3 [ "identificador" => "bib0095" "etiqueta" => "Sahul et al., 2008" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "A Novel Method for Representing Robot Kinematics using Quaternion Theory" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "S. Sahul" 1 => "B.B. Biswall" 2 => "B. Subudhi" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "LibroEditado" => array:4 [ "titulo" => "IEEE Sponsored Conference on Computational Intelligence, Control And Computer Vision In Robotics & Automation, NIT Rourkela" "paginaInicial" => "75" "paginaFinal" => "82" "serieFecha" => "2008" ] ] ] ] ] ] 19 => array:3 [ "identificador" => "bib0100" "etiqueta" => "Salamin, 1995" "referencia" => array:1 [ 0 => array:1 [ "referenciaCompleta" => "Salamin, E. (1995), Applications of Quaternions to Computation with Rotations. <span class="elsevierStyleItalic">Working Paper, Stanford AI Lab</span>, pp. 1-9." ] ] ] 20 => array:3 [ "identificador" => "bib0105" "etiqueta" => "Sánchez-Peña y Alonso, 2005" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Control de Vehículos Espaciales" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "R.S. Sánchez-Peña" 1 => "R.J. Alonso" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "Revista iberoamericana de automática e informática industrial (RIAI)" "fecha" => "2005" "volumen" => "2" "numero" => "3" "paginaInicial" => "6" "paginaFinal" => "24" ] ] ] ] ] ] 21 => array:3 [ "identificador" => "bib0110" "etiqueta" => "Tait, 1890" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "An Elementary Treatise on Quaternions" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "P.G. Tait" 1 => "M.A." ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Libro" => array:3 [ "edicion" => "Third Edition" "fecha" => "1890" "editorial" => "Cambride at the University" ] ] ] ] ] ] 22 => array:3 [ "identificador" => "bib0115" "etiqueta" => "Merchán-Cruz et al., 2011" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Síntesis Genética de Mecanismos para Aplicaciones en Prótesis de Miembro Inferior" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:6 [ 0 => "E.A. Merchán-Cruz" 1 => "E. Lugo-González" 2 => "J. Ramírez-Gordillo" 3 => "R.G. Rodríguez-Cañizo" 4 => "J.G.M. Sandoval-Pineda" 5 => "L.H. 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