{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"institution":[{"id":[{"id":"https:\/\/ror.org\/03mb6wj31","id-type":"ROR","asserted-by":"publisher"},{"id":"https:\/\/www.isni.org\/000000041937028X","id-type":"ISNI","asserted-by":"publisher"},{"id":"https:\/\/www.wikidata.org\/entity\/Q1640731","id-type":"wikidata","asserted-by":"publisher"}],"name":"Universitat Polit\u00e8cnica de Catalunya","acronym":["UPC"]}],"indexed":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T19:53:34Z","timestamp":1769889214327,"version":"3.49.0"},"reference-count":0,"publisher":"Universitat Polit\u00e8cnica de Catalunya","license":[{"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Kinematics is a branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the forces that cause such motion. For serial robot manipulators, kinematics consists of describing the open chain geometry as well as the position, velocity and\/or acceleration of each one of its components. Rigid serial robot manipulators\r\nare designed as a sequence of rigid bodies, called links, connected by motor-actuated pairs, called joints, that provide relative motion between consecutive links. Two kinematic problems of special relevance for serial robots are:\r\n- Singularities: are the configurations where the robot loses at least one degree of freedom (DOF). This is equivalent to:\r\n            (a) The robot cannot translate or rotate its end-effector in at least one direction.\r\n            (b) Unbounded joint velocities are required to generate finite linear and angular velocities.\r\nEither if it is real-time teleoperation or off-line path planning, singularities must be addressed to make the robot exhibit a good performance for a given task. The objective is not only to identify the singularities and their associated singular directions but to design strategies to avoid or handle them.\r\n- Inverse kinematic problem: Given a particular position and orientation of the end-effector, also known as the end-effector pose, the inverse kinematics consists of finding the configurations that provide such desired pose. The importance of the inverse kinematics relies on its role in the programming and control of serial robots. Besides, since for each given pose the inverse kinematics has up to sixteen different solutions, the objective is to find a closed-form method for solving this problem, since closed-form methods allow to obtain all the solutions in a compact form.\r\nThe main goal of the Ph.D. dissertation is to contribute to the solution of both problems. In particular, with respect to the singularity problem, a novel scheme for the identification of the singularities and their associated singular directions is introduced. Moreover, geometric algebra is used to simplify such identification and to provide a distance function in the configuration space of the robot that allows the definition of algorithms for avoiding them.\r\nWith respect to the inverse kinematics, redundant robots are reduced to non-redundant ones by selecting a set of joints, denoted redundant joints, and by parameterizing their joint variables. This selection is made through a workspace analysis which also provides an upper bound for the number of different closed-form solutions. Once these joints have been identified, several\r\nclosed-form methods developed for non-redundant manipulators can be applied to obtain the analytical expressions of all the solutions. One of these methods is a novel strategy developed using again the conformal model of the spatial geometric algebra.\r\n\r\nTo sum up, the Ph.D dissertation provides a rigorous analysis of the two above-mentioned kinematic problems as well as novel strategies for solving them. To illustrate the different results introduced in the Ph.D. memory, examples are given at the end of each of its chapters.<\/jats:p>\n                <jats:p>La cinem\u00e1tica es una rama de la mec\u00e1nica cl\u00e1sica que describe el movimiento de puntos, cuerpos y sistemas de cuerpos sin considerar las fuerzas que causan dicho movimiento. Para un robot manipulador serie, la cinem\u00e1tica consiste en la descripci\u00f3n de su geometr\u00eda, su posici\u00f3n, velocidad y\/o aceleraci\u00f3n. Los robots manipuladores serie est\u00e1n dise\u00f1ados como una secuencia de elementos estructurales r\u00edgidos, llamados eslabones, conectados entres si por articulaciones actuadas, que permiten el movimiento relativo entre pares de eslabones consecutivos. Dos problemas cinem\u00e1ticos de especial relevancia para robots serie son: - Singularidades: son aquellas configuraciones donde el robot pierde al menos un grado de libertad (GDL). Esto equivale a: (a) El robot no puede trasladar ni rotar su elemento terminal en al menos una direcci\u00f3n. (b) Se requieren velocidades articulares no acotadas para generar velocidades lineales y angulares finitas. Ya sea en un sistema teleoperado en tiempo real o planificando una trayectoria, las singularidades deben manejarse para que el robot muestre un rendimiento \u00f3ptimo mientras realiza una tarea. El objetivo no es solo identificar las singularidades y sus direcciones singulares asociadas, sino dise\u00f1ar estrategias para evitarlas o manejarlas. - Problema de la cinem\u00e1tica inversa: dada una posici\u00f3n y orientaci\u00f3n del elemento terminal (tambi\u00e9n conocida como la pose del elemento terminal), la cinem\u00e1tica inversa consiste en obtener las configuraciones asociadas a dicha pose. La importancia de la cinem\u00e1tica inversa se basa en el papel que juega en la programaci\u00f3n y el control de robots serie. Adem\u00e1s, dado que para cada pose la cinem\u00e1tica inversa tiene hasta diecis\u00e9is soluciones diferentes, el objetivo es encontrar un m\u00e9todo cerrado para resolver este problema, ya que los m\u00e9todos cerrados permiten obtener todas las soluciones en una forma compacta. El objetivo principal de la tesis doctoral es contribuir a la soluci\u00f3n de ambos problemas. En particular, con respecto al problema de las singularidades, se presenta un nuevo m\u00e9todo para su identificaci\u00f3n basado en el \u00e1lgebra geom\u00e9trica. Adem\u00e1s, el \u00e1lgebra geom\u00e9trica permite definir una distancia en el espacio de configuraciones del robot que permite la definici\u00f3n de distintos algoritmos para evitar las configuraciones singulares. Con respecto a la cinem\u00e1tica inversa, los robots redundantes se reducen a robots no-redundantes mediante la selecci\u00f3n de un conjunto de articulaciones, las articulaciones redundantes, para despu\u00e9s parametrizar sus variables articulares. Esta selecci\u00f3n se realiza a trav\u00e9s de un an\u00e1lisis de espacio de trabajo que tambi\u00e9n proporciona un l\u00edmite superior para el n\u00famero de diferentes soluciones en forma cerrada. Una vez las articulaciones redundantes han sido identificadas, varios m\u00e9todos en forma cerrada desarrollados para robots no-redundantes pueden aplicarse a fin de obtener las expresiones anal\u00edticas de todas las soluciones. Uno de dichos m\u00e9todos es una nueva estrategia desarrollada usando el modelo conforme del \u00e1lgebra geom\u00e9trica tridimensional. En resumen, la tesis doctoral proporciona un an\u00e1lisis riguroso de los dos problemas cinem\u00e1ticos mencionados anteriormente, as\u00ed como nuevas estrategias para resolverlos. Para ilustrar los diferentes resultados presentados en la tesis, la memoria contiene varios ejemplos al final de cada uno de sus cap\u00edtulos.<\/jats:p>","DOI":"10.5821\/dissertation-2117-168571","type":"dissertation","created":{"date-parts":[[2023,10,14]],"date-time":"2023-10-14T01:31:09Z","timestamp":1697247069000},"approved":{"date-parts":[[2018,9,14]]},"source":"Crossref","is-referenced-by-count":0,"title":["Solving robotic kinematic problems : singularities and inverse kinematics"],"prefix":"10.5821","author":[{"sequence":"additional","affiliation":[]},{"given":"Isiah","family":"Zaplana Agut","sequence":"first","affiliation":[]}],"member":"3865","container-title":[],"original-title":[],"deposited":{"date-parts":[[2026,1,31]],"date-time":"2026-01-31T06:36:19Z","timestamp":1769841379000},"score":1,"resource":{"primary":{"URL":"https:\/\/hdl.handle.net\/2117\/168571"}},"subtitle":[],"editor":[{"given":"Luis","family":"Basa\u00f1ez Villaluenga","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.5821\/dissertation-2117-168571","relation":{},"subject":[]}}