2026-04-13T02:17:19Zhttps://recercat.cat/oai/request

oai:recercat.cat:2117/3551222026-01-21T06:01:29Zcom_2072_1033col_2072_452950

A branch-and-prune method to solve closure equations in dual quaternions Shabani, Arya Porta Pleite, Josep Maria Thomas, Federico Institut de Robòtica i Informàtica Industrial Universitat Politècnica de Catalunya. KRD - Cinemàtica i Disseny de Robots Àrees temàtiques de la UPC::Informàtica::Robòtica Robots Position analysis Multiloop mechanisms Forward kinematics Inverse kinematics Kinematotropic mechanisms Multiaffine systems Branch-and-prune methods Classificació INSPEC::Automation::Robots © 2021 Elsevier Using dual quaternions, the closure equations of a kinematic loop can be expressed as a system of multiaffine quations. In this paper, this property is leveraged to introduce a branch-and-prune method specially tailored for solving such systems of equations. The new method is objectively simpler (in the sense that it is easier to understand and to implement) than previous approaches relying on general techniques such as interval Newton methods or methods based on Bernstein polynomials or linear relaxations. Moreover, it relies on two basic operations —linear interpolation and projection onto coordinate planes— that can be e¿ciently computed. The generality of the proposed method is evaluated on position analysis problems with 0-, 1-, and 2-dimensional solution sets, including the inverse kinematics of serial robots and the forward kinematics of parallel ones. The results obtained on these problems show that the efficiency of the method compares favorably to state-of-the-art alternatives. This work was partially supported by the Spanish Ministry of Economy and Competitiveness through the project DPI2017- 88282-P. Peer Reviewed Postprint (author's final draft) 2021 Article Shabani, A.; Porta, J.; Thomas, F. A branch-and-prune method to solve closure equations in dual quaternions. "Mechanism and machine theory", 2021, vol. 164, p. 104424:1-104424:18. 0094-114X https://hdl.handle.net/2117/355122 10.1016/j.mechmachtheory.2021.104424 eng https://www.sciencedirect.com/science/article/abs/pii/S0094114X21001828?via%3Dihub info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/DPI2017-88282-P/ES/PLANIFICACION CINETODINAMICA DE MOVIMIENTOS ROBOTICOS EFICIENTES Y AGILES/ http://creativecommons.org/licenses/by-nc-nd/3.0/es/ Open Access Attribution-NonCommercial-NoDerivs 3.0 Spain application/pdf