Robot Kinematic Modeling and Control Based on Dual Quaternion Algebra — Part I: Fundamentals. Bruno Vilhena Adorno To cite this version: Bruno Vilhena Adorno. Robot Kinematic Modeling and Control Based on Dual Quaternion Algebra — Part I: Fundamentals.. 2017. hal-01478225 HAL Id: hal-01478225 https://hal.archives-ouvertes.fr/hal-01478225 Preprint submitted on 28 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives| 4.0 International License Robot Kinematic Modeling and Control Based on Dual Quaternion Algebra Part I: Fundamentals Bruno Vilhena Adorno Department of Electrical Engineering, Federal University of Minas Gerais (UFMG) Current address: Av. Antônio Carlos 6627, Belo Horizonte, MG 31270-010 Brazil E-mail address:
[email protected] URL: www.ppgee.ufmg.br/~adorno Abstract. This is the first part of a three-part tutorial on dual quaternion algebra applied to robotics, whose goal is to help readers grasp the main ideas behind dual quaternions and their application to robot kinematic modeling and control. Part I presents the fundamentals of dual quaternion algebra, starting from the basic definitions of complex numbers and rotations in the plane and then extending the idea to rigid motions in the tridimensional case by means of quater- nions and dual quaternions.