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Using the iterative Newton\u2013Euler, we generate the local Hamiltonians and the derivative of the moments at each joint of the robot manipulator. Thus, we can apply decentralized controllers at each joint. We compare and discuss the efficiency of the controllers. We show that the performance of the sliding modes controller is more robust than that of the PD or Bang\u2013Bang controllers.<\/jats:p>","DOI":"10.1017\/s0263574722000741","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T10:15:56Z","timestamp":1658484956000},"page":"4031-4055","source":"Crossref","is-referenced-by-count":8,"title":["Newton\u2013Euler modeling and Hamiltonians for robot control in the geometric algebra"],"prefix":"10.1017","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4738-3593","authenticated-orcid":false,"given":"Eduardo","family":"Bayro-Corrochano","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5152-220X","authenticated-orcid":false,"given":"Jesus","family":"Medrano-Hermosillo","sequence":"additional","affiliation":[]},{"given":"Guillermo","family":"Osuna-Gonz\u00e1lez","sequence":"additional","affiliation":[]},{"given":"Ulises","family":"Uriostegui-Legorreta","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"S0263574722000741_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2006-7_29"},{"key":"S0263574722000741_ref30","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2008.4739356"},{"key":"S0263574722000741_ref4","first-page":"627","article-title":"Robot Control in Terms of Hamiltonian Mechanics","author":"Z\u00e1da","year":"2016","journal-title":"Proc. of the 22nd International Conference Engineering Mechanics"},{"key":"S0263574722000741_ref21","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2012.2192359"},{"key":"S0263574722000741_ref6","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2006930"},{"key":"S0263574722000741_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.06.039"},{"key":"S0263574722000741_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2008.02.004"},{"key":"S0263574722000741_ref14","first-page":"50","volume-title":"IFAC Papers On-Line","author":"Reyes-Baez","year":"2017"},{"key":"S0263574722000741_ref2","doi-asserted-by":"crossref","first-page":"3366","DOI":"10.1109\/ACCESS.2021.3140160","article-title":"Modified linear technique for the controllability and observability of robotic arms\u201d","volume":"10","author":"Aguilar-Ib\u00e1\u00f1ez","year":"2022","journal-title":"IEEE Access"},{"key":"S0263574722000741_ref19","volume-title":"New Foundation of Classical Mechanics","author":"Fujimoto","year":"1986"},{"key":"S0263574722000741_ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2014.2330701"},{"key":"S0263574722000741_ref23","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2009.04.006"},{"key":"S0263574722000741_ref29","volume-title":"Robot Modeling and Control","author":"Spong","year":"2006"},{"key":"S0263574722000741_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-1719-7_25"},{"key":"S0263574722000741_ref26","volume-title":"Introduction to Robotics 2nd edition (Mechanics and Control","author":"Craig","year":"1989"},{"key":"S0263574722000741_ref25","first-page":"381","article-title":"Preliminary sketch of bi-quaternions\u201d","volume":"4","author":"Clifford","year":"1873","journal-title":"Proc. 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