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Newton–Euler modeling and Hamiltonians for robot control in the geometric algebra

Published online by Cambridge University Press:  22 July 2022

Eduardo Bayro-Corrochano Open the ORCID record for Eduardo Bayro-Corrochano [Opens in a new window] ,
Jesus Medrano-Hermosillo Open the ORCID record for Jesus Medrano-Hermosillo [Opens in a new window] ,
Guillermo Osuna-González  and
Ulises Uriostegui-Legorreta
Eduardo Bayro-Corrochano*
Affiliation:
Centro de Investigaciones y Estudios Avanzados, CINVESTAV, Department of Electrical Engineering and Computer Science, Campus Guadalajara, 1145 Del Bosque Ave., El Bajío, 45019, Zapopan, México
Jesus Medrano-Hermosillo
Affiliation:
Centro de Investigaciones y Estudios Avanzados, CINVESTAV, Department of Electrical Engineering and Computer Science, Campus Guadalajara, 1145 Del Bosque Ave., El Bajío, 45019, Zapopan, México
Guillermo Osuna-González
Affiliation:
Centro de Investigaciones y Estudios Avanzados, CINVESTAV, Department of Electrical Engineering and Computer Science, Campus Guadalajara, 1145 Del Bosque Ave., El Bajío, 45019, Zapopan, México
Ulises Uriostegui-Legorreta
Affiliation:
Centro de Investigaciones y Estudios Avanzados, CINVESTAV, Department of Electrical Engineering and Computer Science, Campus Guadalajara, 1145 Del Bosque Ave., El Bajío, 45019, Zapopan, México
*
*Corresponding author. E-mail: eduardo.bayro@cinvestav.mx
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Abstract

The principal objective of the paper is to show the importance of the Hamiltonian in control theory. Instead of using the Lagrangian formulation of electromechanical or robotic systems, our work is focused on robot dynamics by its Hamiltonian. Using the iterative Newton–Euler, 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–Bang controllers.

Keywords

Newton–Euler modelingmotor algebra G+3,0,1dynamic modelHamiltoniansnonlinear controlSE(3) PD controlsliding mode controllocalized controlrobot armstracking
Type
Research Article
Information
Robotica , Volume 40 , Issue 11 , November 2022 , pp. 4031 - 4055
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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