Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra

Jesús Alfonso Medrano-Hermosillo, Ricardo Lozoya-Ponce (), Abraham Efraím Rodriguez-Mata and Rogelio Baray-Arana
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Jesús Alfonso Medrano-Hermosillo: Instituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, Mexico
Ricardo Lozoya-Ponce: Instituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, Mexico
Abraham Efraím Rodriguez-Mata: Instituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, Mexico
Rogelio Baray-Arana: Instituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, Mexico

Mathematics, 2023, vol. 11, issue 3, 1-17

Abstract: The following paper talks about the dynamic modeling and control of robot manipulators using Hamilton’s equations in the screw theory framework. The difference between the proposed work with diverse methods in the literature is the ease of obtaining the laws of control directly with screws and co-screws, which is considered modern robotics by diverse authors. In addition, geometric algebra (GA) is introduced as a simple and iterative tool to obtain screws and co-screws. On the other hand, such as the controllers, the Hamiltonian equations of motion (in the phase space) are developed using co-screws and screws, which is a novel approach to compute the dynamic equations for robots. Regarding the controllers, two laws of control are designed to ensure the error’s convergence to zero. The controllers are computed using the traditional feedback linearization and the sliding mode control theory. The first one is easy to program and the second theory provides robustness for matched disturbances. On the other hand, to prove the stability of the closed loop system, different Lyapunov functions are computed with co-screws and screws to guarantee its convergence to zero. Finally, diverse simulations are illustrated to show a comparison of the designed controllers with the most famous approaches.

Keywords: screw theory; geometric algebra; Hamilton’s equations; sliding mode control; Lyapunov theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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