Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra
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-sc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/3/572 |
| _version_ | 1797623937152057344 |
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| author | Jesús Alfonso Medrano-Hermosillo Ricardo Lozoya-Ponce Abraham Efraím Rodriguez-Mata Rogelio Baray-Arana |
| author_facet | Jesús Alfonso Medrano-Hermosillo Ricardo Lozoya-Ponce Abraham Efraím Rodriguez-Mata Rogelio Baray-Arana |
| author_sort | Jesús Alfonso Medrano-Hermosillo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T09:35:51Z |
| format | Article |
| id | doaj.art-b9442cc1b4c94b5890aed2ecb0f544ca |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T09:35:51Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-b9442cc1b4c94b5890aed2ecb0f544ca2023-11-16T17:21:31ZengMDPI AGMathematics2227-73902023-01-0111357210.3390/math11030572Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric AlgebraJesús Alfonso Medrano-Hermosillo0Ricardo Lozoya-Ponce1Abraham Efraím Rodriguez-Mata2Rogelio Baray-Arana3Instituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, MexicoInstituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, MexicoInstituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, MexicoInstituto Tecnológico de Chihuahua (ITCH), Chihuahua 31310, MexicoThe 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.https://www.mdpi.com/2227-7390/11/3/572screw theorygeometric algebraHamilton’s equationssliding mode controlLyapunov theory |
| spellingShingle | Jesús Alfonso Medrano-Hermosillo Ricardo Lozoya-Ponce Abraham Efraím Rodriguez-Mata Rogelio Baray-Arana Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra Mathematics screw theory geometric algebra Hamilton’s equations sliding mode control Lyapunov theory |
| title | Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra |
| title_full | Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra |
| title_fullStr | Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra |
| title_full_unstemmed | Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra |
| title_short | Phase-Space Modeling and Control of Robots in the Screw Theory Framework Using Geometric Algebra |
| title_sort | phase space modeling and control of robots in the screw theory framework using geometric algebra |
| topic | screw theory geometric algebra Hamilton’s equations sliding mode control Lyapunov theory |
| url | https://www.mdpi.com/2227-7390/11/3/572 |
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