Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised HR Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator
This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback...
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| Published in: | Machines (Basel) Vol. 10; no. 5; p. 333 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Basel
MDPI AG
01.05.2022
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| ISSN: | 2075-1702, 2075-1702 |
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| Abstract | This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback–feedforward controller as a control system application using such a network. The quaternion neural network is trained in real-time by introducing a feedback error learning framework to the controller. Thus, the quaternion neural network-based controller functions as an adaptive-type controller. The designed controller is applied to the control problem of a three-link robot manipulator, with the control task of making the robot manipulator’s end effector follow a desired trajectory in the Cartesian space. Computational experiments are conducted to investigate the learning capability and the characteristics of the quaternion neural network used in the controller. The experimental results confirm the feasibility of using the derived learning algorithm based on the generalised Hamiltonian–Real calculus to train the quaternion neural network and the availability of such a network for a control systems application. |
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| AbstractList | This study derives a learning algorithm for a quaternion neural network using the steepest descent method extended to quaternion numbers. This applies the generalised Hamiltonian–Real calculus to obtain derivatives of a real–valued cost function concerning quaternion variables and designs a feedback–feedforward controller as a control system application using such a network. The quaternion neural network is trained in real-time by introducing a feedback error learning framework to the controller. Thus, the quaternion neural network-based controller functions as an adaptive-type controller. The designed controller is applied to the control problem of a three-link robot manipulator, with the control task of making the robot manipulator’s end effector follow a desired trajectory in the Cartesian space. Computational experiments are conducted to investigate the learning capability and the characteristics of the quaternion neural network used in the controller. The experimental results confirm the feasibility of using the derived learning algorithm based on the generalised Hamiltonian–Real calculus to train the quaternion neural network and the availability of such a network for a control systems application. |
| Author | Hashimoto, Masafumi Takahashi, Kazuhiko Tano, Eri |
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| Cites_doi | 10.3233/AIC-130578 10.1007/s10462-019-09752-1 10.1109/TSP.2015.2399865 10.1109/TNNLS.2015.2440473 10.1109/SICE.2008.4655038 10.4018/978-1-60566-214-5 10.1098/rsos.150255 10.1016/j.neucom.2016.06.014 10.1098/rsos.160211 10.1631/FITEE.1900533 10.1109/LSP.2010.2091126 10.1007/s11063-017-9716-1 10.1007/s11831-019-09344-w 10.1109/ACCESS.2021.3097756 10.1007/s10015-021-00687-x 10.1007/BF00364149 10.1002/9781118590072 10.1007/978-3-030-62365-4_43 10.1007/978-81-322-2074-9 10.1109/SII.2017.8279333 10.1109/ANZCC50923.2020.9318414 10.1109/ICAMechS54019.2021.9661487 |
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| Copyright | 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| SubjectTerms | Adaptive control Algorithms Artificial intelligence Calculus Cartesian coordinates Control systems design Control tasks Controllers Cost function End effectors Engineering Feedback control Feedforward control Machine learning Manipulators Mathematical functions Neural networks Quaternions Robot arms Robot control Robotics Robots Signal processing Steepest descent method Trajectory control |
| Title | Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised HR Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator |
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