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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Bibliographic Details
Published in:Machines (Basel) Vol. 10; no. 5; p. 333
Main Authors: Takahashi, Kazuhiko, Tano, Eri, Hashimoto, Masafumi
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2022
Subjects:
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
ISSN:2075-1702, 2075-1702
Online Access:Get full text
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Summary: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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ISSN:2075-1702
2075-1702
DOI:10.3390/machines10050333