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Comparison of high-dimensional neural networks using hypercomplex numbers in a robot manipulator control

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Abstract

This study considers high-dimensional neural networks based on hypercomplex numbers that form a four-dimensional algebra over the field of real numbers, such as quaternion, coquaternion, hyperbolic-quaternion, bicomplex and dual-complex numbers. In addition, the applicability of the networks in the robot manipulator’s control system is explored. In the control system, the output of the high-dimensional neural network is used as the control input for the robot manipulator to ensure that the end-effector of the robot manipulator tracks the desired trajectory in a three-dimensional space. Computational experiments are conducted on controlling a three-link robot manipulator to evaluate the learning and control performance of the high-dimensional neural networks. The simulation results demonstrate that the quaternion-valued neural network achieves better performance in learning and control tasks compared to other networks.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP20K11980.

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Correspondence to Kazuhiko Takahashi.

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This work was presented in part at the 26th International Symposium on Artificial Life and Robotics (Online, January 21–23, 2021).

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Takahashi, K. Comparison of high-dimensional neural networks using hypercomplex numbers in a robot manipulator control. Artif Life Robotics 26, 367–377 (2021). https://doi.org/10.1007/s10015-021-00687-x

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