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

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.