Comparison of Neural Network–Based Adaptive Controllers Using Hypercomplex Numbers for Controlling Robot Manipulator

Abstract

This study investigates an adaptive controller by applying a neural network, in which all the network parameters, states, signals and functions are expressed using hypercomplex numbers and algebras; its application to dynamics control of a robot manipulator. To design hypercomplex–valued neural networks where each neural network is a multilayer feedforward network with a split–type activation function of neurons using a tapped–delay–line input, we consider the following four types of hypercomplex numbers: complex, hyperbolic, bicomplex and quaternion numbers. In the control system, we utilise a feedback error–learning scheme to conduct the training of the network through a back–propagation algorithm. In the computational experiments, we explore a hypercomplex–valued neural network–based controller as a trajectory control problem of a three–link robot manipulator, in which the position of the end–effector follows to the desired trajectory in a 3–dimensional space. The simulation results validate the feasibility and effectiveness of the quaternion neural network–based controller for this task.