Feedforward–Feedback Controller Based on a Trained Quaternion Neural Network Using a Generalised <inline-formula><math display="inline"><semantics><mi mathvariant="double-struck">HR</mi></semantics></math></inline-formula> Calculus with Application to Trajectory Control of a Three-Link Robot Manipulator

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.

Keywords

• hypercomplex numbers
• quaternion neural network
• generalised Hamiltonian–Real calculus
• feedforward–feedback controller
• robot manipulator