On Port-Hamiltonian Modeling and Control of Systems with Quaternions

Abstract

A quaternion representation is often used to describe the attitude of a spacecraft because it does not have any singular points. However, it becomes difficult to control the attitude described by a quaternion since a quaternion has four parameters despite that the attitude has only three degrees of freedom. In this paper, we employ the concept of port-Hamiltonian modeling to control systems with quaternions to introduce a general nonlinear control system synthesis method in aerospace engineering. It is also shown that the error quaternions are also naturally described by the port-Hamiltonian framework. Furthermore, the additional design parameter achieved by the proposed method is utilized for obstacle avoidance control. A numerical example exhibits the effectiveness of the proposed method.