On trajectory tracking control of port-Hamiltonian systems with quaternions

A quaternion representation is often used to describe the attitude of a rigid body type spacecraft since it does not have any singular point whereas the conventional Euler angle description intrinsically has one. However, the dynamical equation with quaternions become more complicated than those described by Euler angles. In order to control the system with quaternions easily, we apply the authors' previous work on trajectory tracking control for port-Hamiltonian systems and extend it to handle quaternions. In the proposed design procedure, we do not need to solve any additional partial differential equations (PDEs) whereas nonlinear control very often requires to solve them.