  Control of robot orientation in Cartesian space implicates some difficulties,
because the rotation group SO(3) is not contractible, and only globally
contractible state spaces support continuous and globally asymptotically stable
feedback control systems. In this paper, unit quaternions are used to represent
orientations, and it is first shown that the unit quaternion set minus one
single point is contractible. This is used to design a control system for
temporally coupled dynamical movement primitives (DMPs) in Cartesian space. The
functionality of the control system is verified experimentally on an industrial
robot.
