Human eye movements are controlled by six extraocular muscles. Although the eye socket restricts eye movements to almost pure rotations (3 degrees-of-freedom) the brain seems to control it using only 2 degrees of freedom, keeping the torsional component in a strict relationship with the gaze angles (azimuth and elevation), according to Donders’ Law (Tweed et al.,1987). To study the control principles that may lead to such behaviour, we have designed a scaled-up cable-driven robotic eye with six actuators, with cable insertion points closely matching the relative positions of its biological counterpart. Based on this system we have created physical simulation models that allowed us to test several biologically inspired modeling, learning and control methodologies, and compare them on their ability to replicate human behaviour in an artificial system. Our first tests focused on the human saccadic behaviour in head-restrained conditions and fixation at far targets. In these conditions, the eye orientation can be represented by a single-axis rotation between the primary and final gaze orientation. This rotation axis lies in a plane, so-called Listing's plane, where the torsional component is zero. Our results show that an open-loop optimal control law that optimizes duration, accuracy and energy can lead to such behaviour. To the best of our knowledge, this is the first time that compliance to Listing’s law is demonstrated in a 6-muscle model of the human eye. Our current efforts are directed towards studying the role of signal-dependent noise both in open-loop and closed-loop optimal control. Previous work (e.g., Shadmehr, 2012) has suggested that signal-dependent noise is instrumental in replicating the eye-saccade velocity profiles, and 1D simulation studies have confirmed that fact. Our full 3D model will allow the validation of these results in a more realistic system reflecting many of the complexities of the human eye mechanics.