Feedback Linearization of the Rotational Dynamics of a Flock of Target Tracking Visual Sensor Array using Tait-Bryan Parameterization

Using Tait-Bryan (TB) Parameterization, we revisit the visual sensor pointing control problem as a constrained dynamics on SO(3) from the point of view of a nonlinear multi input multi output (MIMO) system. The attitude of every sensor is assumed to satisfy a constraint, such as the ones proposed by Donders and Listing for the monocular and binocular eyes and the head rotation problems. While studying the problem of controlling the pointing direction of human head, the constraint, proposed by Donders, is that for every human head rotating away from its primary pointing direction, the rotational vectors are restricted to lie on a surface called the Donders’ surface. This paper assumes the existence of Donders’ surfaces for an array of visual sensors in a flock, tasked with the goal of tracking a point target in IR³. We assume that the Donders’ surfaces are described by a quadratic equation on the coordinates of the rotation vector. The inputs to the MIMO system are three external torque triplet, one for each visual sensor. The three output signals from each sensor are chosen as follows. Two of the signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders’ surface. Thus we have a square system and recent results have shown that this system is feedback linearizable on a suitable neighborhood N of the state space. We estimate a lower bound on the size of N by computing distance between the Donders’ and the associated Singularity surface. Our results are discussed for the monocular and the trinocular cases and a comparison is made from the point of view of the observed singularities. Analysis of the feedback linearizing control problem, from the point of view of ‘three eyed visual sensing’ is new.