Binaural sound localization is known to be improved by incorporating the movement of the sensor. "Active" schemes based on this paradigm can overcome conventional limitations such as front-back ambiguity and source range recovery. Starting from a Gaussian prior on the relative position of a source, this paper determines the motion of a binaural sensor which leads to the most effective path for localization. To this aim, a reward function is defined as the conditional expectation, over the yet unknown N next observations, of the entropy of the N-step-ahead posterior pdf of the relative source position. The optimal motion of the binaural sensor is obtained from a constrained optimization problem involving the automatic differentiation of the reward function. The method is validated in simulation, and is being implemented on a real-life robotic test bed.