This paper addresses the problem of virtual pedestrian autonomous navigation for crowd simulation. It describes a method for solving interactions between pedestrians and avoiding inter-collisions. Our approach is agent-based and predictive: each agent perceives surrounding agents and extrapolates their trajectory in order to react to potential collisions. We aim at obtaining realistic results, thus the proposed model is calibrated from experimental motion capture data. Our method is shown to be valid and solves major drawbacks compared to previous approaches such as oscillations due to a lack of anticipation. We first describe the mathematical representation used in our model, we then detail its implementation, and finally, its calibration and validation from real data.