We design a method to control the motion of a manipulator robot while strictly enforcing collision avoidance in a dynamic obstacle field. We rely on model predictive control while formulating collision avoidance as a hard constraint. We express the constraint as the requirement for a signed distance function to be positive between pairs of strictly convex objects. Among various formulations, we provide a suitable definition for this signed distance and for the analytical derivatives needed by the numerical solver to enforce the constraint. The method is completely implemented on a manipulator "Panda" robot, and the efficient open-source implementation is provided along with the paper. We experimentally demonstrate the efficiency of our approach by performing dynamic tasks in an obstacle field while reacting to non-modeled perturbations.