The first task is related to the understanding of the physical nature of cooperative manipulation and finding a way to fairly precise characterization of cooperative system statics, kinematics and dynamic. After successfully completing this task, within the framework of the second task, the problem of coordinated motion of the cooperative system is completed. The starting point in dealing with the three tasks above the cooperative manipulation is the assumption that the problem of force uncertainty in cooperative manipulation can be overcome by introducing the elastic properties into the cooperative system, at least in part where force uncertainty appears. Coordinated motion and control in cooperative manipulation problem resolved as coordinating and controlling the movement of mobile elastic structure, taking into account specific features of cooperative manipulation. Coordinated motion and control law in cooperative manipulation are synthesized on the basis of non-linear model in which the problem of uncertainty is resolved, which did not occur in the available literature.