A sufficiently convenient algorithm for constructing differentiable control functions that guarantee the translation of a wide class of nonlinear non-stationary systems of ordinary differential equations from the initial state to a given point in the phase space, with account of the control constraint and the non-stationary perturbation. Constructive sufficient conditions are imposed on the right part of the controlled system, under which the indicated translation is possible. The problem of motion control by a robot manipulator when moving a body of variable mass to a given point is considered and its numerical simulation is carried out.