The paper presents an approach to provide the motion of a quadrotor along a given trajectory under the influence of step perturbations. The proposed approach is based on the use of a speed regulator, introduced in the works of Veremey E.I. as one of the elements of a special multi-purpose structure controller. Due to its structure, the speed controller gives for the closed-loop system the property of astatism for regulated variables, which means that the error between the actual motion and the desired trajectory converges to zero in the presence of step disturbances. In this work the controller that provides a quadrotor motion along a given trajectory, is based on four linear simplified mathematical models. Each of such simplified models describes the motion for one of the regulated variables and is used to design control law for each specific scalar regulated variable, that gives the astatism property for this variable. As a result the controller is formed to regulate the position in space and the yaw angle of quadrotor. In the end the paper presents graphs of transients of changes in position and orientation in the space under the action of the proposed control to illustrate its effectiveness; simulation is carried out in MATLAB-Simulink environment for a particular quadrotor model.