The article considers the development of a control algorithm for the actuating links of a manipulator with a parallel-serial structure. The authors suggest a two-stage procedure for resolving the problem of controlling the robot operating body motion into a set neighborhood of the final state for a set time. The first stage covers the process of solving the problem of defining the manipulator generalized coordinates at the set coordinates of the operating body. Then the problem of determining the laws of the formation of reference influences for the actuators is solved, which ensures the movement of the working body in the vicinity of a given point. The technique for the synthesis of dynamic algorithms for stabilizing the effector relative to a given position and implementing the program paths is based on generating the control signals of actuators by solving the inverse dynamic problem using a control signal generation algorithm provided that deviations from the current program path values are the solutions of a second-order differential equation. The laws of change in control voltages are obtained. The results of numerical modeling are presented, confirming the efficiency of the proposed algorithm on the example of a specific manipulator.