In case of action of internal and external uncontrollable influences the control of the multi-axis robot manipulator requires continuous adaptation of the controller. The methods of adaptation of the classical PID-regulator on the basis of a direct search method, namely, the simplex invariant method are offered. The structure of the offered algorithms is similar to the structure of the known algorithms on the basis of artificial neural networks. Two configurations of the adaptive PID-regulator are considered: in the first direct setup of coefficients is carried out; in the second an additional influence which is added to the PID-regulator output is created in the function of the error of tracking. In this paper the two-link robot manipulator with loading in a gripper is used as a control object. The comparison of the paths of the movement of the robot with use of different adaptive regulators on the basis of artificial neural networks and a simplex invariant method is provided. The results of the control of the robot manipulator with a permanent and alternating load are given, zones of effective application of the offered adaptation algorithms are defined. Mathematical simulation showed that the offered method effectively solves adaptation problems in the conditions of drift of the parameters of the robot manipulator.