This paper presents a task of a mobile object positioning in the presence of determinate disturbances. A mobile object is described by kinematics and dynamics equations of a solid body in a three dimensional space. The control inputs of the mobile object are forces and torques. Design of the adaptive control is based on the position-path control method for the mobile objects. This article presents two algorithms of the adaptive position-path control. The first algorithm is the adaptive position-path control with an integration component and reference model. The second algorithm is the adaptive position-path control with a reference model and an extended mobile robot model. The authors propose a unit diagram for a direct adaptive position-path control system with a reference model. The article also presents the design procedures for the adaptive position-path control systems and stability analysis of the closed-loop system, as well as the computer simulation results of the designed adaptive closed-loop systems with both constant and variable disturbances. The authors make conclusions on the basis of the analysis and modeling results. The main advantage of the proposed method is separation of the basic position-path regulator and adaptation algorithms. The parameters of the position-path controller are the parameters of the reference model. Therefore, a classical structure of the adaptive control with a reference model requires a change in the parameters of the model. The adaptation algorithms presented in this paper can be applied for the parameters of the additional dynamic units.