The technological operation of AUV docking is considered. An approach to its solution and modeling is proposed. A system for determining the relative position based on cameras and active-light markers is described. Active markers are offered to improve detection in dark deep water. A system of equations for modeling the dynamics of an underwater vehicle is described and a complete mathematical modeling of the whole pipeline of the positioning system is performed: image synthesis based on scene geometry, position determination based on the solution of the PnP problem, generating control based on synthesized measurements and modelling of the corresponding movement of the AUV. The presented model can be used to test various scenarios for the execution of a docking operation.