Automated control of spatial motion of remotely operated underwater vehicle (ROV) is a known scientific problem since as an object of control it is essentially nonlinear. Operational control of ROV is a multi-dimensional problem. The synthesis of regulators separately for each degree of freedom is complicated by mutual influence of kinematic parameters of ROV. Nonlinearity of the restrictions type, typical for ROV, leads to the occurrence of strong and degrees of freedom. This degrades the quality of automated control system (SAC) as a whole. We obtained a matrix notation of the basic law of dynamics of marine movable object as a solid body. Own and added masses and moments of inertia of the body and the fluid are brought into a separate matrix. This makes it possible to apply the resulting equation without structural changes to study the dynamics of spatial motion of ROV with different parameters. The equation is used in direct form to model the motion of ROV and in the inverse form for the synthesis of SAC over its spatial motion. An inverse regulator (IR) of ROV with six degrees of freedom is synthesized based on the method of inverse dynamics and decomposition of the reference model. We simulated the work of inverse controller IR of ROV and demonstrated a loss of manageability by the weak rotating degrees of freedom. The fundamentals of the method for maintaining manageability with automated control of a multidimensional object are formulated. The essence of the method is in driving the contours of SAC out of the modes of saturation by scaling control errors. We designed SAC of spatial motion of ROV based on the synthesized IR and the unit for maintaining manageability. It provides controlled motion of ROV by six degrees of freedom without losing manageability. A simulation of the developed SAC of spatial motion of ROV is performed. The simulation results revealed that the unit for maintaining manageability provides for the operation of SAC on the verge of saturation of its contours. This enables the ROV motion by six degrees of freedom without losing manageability.