This paper presents the developed by the authors step-by-step neuroevolution based approach to designing control systems for complex multicoordinate interrelated plants (MIP). The proposed approach allows us to build the structure of the automatic control system (ACS) for the MIP on the basis of the single complex neural controller (NC) with multiple inputs and outputs as well as to implement the effective training of its multilayer neural network (NN) by means of the evolutionary based algorithm, taking into account the mutual influence of all variables of the MIP in an optimal way. In order to study and validate the efficiency of the presented approach the design of the ACS for the spatial motion of caterpillar mobile robot (MR) able to move on inclined and vertical ferromagnetic surfaces is carried out in this work. The developed ACS based on the NC with optimal structure allows us to achieve high quality indicators of spatial motion control, taking into account the mutual influence of control channels of the MR’s speed and angle that confirms the high efficiency of the proposed approach.