An adaptive neural network system SONCS (Self-Organizing Neural-net-Controller System) is applied to control problems of cruising type AUVs (Autonomous Underwater Vehicles) which are required to keep a constant altitude over a seabed with complicated geometry. An appropriate controller associated with a network which includes the characteristics of the topography and the dynamics of the robot, is generated by self-training without help of supervisors. It is also shown on computer simulation that when the topography changes the controller of the robot is adjusted adaptively with additional training through the same procedure.