his paper presents experimental results of an original approach to the Neural Network learning architecture for the control and the adaptive control of mobile robots. The basic idea is to use non-recurrent multi-layer-network and the backpropagation algorithm without desired outputs, but with a quadratic criterion which spezify the control objective. To illustrate this method, we consider an experimental problem that is to control cartesian position and orientation of an non-holonomic wheeled cart. The results establish that the neural net learns on-line the kinematic constraints of the robot. After several on-line learning lessons the net is able to control the robot at any configurations in a limited cartesian space.