This thesis presents a complete vision-based navigation system that can plan and follow an obstacle-avoiding path to a desired destination on the basis of an internal map updated with information gathered from its visual sensor. For vision-based self-localization, the system uses new floor-edges-specific filters for detecting floor edges and their pose, a new algorithm for determining the orientation of the robot, and a new procedure for selecting the initial positions in the self-localization procedure. Self-localization is based on matching visually detected features with those stored in a prior map. For planning, the system demonstrates for the first time a real-world application of the neural-resistive grid method to robot navigation. The neural-resistive grid is modified with a new connectivity scheme that allows the representation of the collision-free space of a robot with finite dimensions via divergent connections between the spatial memory layer and the neuro-resistive grid layer. A new control system is proposed. It uses a Smith Predictor architecture that has been modified for navigation applications and for intermittent delayed feedback typical of artificial vision. A receding horizon control strategy is implemented using Normalised Radial Basis Function nets as path encoders, to ensure continuous motion during the delay between measurements. The system is tested in a simplified environment where an obstacle placed anywhere is detected visually and is integrated in the path planning process. The results show the validity of the control concept and the crucial importance of a robust vision-based self-localization process.