Because of their apparent simplicity, Braitenberg vehicles have been extensively used in robotics on an empirical basis. However, the lack of a backing up formal theory turns their application into an educated guess of parameter tuning. This paper provides a mathematical model of Braitenberg vehicles 2 and 3 as non-linear dynamical systems, which serves as a theoretical ground to fully exploit them for robotic applications and to create animated agents in artificial life or computer games. The behaviour of the vehicles is analysed using theory of dynamical systems under general conditions, and hints on how to generate desired behaviours are given. Results show that vehicles 2 and 3 can be used to implement bio-inspired navigation like; target reaching and stimulus avoidance, which constitute a set of navigation primitives or basis for navigation behaviour. Through a new theoretical approach, his work paves the way to a proper understanding of Braitenberg vehicles and to an extension of their applicability.