Taxis is a well-known steering technique used by simple animals to approach a stimulus in the real world. However, no mathematical motion model of taxis can be found in the literature. This article derives the differential ordinary equations describing the motion of a Braitenberg vehicle, a widely used taxis model. A qualitative technique for non-linear dynamical systems analysis is applied to investigate the motion generated by the model. Validation of the analysis is performed through several simulations, and conditions for the stimulus source to be reached are obtained. This work fills the theoretical hole in formal models of Braitenberg vehicles and thereby provides theoretical support for the many previous experimental uses of those vehicles for steering tasks.