On the convergence of Braitenberg vehicle 3a immersed in parabolic stimuli

Braitenberg vehicles are well known models of animal behaviour prone to be used as a mobile robot controller. Due to the qualitative simplicity of their behaviour they are used for teaching robotics, whilst the lack of a quantitative theory makes its use for research purposes troublesome. This paper contributes to our formal understanding of Braitenberg vehicle 3a by presenting some convergence properties of its trajectories under parabolic shaped stimuli or potential functions. We show new features of the vehicle motion unreported in robotics like, their conditional stability, their oscillatory behaviour and the existence of a preferred convergence direction. Quantitatively identifying the behaviour of Braitenberg vehicles allows to use them in robotics on a sound basis, not just relying on incomplete qualitative understanding as done by earlier works.