A drift diffusion model of biological source seeking for mobile robots

Braitenberg vehicles have been used in multiple real world robotic implementations of bio-inspired local navigation. While sensor based control strategies - including existing models of Braitenberg vehicles - typically neglect sensor noise, real robot implementations suffer from different levels of noise, especially in the case of low cost robots and highly stochastic environments. This paper presents a novel drift-diffusion model of Braitenberg vehicle 3a - a bio-inspired source seeking controller for non-holonomic robots - accounting for the sensor noise. The stochastic differential equations obtained provide means to accurately simulate the behaviour of this bio-inspired control mechanism. Although these equations do not have analytic solutions in general, under some simplifying assumptions, we obtain the deterministic equations for the average and dispersion of the vehicles while performing source seeking. Moreover, we found an analytic bound for the distribution of the heading direction of the robots. Simulations illustrate and confirm the theoretical results presented.