Temporal changes in stimulus perception improve bio-inspired source seeking
Braitenberg vehicles are well known qualitative models of sensor driven animal source seeking (biological taxes) that locally navigate a stimulus function. These models ultimately depend on the perceived stimulus values, while there is biological evidence that animals also use the temporal changes in the stimulus as information source for taxis behaviour. The time evolution of the stimulus values depends on the agent's (animal or robot) velocity, while simultaneously the velocity is typically the variable to control. This circular dependency appears, for instance, when using optical flow to control the motion of a robot, and it is solved by fixing the forward speed while controlling only the steering rate. This paper presents a new mathematical model of a bio-inspired source seeking controller that includes the rate of change of the stimulus in the velocity control mechanism. The above mentioned circular dependency results in a closed-loop model represented by a set of differential-algebraic equations (DAEs), which can be converted to non-linear ordinary differential equations (ODEs) under some assumptions. Theoretical results of the model analysis show that including a term dependent on the temporal evolution of the stimulus improves the behaviour of the closed-loop system compared to simply using the stimulus values. We illustrate the theoretical results through a set of simulations.