Ants-inspired non-gradient based navigation of non-holonomic robots for environmental extremum seeking and tracking hidden paths

A Dubins-car like robot travels within an area in which an unknown scalar field exists. Only sensors that measure the field value at the current location are available. We present a biologically inspired navigation law that drives the robot to the set of the field maximizers and if they constitute a whole curve, also endows the robot with the capacity of tracking this curve. These are justified by mathematically rigorous non-local convergence results and are confirmed via computer simulations. The proposed algorithm does not use gradient estimation and is non-demanding with respect to computation and motion.