Robust hybrid source-seeking algorithms based on directional derivatives and their approximations

A family of hybrid control algorithms is developed that steer a nonholonomic autonomous vehicle to the source of a scalar signal present in the environment. In an idealized setting, we develop a general hybrid control scheme that globally asymptotically stabilizes the vehicle position about the source. Pursuing a practical implementation, a series of perturbations to the family of controllers is introduced, resulting in a semi-global practical stability of the vehicle position about the source. An example of a recently developed conjugate direction-based controller fitting into this family is developed and demonstrated by simulation and experiment.