Extremum seeking for motion optimization: From bacteria to nonholonomic vehicles

What do E. coli bacteria and GPS-denied unmanned vehicles have in common? In the absence of position and attitude measurements, both bacteria and autonomous vehicles have to rely on solving real-time optimization problems based on other available signal measurements, such as concentration of chemical agents, thermal or light intensity, or other environmental signals such as acoustic or electomagnetic. We overview extremum seeking, a method for non-model based optimization that we have been developing over the last ten years, and its applications to autonomous vehicles. The use of extremum seeking for navigating vehicles in GPS-denied environments is a rather challenging technical problem because the nonholonomically constrained vehicle kinematics violate the standard assumptions of exponential stability of the plant in the classical theory of extremum seeking. We review applications to nonholonomic vehicles in both two and three dimensions.