Gradient climbing in formation via extremum seeking and passivity-based coordination rules

We consider a gradient climbing problem where the objective is to steer a group of vehicles to the extrema of an unknown scalar field distribution while keeping a prescribed formation. We address this task by developing a scheme in which the leader performs extremum seeking for the minima or maxima of the field, and other vehicles follow according to passivity-based coordination rules. The extremum-seeking approach generates approximate gradients of the field locally by "dithering" sensor positions. We show that if there is sufficient time-scale separation between the fast dither and slow gradient motions of the leader vehicle, the followers only respond to the gradient motion, and filter out the dither component, while keeping the prescribed formation.