  In this paper, a combined formation acquisition and cooperative extremum
seeking control scheme is proposed for a team of three robots moving on a
plane. The extremum seeking task is to find the maximizer of an unknown
two-dimensional function on the plane. The function represents the signal
strength field due to a source located at maximizer, and is assumed to be
locally concave around maximizer and monotonically decreasing in distance to
the source location. Taylor expansions of the field function at the location of
a particular lead robot and the maximizer are used together with a gradient
estimator based on signal strength measurements of the robots to design and
analyze the proposed control scheme. The proposed scheme is proven to
exponentially and simultaneously (i) acquire the specified geometric formation
and (ii) drive the lead robot to a specified neighborhood disk around
maximizer, whose radius depends on the specified desired formation size as well
as the norm bounds of the Hessian of the field function. The performance of the
proposed control scheme is evaluated using a set of simulation experiments.
