Planar Cooperative Extremum Seeking with Guaranteed Convergence Using A Three-Robot Formation

TL;DR

This paper presents a control scheme for a team of three robots to simultaneously form a specified formation and locate the maximum of an unknown signal field, with guaranteed exponential convergence.

Contribution

It introduces a novel combined formation acquisition and extremum seeking control method with proven convergence guarantees for three robots on a plane.

Findings

Robust exponential convergence to formation and source location.

Effective gradient estimation using signal strength measurements.

Validated performance through simulation experiments.

Abstract

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.