Cooperative Curve Tracking in Two Dimensions Without Explicit Estimation of the Field Gradient

TL;DR

This paper presents a simple, gradient-free control law for two agents to accurately track a level curve in a plane without explicit field gradient estimation, demonstrating robustness to noise and fast convergence.

Contribution

It introduces a novel control strategy that enables level curve tracking without gradient estimation, applicable in noisy environments.

Findings

Successful tracking of noisy level curves in simulations

High accuracy and fast convergence achieved

Gradient-free control law effective in practical scenarios

Abstract

We design a control law for two agents to successfully track a level curve in the plane without explicitly estimating the field gradient. The velocity of each agent is decomposed along two mutually perpendicular directions, and separate control laws are designed along each direction. We prove that the formation center will converge to the neighborhood of the level curve with the desired level value. The algorithm is tested on some test functions used in optimization problems in the presence of noise. Our results indicate that in spite of the control law being simple and gradient-free, we are able to successfully track noisy planar level curves fast and with a high degree of accuracy.