Cooperative Curve Tracking in Two Dimensions Without Explicit Estimation of the Field Gradient
For multi-agent systems in environmental monitoring or source seeking, this provides a simple, gradient-free method for level curve tracking without explicit field gradient estimation.
The paper designs a gradient-free control law for two agents to cooperatively track a level curve in a noisy planar field, proving convergence to the desired level and demonstrating fast, accurate tracking on test functions.
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.