The Isoline Tracking in Unknown Scalar Fields with Concentration Feedback

TL;DR

This paper introduces a simple PI-like control method for a sensing vehicle to accurately track a desired isoline in unknown scalar fields, even in GPS-denied environments, validated through simulations.

Contribution

It proposes a novel sliding surface based error in a PI controller for isoline tracking, applicable to various vehicle models and environments.

Findings

Global regulation to the desired isoline for circular fields

Steady-state error can be minimized by tuning P gain

Effective in GPS-denied environments, validated via UAV simulations

Abstract

The isoline tracking of this work is concerned with the control design for a sensing vehicle to track a desired isoline of an unknown scalar field. To this end, we propose a simple PI-like controller for a Dubins vehicle in the GPS-denied environments. Our key idea lies in the design of a novel sliding surface based error in the standard PI controller. For the circular field, we show that the P-like controller can globally regulate the vehicle to the desired isoline with the steady-state error that can be arbitrarily reduced by increasing the P gain, and is eliminated by the PI-like controller. For any smoothing field, the P-like controller is able to achieve the local regulation. Then, it is extended to the cases of a single-integrator vehicle and a doubleintegrator vehicle, respectively. Finally, the effectiveness and advantages of our approaches are validated via simulations on the fixed-wing UAV and quadrotor simulators.