Coordinate-free control for the isoline tracking of an unknown scalar field

In this work, we study the isoline tracking problem in the GPS-denied environment where a sensing vehicle is controlled to slide on a desired isoline of a scalar field. By only using the strength-based measurements, our key idea lies in the design of a Proportional Integral (PI) controller to drive a new error term, which resembles the role of the sliding surface in the sliding mode control method, to zero. If such a goal is achieved, the isoline tracking task is then automatically completed, leading to our PI-like controller. We show the convergence of the closed-loop tracking system, and include both numerical simulations and real experiments to validate the performance of the proposed controllers by using various types of vehicles.