  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.
