Controlling UAVs by Sensing the Electric or the Magnetic Field Around Power Lines

We provide a procedure for estimating the relative position of a drone with respect to three-phase power lines. This is done by making use of the root mean square (rms) measurements of the electric/magnetic fields emanating from the power lines. Maxwell’s equations are used to derive the sensor measurement model showing that the total rms electric/magnetic field is a measure of the relative position of the drone. The squared inverse of the total rms electric/magnetic field serves as a potential function for a Hamiltonian, which in turn is a Lyapunov function. It is shown that the gradient of this potential function always points to the (convex hull of the) power lines. Based on Lyapunov analysis, a control algorithm is developed that forces a drone to follow the gradient of the potential to the power lines. This controller provides the capability to inspect power lines or carry out installation tasks on them. Simulations are presented to illustrate the efficacy of the approach.