  While multiple studies have proposed methods for the formation control of
unmanned aerial vehicles (UAV), the trajectories generated are generally
unsuitable for tracking targets where the optimum coverage of the target by the
formation is required at all times. We propose a path planning approach called
the Flux Guided (FG) method, which generates collision-free trajectories while
maximising the coverage of one or more targets. We show that by reformulating
an existing least-squares flux minimisation problem as a constrained
optimisation problem, the paths obtained are $1.5 \times$ shorter and track
directly toward the target. Also, we demonstrate that the scale of the
formation can be controlled during flight, and that this feature can be used to
track multiple scattered targets. The method is highly scalable since the
planning algorithm is only required for a sub-set of UAVs on the open boundary
of the formation's surface. Finally, through simulating a 3d dynamic particle
system that tracks the desired trajectories using a PID controller, we show
that the resulting trajectories after time-optimal parameterisation are
suitable for robotic controls.
