  Existing studies on formation control for unmanned aerial vehicles (UAV) have
not considered encircling targets where an optimum coverage of the target is
required at all times. Such coverage plays a critical role in many real-world
applications such as tracking hostile UAVs. This paper proposes a new path
planning approach called the Flux Guided (FG) method, which generates
collision-free trajectories for multiple UAVs while maximising the coverage of
target(s). Our method enables UAVs to track directly toward a target whilst
maintaining maximum coverage. Furthermore, multiple scattered targets can be
tracked by scaling the formation during flight. FG is highly scalable since it
only requires communication between sub-set of UAVs on the open boundary of the
formation's surface. Experimental results further validate that FG generates
UAV trajectories $1.5 \times$ shorter than previous work and that trajectory
planning for 9 leader/follower UAVs to surround a target in two different
scenarios only requires 0.52 seconds and 0.88 seconds, respectively. The
resulting trajectories are suitable for robotic controls after time-optimal
parameterisation; we demonstrate this using a 3d dynamic particle system that
tracks the desired trajectories using a PID controller.
