Formation Control for UAVs Using a Flux Guided Approach

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.