Collision avoidance in circular motion of a fixed-wing drone formation based on rotational modification of artificial potential field

In coordinated circular motion of a group of autonomous unmanned aerial vehicles (UAVs or drones), it is important to ensure that collisions between them are avoided. A typical situation occurs when one of the drones in a circular formation needs to overtake the drone ahead. The reason for such an overtake may be due to a given geometry of the UAV formation, when this configuration of a given relative position of the drones has changed for some reason. In this case, the limited maneuverability of UAVs of exactly fixed-wing type requires taking into account the peculiarities of their dynamics in the synthesis of the collision avoidance algorithm. The impossibility of the airspeed for a fixed-wing type UAV to drop below a certain minimum value also plays a role here. In this paper, we propose to use an approach based on vortex vector fields, which are essentially a rotational modification of the artificial potential field (APF) method. In this case, the path following algorithm developed in our previous works provides the circular motion. As a result, a collision avoidance algorithm has been developed that works efficiently by maintaining a coordinated circular motion of the autonomous drone formation without unnecessary turns. The proposed algorithm was named Artificial Potential Field for Circular Motion (abbreviated as APFfCM). Using the direct Lyapunov method, it is shown that the trajectories of the formation system have uniform boundedness (UB) when using the proposed control algorithm. Due to the boundedness of the candidate Lyapunov function, it is guaranteed that no collision event between drones will occur. Thus the control objective of providing coordinated circular motion for an autonomous fixed-wing type drone formation without collisions is achieved. Fixed-wing (“flying wing”) UAV models in MATLAB/Simulink environment demonstrate the effective performance of the proposed algorithm. These models have both full nonlinear dynamics and implementation of tuned autopilots stabilizing angular and trajectory motion.