Synergetic Control Framework for Autonomous UAV Swarm Coordination

This study presents a synergetic control approach for coordinating the motion of a UAV swarm based on self-organization principles and energy potential interactions. The proposed method effectively addresses the known limitations of traditional potential field techniques by introducing a procedure for synthesizing the synergetic control of swarm motion using a virtual force field with symmetric attraction and repulsion functions. A Lyapunov/LaSalle stability analysis and a geometric safety radius argument show that this keeps the swarm's motion conflict-free, subject to the platform's kinematic constraints, and supports stable formation maintenance. Damping terms are incorporated into the equations of motion to eliminate self-oscillations and, via an energy (Lyapunov) argument, we show that the resulting system converges to the critical point set of the total interaction potential. A synergetic controller based on virtual pendulum meters is introduced to prevent stagnation. A specialized mathematical framework is developed to mitigate the curse of dimensionality, as confirmed through simulations, although the per-step computational cost scales approximately quadratically with swarm size. The swarm formation time increases sublinearly with the number of UAVs, highlighting the approach's scalability. A swarm self-organization modeling study reveals three characteristic phases: namely, chaotic motions, transitional reconfiguration, and ordered swarm behavior. The formation process corresponds to a gradual minimization of inter-UAV interaction energy, while stable collective motion is achieved by maintaining a constant polarization of vehicle heading angles. Through simulations, parameter ranges that provide optimal synergetic properties during swarm formation and coordinated movement are identified. The findings are further illustrated, as a proof of concept, through real-world experimental tests of swarm control.