Synergetic Control Framework for Autonomous UAV Swarm Coordination

Abstract

Highlights What are the main findings? A synergetic control method for UAV swarm coordination based on self-organization principles and symmetric virtual force fields is proposed. A Lyapunov/LaSalle stability analysis and a geometric safety radius argument show that the method keeps the swarm’s motion conflict-free, subject to the platform’s kinematic constraints, and maintains a stable formation without requiring a predefined initial arrangement of vehicles beyond the placement safety and connectivity conditions of (63) and (64). Through simulation studies, three characteristic phases of swarm self-organization are identified (chaotic motion, transitional reconfiguration, and ordered swarm behavior), and the sublinear scalability of formation time with swarm size (up to 100 UAVs) is confirmed—a distinct, more favorable quantity than the per-step computational cost, which scales approximately quadratically. These findings are illustrated, as a proof of concept, through a real-world quadcopter experiment achieving swarm formation within 27 s. What are the implications of the main findings? Within an identified favorable parameter region (Section 3.1), the proposed approach overcomes the key limitations of traditional artificial potential field methods (local minima, stagnation) through virtual pendulum gradient meters and damping terms, offering a scalable solution for autonomous multi-UAV coordination—with polynomial (not exponential) computational cost—which is applicable to both centralized and distributed control architectures. The identified optimal virtual force field parameters (α = 2, β = 3) and pendulum meters (Equation (61)) provide practical guidelines for tuning of the synergetic controller collision-free swarm robotics systems capable of stable self-organization under stochastic initial conditions from initial configurations satisfying the placement safety and connectivity conditions of (63) and (64). Abstract 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.