Flocking phase transition and threat responses in bio-inspired autonomous drone swarms

Abstract

Collective motion inspired by animal groups offers powerful design principles for autonomous aerial swarms. We present a bio-inspired 3D flocking algorithm in which each drone interacts only with a minimal set of influential neighbors, relying solely on local alignment and attraction cues. By systematically tuning these two interaction gains, we map a phase diagram revealing sharp transitions between swarming and schooling, as well as a critical region where susceptibility, polarization fluctuations, and reorganization capacity peak. Outdoor experiments with a swarm of ten drones, combined with simulations using a calibrated flight-dynamics model, show that operating near this transition enhances responsiveness to external disturbances. When confronted with an intruder, the swarm performs rapid collective turns, transient expansions, and reliably recovers high alignment within seconds. These results demonstrate that minimal local-interaction rules are sufficient to generate multiple collective phases and that simple gain modulation offers an efficient mechanism to adjust stability, flexibility, and resilience in drone swarms.

Figures (9)

• Figure 1: Phase-diagram structure of collective motion under varying attraction and alignment strength. Heatmaps show the average polarization (A), dispersion (B), polarization fluctuations (C), and the transects at $\gamma_{\rm Att}=0.5$ (D), which are the focus of this study. For each parameter pair $(\gamma_{\rm Ali}, \gamma_{\rm Att})$, we ran ten 300-s simulations with a swarm of 10 drones and report the means across runs.
• Figure 2: Representative collective-motion patterns in the drone swarm. (A) Schooling: a highly aligned and cohesive state. (B) Swarming: a compact but weakly aligned state.
• Figure 3: Swarm polarization (A,B), dispersion (C,D), and minimal inter-agent distance (E,F) calculated along 3D. (A,C,E) field experiments with Parrot Bebop 2 UAVs and (B,D,F) numerical simulations. All experiments used $\gamma_{\rm Att} = 0.5$, while $\gamma_{\rm Ali}$ varied between $0.025$ and $0.4$. The baseline condition consisted of a swarm of 10 drones, and the test condition introduced an additional intruder drone. Simulations included 100 runs for each $\gamma_{\rm Ali}$ value, with a fixed duration of five minutes per value, whereas in the field experiments the duration for each $\gamma_{\rm Ali}$ value varied. The graphs show the means and standard deviations. The horizontal dotted line shown in (A,B) corresponds to random polarization for $N$ agents, approximately $0.5 \sqrt{\pi/N} = 0.28$ for $N=10$.
• Figure 4: Baseline Dynamics of a ten-UAV swarm near the critical region. (A) Time evolution of polarization and dispersion, color-coded by metric. The orange curve indicates the time-dependent variations of $\gamma_{\rm Ali}$ during this run. (B) Enlarged view of the critical region ($\gamma_{\rm Att}=0.5$; $\gamma_{\rm Ali}=0.175$ and $\gamma_{\rm Ali}=0.2$), showing six selected timestamps. (C) Corresponding swarm configurations in the $X$-$Y$ plane, where points represent the drones’ instantaneous positions and tails indicate their trajectories over the preceding five seconds (see SI Movie S\ref{['supp:crit_base']}).
• Figure 5: Swarm dynamics across repeated phase transitions between swarming and schooling. The ten-UAV swarm was tested under baseline conditions while the alignment strength $\gamma_{\rm Ali}$ was alternated between low (0.075) and high (0.4) values for $\gamma_{\rm Att}=0.5$, corresponding respectively to swarming and schooling behaviors. (A) Time evolution of polarization and dispersion, color-coded by metric. The orange curve indicates the time-dependent variations of $\gamma_{\rm Ali}$ throughout the run. (B) Enlarged view of a full switching cycle (swarming → schooling → swarming), highlighting six selected timestamps. (C) Corresponding $X$-$Y$ swarm configurations, where points represent the drones’ instantaneous positions and tails trace their trajectories over the previous five seconds (see SI Movie S\ref{['supp:phase_switch']}).