Flocking behavior for dynamic and complex swarm structures

Maintaining the formation of complex structures with multiple UAVs and achieving complex trajectories remains a major challenge. This work presents an algorithm for implementing the flocking behavior of UAVs based on the concept of Virtual Centroid to easily develop a structure for the flock. The approach builds on the classical virtual-based behavior, providing a theoretical framework for incorporating enhancements to dynamically control both the number of agents and the formation of the structure. Simulation tests and real-world experiments were conducted, demonstrating its simplicity even with complex formations and complex trajectories.

💡 Research Summary

The paper addresses the challenge of maintaining complex formations and executing intricate trajectories with multiple unmanned aerial vehicles (UAVs). It introduces a novel algorithm called FlockingBehavior, which builds upon the classical virtual‑structure concept but replaces the static reference frame with a Virtual Centroid (VC). The VC acts as a global reference point whose trajectory is defined by the user; each UAV’s desired pose is then computed online as the product of the VC transformation σ_W^VC(t) and a per‑agent formation transform G_i^VC(t). This formulation eliminates the need to generate individual trajectories for every UAV, simplifying the design of coordinated flights.

The authors formalize the problem as finding a function F that maps the VC trajectory and the formation description to a reference pose for each agent (Equation 1). Three simplifying assumptions are made: (1) generated trajectories respect the UAVs’ speed limits, (2) each UAV can precisely follow its reference pose, and (3) the environment is free of obstacles. Under these assumptions, the classic Reynolds flocking rules—cohesion, separation, and alignment—are expressed as quantitative constraints (Equations 2‑4) using parameters d_min, d_max, and δ.

Structure generation is illustrated with regular polygon formations. The formation transform G_i^VC is defined by an identity rotation and a translation vector T_i that places agents uniformly around a circle of radius d_max (Equations 7‑8). A geometric feasibility condition (Equation 9) guarantees that the minimum inter‑agent distance d_min is respected. Because the formation is treated as a rigid body, the distances between agents and between each agent and the VC remain constant, automatically satisfying cohesion and separation, while alignment is trivially met because the agents have zero relative velocity in the VC frame.

Dynamic structure handling extends the static virtual‑structure approach. The algorithm permits G_i^VC(t) to change over time, enabling the swarm to morph its shape during flight or to add/remove agents on‑the‑fly, provided the d_min constraint is maintained. The VC trajectory is supplied by an external planner (e.g., a 3‑D cubic polynomial trajectory generated by Aerostack2). Each UAV computes its pose online in an open‑loop fashion, relying solely on the VC information. This design reduces communication overhead and treats all agents symmetrically, avoiding the single‑point‑of‑failure issue inherent in leader‑follower schemes.

The experimental validation uses Bitcraze Crazyflie 2.1 quadrotors and a high‑fidelity simulator. Scenarios include three‑drone equilateral triangles, as well as larger formations (five and seven drones). The swarm follows straight lines, curved paths, and “facing” trajectories where the formation’s front aligns with the direction of motion. Metrics derived from Equations 2‑4 confirm that cohesion, separation, and alignment constraints are respected throughout steady‑state flight. The authors also demonstrate successful in‑flight reconfiguration and agent addition/removal without loss of formation integrity. All source code, simulation environments, and experimental videos are publicly released, facilitating reproducibility.

The paper’s contributions are threefold: (1) a generalized VC‑based flocking algorithm that imposes no limits on the number of agents or formation complexity, (2) the ability to modify the formation geometry and swarm size dynamically during execution, and (3) an open‑source ROS 2 implementation that can be integrated with existing aerial‑robotics frameworks. Limitations include the reliance on obstacle‑free environments, the assumption of perfect tracking, and the lack of closed‑loop robustness analysis under communication delays or model uncertainties. Future work should address obstacle avoidance, incorporate feedback‑based control to handle model errors, and evaluate the algorithm’s performance under realistic network conditions.