3D Swarm Simulation
This 3D simulation extends the same APF and consensus framework to full formation flight. Seven quadcopters fly a DCM-aligned wedge through 15 debris obstacles, using LQR optimal control for velocity tracking and the Dryden model for wind gust rejection. The metrics below track formation health over the full 90–second figure–8 trajectory.
Flight Metrics
Telemetry extracted from the simulation data: formation convergence, graph connectivity, control effort, and obstacle proximity events.
Formation Error. This measures the average distance of each drone from its assigned position in the wedge formation. When the error is zero, the swarm is perfectly aligned. The error drops from an initial 26.9 m to a steady state of 1-3 m within the first 15-20 s, showing the consensus controller converges the formation quickly. Residual error persists due to continuous wind gusts (sigma = 2 m/s) and APF deflections around obstacles.
Algebraic Connectivity (λ₂). This is the second smallest eigenvalue of the communication graph. A value greater than zero means the network is connected and drones can share information. Higher values indicate stronger connectivity. Here λ₂ stays between 4 and 7 throughout the run, well above zero, confirming the formation maintains a complete communication graph at all times - even during obstacle avoidance and wind gusts.
Control Effort. This is the maximum thrust demanded from any single drone at each timestep. Initial formation acquisition requires a peak of 26.0 N, well within the 45 N per-axis limit. During cruise the effort settles to 1-3 N, with brief spikes when a drone brakes around an obstacle or rejects a wind gust. The LQR controller keeps all commands within safe limits.
Proximity Events. Each marker represents a drone passing within 3.5 m of an asteroid surface. The vertical position identifies which drone and which asteroid; the horizontal position marks when it occurred. Events are distributed across all 7 drones and 15 obstacles, with the highest density during the figure-8 waypoint clusters at 15-30 s and 60-75 s. This confirms the APF repulsion actively steers drones through corridor passages rather than avoiding every obstacle from a distance.