2D Corridor Path Planning
This 2D slalom corridor isolates APF guidance in a controlled planar environment, enabling systematic characterization of how the avoidance gain ka affects trajectory shape, safety clearance, and transit speed. The interactive player below lets you explore each gain value, while the analysis charts quantify the trade–offs across the full parameter space.
Gain Sweep Overlay
Trajectories for ten values of k_avoid through the same slalom layout. Low gains (0.05–0.2) cut inside each gate, taking the tightest line. Mid-range gains (1–4) track a clean slalom. High gains (6–10) take wide, cautious arcs that bulge outward between gates.
All 10 gain values overlaid on the slalom corridor. Low gains cut corners, intermediate gains stall at the centerline, ka=4 threads the slalom cleanly, and high gains push wide from early repulsion.
Results Summary
| k_a | Gates Reached | Y Span | Worst Clearance | Behavioral Summary |
|---|---|---|---|---|
| 0.05 | All 4 + goal | 2.1 m | 0.17 m (O11) | Hugs inside edges of every gate, grazing O11 by 17 cm. Fast passage but minimal safety margin. Path stays almost entirely in the upper half of the corridor. |
| 0.2 | All 4 + goal | 2.3 m | 0.29 m (O11) | Slightly wider than 0.05, still cuts corners aggressively. Remains in the upper half of the corridor. Clearance improves but is still below the 0.5 m caution threshold at O11. |
| 0.5 | All 4 + goal | 4.9 m | 0.40 m (O11) | First gain to cross the corridor centerline (y goes to −2.4 m). Begins showing a true zigzag pattern as repulsion is strong enough to deflect the drone downward between gates. |
| 2 | Gates 1–3 | 2.7 m | 0.60 m (O9) | Stalls at x = 6.2 m, never reaches gate 4. After passing gate 3 the drone drifts upward and encounters a local equilibrium between attraction toward the goal and repulsion from O11 and O7/O8. Velocity drops near zero. |
| 4 | All 4 + goal | 7.6 m | 0.41 m (O11) | Optimal gain. Full zigzag through all gates with wide, clean arcs. The repulsion is just strong enough to deflect into each gate opening without overshooting. The drone completes the course with the widest y-span and best combination of clearance and efficiency. |
| 10 | Gate 1 only | 1.7 m | 0.17 m (O9) | Repulsion overwhelms attraction immediately. The drone is pushed back toward the start after passing gate 1, never reaching gate 2. Total forward progress is only 3.2 m. The APF field near O1/O2 creates an impassable barrier. |
Clearance Trade-Study Heatmap
Trade-study matrix correlating GNC safety margins across all 10 gain values and 15 obstacles. This heatmap identifies exactly which obstacles act as critical bottlenecks for each control regime. Red and orange cells denote violations of the 0.5m safety limit, yellow indicates marginal clearance, and green indicates safe passage.
Minimum distance per (gain, obstacle) pair. Red indicates critical clearance below 0.2m; green is safe above 0.5m. The ka=4 row is the only gain with safe clearance across all 15 obstacles.
Speed Profile Overlay
Instantaneous speed over time for each gain. Low-gain trajectories maintain near-cruise speed through the slalom. High-gain trajectories brake through each gate, then accelerate in the straightaways between them.
Velocity vs time across all gains. Low gains maintain near-cruise speed; ka=2 stalls at the centerline; ka=4 shows clean braking at each gate; high gains fail to escape gate 1 repulsion.
Gain Bifurcation & Dynamical Regimes
State bifurcation diagram plotting the control parameter (k_avoid) against the final forward position reached by the drone. Bubble size represents lateral swing effort (y-span), while color indicates the overall worst clearance. This view reveals the discrete phase transitions and behavioral regimes of the system.
Max forward progress vs ka reveals four regimes: corner-cutting (I), local equilibrium stall (II), optimal slalom (III), and saturating pushback (IV). Marker color indicates worst-case clearance.
Parameter Space Design Envelope
Deterministic and Monte Carlo safety envelope maps. The top panel shows the success/failure outcome in the k_avoid × ρ0 parameter plane for the hand-designed slalom corridor. The bottom panel shows failure probability contours across 20 randomized heavy-density layouts, delineating the robust GNC operating envelope.
Failure probability across (ka, ρ0) space from 20 random obstacle layouts. Dark regions identify the robust design envelope; ka=4, ρ0=3.5 lies well inside the safe zone.