Decentralized Drone Swarm Coordination via Broadcast-as-Shared-State and Hierarchical PCA-Tree Bisection

A four-layer decentralized coordination architecture for drone swarms built on a single primitive: broadcast-as-shared-state with locally-deterministic per-drone computation against a PCA tree of the target manifold. The four layers (assignment, recovery, priority allocation, localization) are independently provable, empirically validated across N=10 to N=10,000, and compose without interference.

Layer 1 (Assignment): hierarchical PCA-tree bisection lands within 1.43% of the Hungarian optimum at N=10,000. Empirical fit form a + b/√N (M5) beats five alternatives by AIC/BIC: gap = 1.27% [1.22, 1.33] + 14.12 [11.74, 16.50] / √N. CBBA reference comparator at N=100: hierarchical needs 14× fewer messages while landing at a 3.0% gap (vs CBBA's 7.7% in this simplified single-task variant).

Layer 2 (Recovery): closest-surplus patch protocol guarantees 0.9% reassignment per single drone loss; cluster recovery yields exactly K reassignments with 0 unfilled when surplus >= K (Lemma 7). Tiered redundancy reduces flight cost 56% when threat correlates with priority.

Layer 3 (Priority): sub-manifold shadow allocation provides priority-aware redundancy via the same broadcast primitive.

Layer 4 (Localization): cooperative localization via fiducial selection at depth log₂(n) of the PCA tree. Under realistic heavy-tailed noise (10% outliers at 5σ), 30 seeds × 2000 ticks: Layer 4 = 0.082m [0.072, 0.092] vs INS-only 0.409m and sparse-GPS-only 0.252m at t=78s — Layer 4 is the only one that does not degrade monotonically over the mission.

Adversarial robustness: witness-alarm primary defense via mutual physical observation; 100% detection above 5σ-magnitude threshold under heavy-tailed noise; 1.3% false-positive rate at the 10σ operating point. Includes formal slot-disjointness lemma, three-part composition theorem (3a/3b/3c), and a rigorous O(1/√N) bound on the rounding contribution to optimality gap.

Code and data availability. All source code, simulator, benchmark scripts (12 with bootstrap 95% CIs on every headline number), figures, and the rendered four-phase demo are archived at Zenodo under DOI 10.5281/zenodo.19954678 and mirrored at github.com/jmcentire/drone-swarm-coordination.