Autonomous Traffic Control Systems (ATCS) in Low Earth Orbit: Multi-Objective Optimization Models, 2026 Orbital Debris Kinematics, and Sub-12.5ms Hardware-Rooted Post-Quantum Governance

Modern Low Earth Orbit (LEO), particularly within the 340 km to 570 km operational shells, faces unprecedented spatial density and non-linear conjunction frequency due to the rapid deployment of commercial mega-constellations and historical fragmentation debris. With tracked objects exceeding 46,110 (including ~16,234 active payloads, of which Starlink accounts for 10,759 operational units and 5,897.9 tonnes out of 7,464.6 tonnes in Lower LEO) alongside 54,000 objects 10 cm and 1.2 million Lethal Non-Trackable (LNT, 1–10 cm) debris fragments, traditional Human-in-the-Loop (HITL) ground-based conjunction assessment has surpassed its structural capacity—evidenced by 144,404 autonomous Collision Avoidance Maneuvers (CAMs) executed by a single constellation within six months at a Probability of Collision (PoC) threshold of 10^-5. This monograph establishes a rigorous cyber-physical Multi-Objective Optimization (MOO) framework for next-generation Autonomous Traffic Control Systems (ATCS) operating under strict Hardware-In-The-Loop Optimization (HITLO) and Human-in-Command (HIC) constitutional constraints. First, we formalize the eigenvalue optimization of B-plane miss-distance maximization against propellant budget (Delta-v) minimization (ranging from baseline 26.5 mm/s retrograde burns to 0.1–1.4 m/s multi-axis Reinforcement Learning trajectories), explicitly incorporating a Poisson-distributed Secondary Collision Risk penalty across orbital tube boundaries. Second, we resolve the inter-satellite link (ISL) cryptographic bottleneck by synthesizing decoy-state/Twin-Field Quantum Key Distribution (QKD, peaking at 30 kbps / 300 kbit/night at QBER 6.91% ± 1.04% for asynchronous master-key provisioning) with NIST FIPS 203 Module-Lattice-Based Key-Encapsulation Mechanism (ML-KEM / Kyber-768) accelerated on radiation-tolerant Hardware Root of Trust (HRoT) FPGAs. Utilizing Unified Polynomial Arithmetic Modules (UniPAM) and Number Theoretic Transform (NTT) reduction from O(n^2) to O(n log n), cryptographic encapsulation/decapsulation is bounded within tens of microseconds, guaranteeing end-to-end deterministic autonomous maneuver consensus within the strict < 12.5 ms real-time optimization (RTO) window. Autonomous Infrastructure & Deterministic Quantum Systems Monograph Series Official Reserved DOI: 10.5281/zenodo.24045847 Author: Hasebe, Yoko (長谷部 洋子) Affiliation: Lead Researcher, Autonomous Infrastructure Systems, Autonomous Living & Physical Infrastructure Institute, Iwakuni, Yamaguchi, Japan License & Integrity Covenant: Creative Commons Attribution 4.0 International (CC BY 4.0) with Strict No-Learn Covenant (NLL-v1.0-2026)