Hierarchical Coordinated Take-off & Merging Management

• HCTMM is a hierarchical strategy that separates system-level scheduling from vehicle-level trajectory optimization to ensure safe and efficient take-off and merging.
• It employs zone-based scheduling, safe sequencing, and MILP/MIQP formulations to reduce delays and avoid conflicts in mixed traffic environments.
• The framework integrates advanced control laws, MPC, and CBF methods to achieve real-time optimization and robust performance across aerial and terrestrial domains.

Hierarchical Coordinated Take-off and Merging Management (HCTMM) is a systems strategy for orchestrating take-off and merging operations of multiple vehicles—both in terrestrial (road, ramp) and aerial (UAM corridor, UAV) domains—under stringent safety, efficiency, and capacity constraints. HCTMM frameworks typically employ multi-layered, modular architectures that couple sequencing and scheduling solutions with dynamic trajectory optimization, often leveraging decomposition and advanced control methods to guarantee operational robustness in complex, multi-agent environments. The defining feature is a hierarchical separation between tactical, system-level coordination—such as scheduling, pairing, and sequencing—and operational, vehicle-level control—such as trajectory refinement and dynamic constraint satisfaction.

1. Structural Foundations: The Hierarchical Paradigm

HCTMM systems universally adopt a layered control architecture that divides the coordination challenge into:

• Upper (Tactical) Level: System-wide scheduling, sequencing, and pairing—responsible for resolving conflicts, harmonizing flow, and enforcing global safety rules. For example, dynamic scheduling of take-off and merge times, safe merging pair selection, or zone-based sequence assignment (Liu et al., 21 Aug 2025, Li et al., 2023, Chalaki et al., 2019).
• Lower (Operational) Level: Decentralized, vehicle-level trajectory optimization—where each agent solves for its own motion profile subject to the instructions or constraints received from above, while satisfying dynamic, safety, and comfort criteria (Zou et al., 2017, Sabouni et al., 2023, Zhang et al., 2023).

Some frameworks incorporate additional mid-layer modules (e.g., game-theory or virtual vehicle proxies (Wang et al., 15 Jul 2025)) or auxiliary controllers (lateral MPCs, communication modules (Li et al., 2023, Yan et al., 6 Jun 2025)).

The hierarchical separation provides scalability, permits the incorporation of communication limitations, and enables modular tuning of subsystems—a critical aspect when deploying in mixed environments (e.g., CAV/HDV mixtures, dense UAM airspace).

2. Sequencing, Scheduling, and Pairing Algorithms

At the tactical layer, HCTMM centers on discrete scheduling, merging sequence synthesis, and conflict-free assignment:

• Zone-Based Scheduling: Areas are partitioned into zones; each vehicle optimizes arrival/departure times at each zone under system-wide safety, release/deadline, and resource constraints (Chalaki et al., 2019, Liu et al., 21 Aug 2025).
• Safe Sequencing Policies: In mixed traffic, coordinators construct “safe sequences”—merging orders prioritizing cooperative vehicles or vehicles with sufficient gaps, using measures such as gap-based criteria (Δ⁻ᵢ, Δ⁺ᵢ), disruption minimization, and velocity prioritization (Sabouni et al., 2023).
• Merging Pair Selection: For UAM, candidate pairs are formed and evaluated for both “safety” (minimum separation) and “validity” (merging maneuver completion before conflict) before dynamic merging points are assigned (Liu et al., 21 Aug 2025).
• MILP/MIQP Formulations: Binary/integer programming models enforce one-to-one mapping, cooperative grouping, density harmonization, and constrain ordering such that physical and operational limits are respected (Li et al., 2023, Zhang et al., 2023).

This tactical scheduling can substantially reduce delays (e.g., 21–33% travel time improvement versus signalized control (Chalaki et al., 2019)) and guarantee robust conflict avoidance even in dense or heterogeneous settings.

3. Vehicle-Level Motion Optimization and Control Laws

The operational layer focuses on translating system assignments into executable trajectories:

• Trajectory Optimization: Optimal Control Problems (often with free terminal time) minimize operational costs (flight time, thrust/fuel consumption), subject to simplified or full vehicle dynamics, as well as operational constraints (collision avoidance, boundary constraints, mechanical limits) (Liu et al., 21 Aug 2025).
• Control Law Synthesis: For underactuated VTOL UAVs, a cascaded control architecture synthesizes command force and applied torque via saturation functions, auxiliary dynamics, and quaternion-based attitude extraction (Zou et al., 2017).
• MPC and CBF Integration: Model Predictive Control schemes—augmented by Control Barrier Functions—enforce real-time safety constraints while optimizing for energy and time efficiency. High Order CBFs are employed to maintain forward invariance of critical safety sets (e.g., safe gaps) (Sabouni et al., 2023).
• Nonlinear Programming in Corridors: Vehicle motion within spatial-temporal corridors is formulated as NLPs, with cost terms for comfort, smoothness, curvature, and deviation from guidance trajectories. Kinematic bicycle models and actuator limits are standard (Zhang et al., 2023).

The adoption of pseudo-spectral methods (e.g., GPOPS-II), explicit Lyapunov function construction for stability, and experience-guided control selection further enhance system robustness and real-time feasibility.

4. Safety Assurance and Stability Guarantees

A defining requirement is provable safety and system stability:

• Constraint Satisfaction: Safety is enforced via explicit collision avoidance constraints, critical distance thresholds (Wang et al., 15 Jul 2025), control bounds, MPC terminal constraints, and CBF-based invariance of safe sets (Sabouni et al., 2023, Liu et al., 21 Aug 2025).
• Stability Proofs: Rigorous Lyapunov analysis and closed-loop transfer function derivations (l₂ norm string stability, asymptotic local stability) provide formal guarantees of disturbance attenuation and convergence of inter-vehicle errors (Li et al., 2023).
• Simulation Validation: Extensive simulation studies report metrics on spacing deviations, velocity convergence, fuel and energy consumption, and computational burden. Hierarchical sequencing and cooperative control consistently outperform FIFO or game-theoretic benchmarks in safety and efficiency (Li et al., 2023, Wang et al., 15 Jul 2025).
• Robustness in Mixed and Dense Environments: By conservative sequencing and explicit gap controls, HCTMM systems maintain safety even during high-density or uncooperative traffic scenarios (e.g., CAV/HDV mixtures), eliminating abrupt decelerations and unsafe merges (Sabouni et al., 2023).

5. Algorithmic and Computational Efficiency

Designing for operational feasibility and scalability is a central theme:

• Dimensionality Reduction: Structural airspace design restricts take-off and merge operations to well-defined spatial domains (e.g., 2D planes via coordinate translation/rotation), reducing the state/control variables and simplifying obstacle avoidance (Liu et al., 21 Aug 2025).
• Decoupling: By constructing interactive spatio-temporal corridors or virtual vehicle proxies, high-dimensional coupled optimization problems are partitioned into tractable, independent vehicle-level optimizations (Zhang et al., 2023, Wang et al., 15 Jul 2025).
• Computational Metrics: Simulation evidence demonstrates that hierarchical HCTMM strategies are orders-of-magnitude faster and more scalable than exhaustive or centralized search approaches (e.g., average solver times 4–6 s vs >6 s in exhaustive search for UAM) (Liu et al., 21 Aug 2025).

The coordinated multi-agent optimization, enabled by modular architecture and dimensionality reduction, supports real-time deployment under high traffic loads.

6. Extensions: 3D Aerial Highways and Integrated Networked Control

Emerging work adapts HCTMM principles to UAM and multi-UAV scenarios with integrated motion and communication control:

• LLM-Based Control: Dual-agent architectures employing LLMs for both strategic (HAPS-level) and tactical (onboard UAV) decision-making achieve superior system rewards, collision avoidance, and network throughput (Yan et al., 6 Jun 2025).
• Integrated Scheduling and Communication: Strategic meta-controllers optimize high-level access and handover policies, while tactical agents balance motion (lane, altitude, speed) and radio access choices for seamless, Pareto-efficient operation in integrated terrestrial/non-terrestrial networks (Yan et al., 6 Jun 2025).
• Flexible 3D Coordination: By extending state/action spaces to include altitude, lane, and heading along with communication channel selection, such frameworks generalize HCTMM to next-generation 3D aerial highways.

7. Comparative Performance and Impact

Hierarchical coordinated management strategies (HCTMM) consistently deliver:

Framework	Safety Metric	Travel/Energy Reduction	Scalability
HCTMM (zone-based scheduling)	Maintains min gaps	21–33% faster than signalized (Chalaki et al., 2019)	Real-time (<25 ms/veh)
HCTMM (virtual car-following)	String stability ($l_2$), rapid error decay	Smoother acceleration	<0.1 s control step
HCTMM (spatio-temporal corridors)	Robust conflict-free	Lower computation burden	N/A
HCTMM (LLM-based UAV control)	$\delta_c < 0.08$ collision rate	Highest reward, fastest convergence (Yan et al., 6 Jun 2025)	Order-of-magnitude speedup
HCTMM (UAM airspace structuring)	No airborne holding, safe merging	Shorter computation time	Maintained below planning threshold

These frameworks are verified across mixed traffic types, aerial and terrestrial domains, and demonstrate advantages in safety margin, time/fuel economy, and capacity expansion relative to traditional queueing, signalized, or non-hierarchical methods.

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HCTMM underpins a broad class of multi-agent coordination strategies, leveraging hierarchical decomposition, modular coupling, and rigorous optimization to deliver certified safe, efficient, and scalable take-off and merging management in complex operational environments. Research continues to expand its domains of applicability, computational reach, and integration with communication and networked control primitives, particularly as autonomous and aerial mobility infrastructures mature.