HULK: Large-scale Hierarchical Coordination under Continual and Uncertain Temporal Tasks

Abstract: Multi-agent systems can be extremely efficient when working concurrently and collaboratively, e.g., for delivery, surveillance, search and rescue. Coordination of such teams often involves two aspects: selecting appropriate subteams for different tasks in various areas, and coordinating agents in the subteams to execute the associated subtasks. Existing work often assumes that the tasks are static and known beforehand, where an integer program can be formulated and solved offline. However, in many applications, the team-wise tasks are generated online continually by external requests, and the amount of subtasks within each task is uncertain, e.g., the number of packages to deliver or victims to rescue. The aforementioned offline solution becomes inadequate as it would require constant re-computation for the whole team and global communication to broadcast the results. Thus, this work tackles the large-scale coordination problem under continual and uncertain temporal tasks, specified as temporal logic formulas over collaborative actions. The proposed hierarchical framework, HULK, consists of two interleaved layers: the rolling assignment of currently known tasks to subteams within a certain horizon, and the dynamic coordination within a subteam given the detected subtasks during online execution. Thus, coordination is performed hierarchically at different granularities and triggering conditions, improving computational efficiency and robustness. The method is validated rigorously over large-scale heterogeneous systems under various temporal tasks and environment uncertainties.

• The paper introduces HULK, a hierarchical framework that efficiently decomposes and assigns uncertain temporal tasks in heterogeneous multi-agent systems.
• It employs a receding-horizon search and MILP-based subteam formation to optimize planning and reduce mission response times by up to 50x.
• Empirical validations show robust scalability with 150 agents and high success rates even under elevated agent failure probabilities.

Large-scale Hierarchical Coordination under Continual and Uncertain Temporal Tasks: An Expert Analysis

Introduction and Motivation

The paper "HULK: Large-scale Hierarchical Coordination under Continual and Uncertain Temporal Tasks" (2605.08722) addresses the challenge of coordinating large-scale heterogeneous multi-agent systems (MAS) for collaborative tasks characterized by continual online generation, uncertainty in specification, and temporal logic constraints. Previous approaches predominantly focus on static, offline task assignment, often using centralized optimization methods that lack scalability and adaptability in settings where new missions and uncertainties arise dynamically. This work provides a hierarchical methodology to bridge this gap, targeting applications such as autonomous delivery, surveillance, and search and rescue.

Problem Formulation

The authors formalize the MAS setting with $N$ heterogeneous agents performing concurrent actions over a shared workspace. Crucially, missions are specified as syntactically co-safe LTL (sc-LTL) formulas, encompassing collaborative tasks with uncertain numbers and locations of subtasks. A significant departure from Counting LTL (cLTL)-style prior work is that both the quantity and location of subtasks are only partially observable at assignment time. Task accomplishment not only demands collaborative execution but also satisfaction of precedence and temporal constraints.

The optimization objective is to synthesize collective action plans that minimize the average mission response time, with dynamic missions released and completed at arbitrary points. The continual nature of demands and environmental uncertainty generate a nontrivial online combinatorial assignment and scheduling problem.

Hierarchical Solution Architecture

High-level Task Decomposition and Assignment

The Hierarchical Uncertainty-aware Large-scale tasK assignment (HULK) framework decomposes global missions into partially ordered sets (posets) of tasks derived from the mission’s automaton representation. This abstraction allows the exploitation of both sequential and parallel execution, improving computational tractability compared to flat approaches.

Assignment of tasks to agent subteams is performed via a receding-horizon search-based algorithm that expands a tree of partial assignments. Each candidate node represents a set of tasks allocated to subteams under agent capacity constraints. The selection of an optimal assignment optimizes a metric evaluating progress and predicted completion times, integrating both resource (capacity) and navigation costs. Subteam sizes are not fixed a priori and are determined adaptively per planning cycle.

Subteam Formation

Once high-level assignments are made, the actual mapping of agents to subteams is formalized as a redundancy-aware constrained min-max assignment formulated as a MILP. Agents are allocated to subteams to collectively ensure all requirements are met, subject to vehicle dynamics and prior tasks.

Local Coordination Strategies

To address variability in the realization of subtasks, the framework distinguishes three archetypes:

• Static and Known Subtasks: Formulated as collaborative multi-vehicle routing problems, solved by MILP with explicit coupling constraints.
• Static and Unknown Subtasks: Addressed via Simultaneous Exploration and Coordination (SEC); the agent team dynamically explores unknown regions, detects new subtasks online, and continually replans assignments in batches.
• Dynamic and Known Subtasks: Managed via Dynamic Coalition Formation (DCF), rapidly reforming agent coalitions to target moving objectives, where optimal plans can be rendered obsolete by subtask mobility.

Notably, the case of tasks with both dynamic and unknown subtasks is discussed but not directly handled, due to intractable completion estimation and inherent observability limits.

Experimental Validation and Empirical Results

HULK is validated in large-scale simulation involving up to 150 heterogeneous agents and varied complex mission specifications. Missions are drawn from templates combining delivery, surveillance, and dynamic capture, defined as sc-LTL formulas instantiated at random intervals.

Key Quantitative Results

• Planning Efficiency: The HULK framework reduces planning time by up to 50x compared to non-hierarchical MILP and sampling-based planners. For instance, MILP-based baselines struggle with assignments beyond modest scale, with some approaches reporting infeasible plan times (exceeding 15 minutes).
• Responsiveness and Robustness: Average system response time is minimized ($\sim$62.7s) compared to centralized and greedy approaches, which exceed 88s and 112s, respectively, for comparable loads.
• Scalability: When scaling system size to 150 agents and 80 tasks, planning time grows sublinearly (average increase from 1.6s to 1.8s), confirming the computational advantages of hierarchical decomposition.
• Resilience: Success rate remains at 100% for agent failure probabilities $\alpha = 0.05$ even with large agent populations, with minimal degradation (to 97%) at higher failure rates, demonstrating robustness to faults.

Comparative Insights

Non-hierarchical and naive approaches (assigning globally via MILP or greedy allocation per agent) are hampered by combinatorial explosion, inability to adapt to online specification changes, and poor capital utilization—demonstrated by excessive agent travel and suboptimal assignments in dynamic settings.

Implications and Future Directions

This work advances the field by demonstrating the feasibility of online, scalable MAS coordination under LTL-style temporal and collaboration requirements with environmental and mission uncertainty. The introduction of task-centric poset decomposition for MAS mission assignment and the unification of centralized and decentralized assignment/planning strategies at different levels is especially notable.

Practically, the approach enables deployment of heterogeneous robot fleets in rapidly evolving, information-limited, and collaborative settings (e.g., disaster response, urban logistics), where continual adaptation to new tasks is mandatory. The robust empirical performance—including in the presence of agent failures—suggests practical viability in real-world deployments.

Theoretically, HULK exemplifies the benefits of separating the temporal logic synthesis and resource allocation phases, leveraging automata-based decompositions alongside online search and MILP. The modularity enables extensibility and facilitates integration with higher-level human interaction, more complex motion constraints, and richer agent models, outlined as future directions.

Conclusion

The HULK framework constitutes a rigorous, empirically validated, and scalable methodology for multi-agent coordination under continual, uncertain temporal task streams. By hierarchically decoupling global mission assignment from local dynamic coordination, it achieves superior computational efficiency, responsiveness, and robustness versus conventional centralized and decentralized approaches. This architecture establishes a foundation for the practical deployment of MAS in complex, uncertain, and evolving task environments, with onward avenues including richer specification handling and direct integration with human operators.