Multi-Agent Cooperation Architecture

• Multi-Agent Cooperation Architecture is a framework that formalizes agent coordination using automata and regular languages to ensure precise mission compliance.
• It employs task decomposition and learning-based local supervisor synthesis, enabling scalable distributed control of complex global objectives.
• The system integrates compositional verification with automatic motion planning, as validated by multi-robot experimental demonstrations in dynamic environments.

A multi-agent cooperation architecture is a system-level framework that governs how multiple autonomous agents coordinate, communicate, and jointly execute tasks—often in the context of shared or complex objectives that individual agents cannot achieve alone. Modern architectures leverage a diverse set of mechanisms including formal languages, learning-based supervisory synthesis, dynamic planning, decentralized control, and hierarchical abstraction to ensure that collective behavior is robust and scalable under dynamic, uncertain, or partially observable conditions. Core themes in this area include task decomposition, supervisor synthesis via automata and regular languages, compositional verification, and the automated synthesis of integrated mission and motion plans.

1. Formal Specification and Agent Modeling

The architecture is fundamentally grounded in the formalism of discrete event systems (DES), utilizing deterministic finite automata (DFA) to model both individual agent dynamics and the shared environment. Each agent $G_i$ is represented as

$G_i = (Q_i, \Sigma_i, q_0, \delta_i, Q_{mi}),$

where $Q_i$ is the set of states, $\Sigma_i$ the local event set (partitioned into controllable $\Sigma_{i,c}$ and uncontrollable $\Sigma_{i,uc}$), $q_0$ the initial state, $\delta_i$ the transition function, and $Q_{mi}$ the set of marked states.

Global performance requirements—i.e., the system “mission”—are formalized as regular languages $L \subseteq \Sigma^*$ and specified as prefix-closed languages. The automata theoretical foundation allows mission objectives to be decomposed, verified, and enforced through synchronous product, natural projection, and prefix closure operations.

Significance: The explicit representation of both agent and mission dynamics with automata and regular languages enables precise specification and controllable synthesis of system-wide cooperative behavior, making it possible to guarantee correctness-by-construction during both developmental and operational phases.

2. Task Decomposition and Local Supervisor Synthesis

A core architectural principle is the divide-and-conquer decomposition of the global mission into local missions. For each agent $G_i$, a local mission specification $L_i$ is generated using the natural projection operator:

$L_i = P_i(L),$

where $P_i$ projects the global language $L$ onto the local event set $\Sigma_i$. This ensures $L_i \subseteq L(G_i)$ and that $L_i$ is prefix-closed. When the global mission is separable ($L = \bigcap_{i} P_i(L)$), the architecture allows complete distributed synthesis such that the composition of local supervisors satisfies the global objective.

Supervisor synthesis follows a learning-based approach. Modified $L^*$ algorithms—specifically, $L^*_{ls}$ for local synthesis—are employed to compute the supremal controllable sublanguage of $L_i$, iteratively removing illegal (uncontrollable) behaviors:

$$\text{sup } C_i(L_i) = L_i - [ (L(G_i) - L_i) / \Sigma_{i,uc} ] \Sigma_i^*$$

Supervisors $S_i$ are synthesized so that $L(S_i \parallel G_i) = \text{sup } C_i(L_i)$, guaranteeing that only admissible and controllable behaviors are enacted by each agent.

Significance: This approach enables scalable synthesis across numerous agents, as each agent’s supervisor is constructed in isolation, subsequently ensuring that their parallel composition enforces the overall global mission.

3. Compositional Verification and Integration

To ensure the correctness and composability of local supervisors, the architecture leverages compositional verification via an assume-guarantee reasoning framework. This is realized by another modified $L^*$ algorithm, $L^*_{CV}$, which learns weakest assumptions $A_i$ necessary for each supervised agent module $M_i := S_i \parallel G_i$. Verification is performed via the assume-guarantee rule:

$\langle A_i \rangle M_i \langle L \rangle$

for all agents, ensuring $\parallel_{i} M_i \models L$.

The symmetric rule (SYM-N) and counterexample-guided refinement are used to iteratively converge to provably correct and minimally restrictive supervisors.

Significance: Compositional verification mitigates the state explosion problem typical of monolithic system verification, allowing the framework to scale to multi-robot and large-scale distributed systems.

4. Automatic Motion Planning Integration

Upon completion of the high-level mission plans, the architecture synthesizes integrated local mission–motion plans. A labeling $\pi_i: \Sigma_i \to V$, where $V$ denotes spatial regions, bridges high-level events to concrete environmental locations. The integrated plan $LP_i$ is a prefix-closed language over $(V \cup \Sigma_i)^*$, meeting the following requirements:

1. It starts at the agent’s initial region.
2. Occurrence of each mission event is synchronized with a corresponding region visit via $\pi_i$.
3. The motion trace is a valid run in the agent’s motion model $G^m_i$.

A third $L^*$-based algorithm ($L^*_{MP}$) generates a motion plan satisfying these constraints, with membership queries verifying both region compliance and motion feasibility. Counterexample-guided replanning addresses uncertainties or environmental changes that might render a prior plan infeasible.

Significance: The automated synthesis and binding of mission and motion planners closes the control-theoretic loop, allowing the architecture to operate reliably in real-world, time-varying conditions.

5. Experimental Demonstration and Hardware-Software Realization

The paper demonstrates the practical deployment of the architecture in a cooperative multi-robot scenario involving three robots (G₁, G₂, G₃) in an environment abstracted as rooms and doors. Mission requirements—such as fire event response, synchronized door-opening, and rendezvous—are encoded as regular languages and projected onto local event sets.

The synthesized supervisors, represented as StateFlow automata, are implemented on each robot’s high-level onboard computer. The system architecture comprises:

• A high-frequency localization system (Aruco-based visual markers) and wireless communication (TCP/IP and UDP) for status and command dissemination.
• Dual-layer boards: a real-time low-level controller (xMOS) for sensors/actuators and a high-level board (e.g., BeagleBone) for supervisor logic and inter-robot coordination.

Hardware experiments confirm that the system maintains compliance with global mission constraints even under unanticipated disturbances such as closed or malfunctioning doors, demonstrating robust replanning and real-time operation.

Significance: The fully implemented scenario validates the end-to-end process of formal synthesis, supervisor generation, and plan execution, highlighting the feasibility and stability of the architecture in physical, distributed multi-agent settings.

6. Architectural Implications and Theoretical Advances

This architecture extends traditional supervisory control and formal synthesis methodologies into learning-driven multi-agent domains where system, agent, or environmental models may be partially unknown or dynamic. By interleaving automata-theoretic task decomposition, modular supervisor design, compositional assume-guarantee verification, and dynamic plan adaptation, the architecture guarantees satisfaction of global cooperative specifications through rigorously constructed local policies.

Key architectural properties include:

• Divide-and-conquer scalability, enabled by projection-based task decomposition and local supervisor learning.
• Robustness against model uncertainty via iterative, counterexample-driven learning algorithms.
• Compositional soundness, leveraging formal verification to ensure that the aggregate of local behaviors meets collective objectives.
• Practical deployability, evidenced by successful experimental demonstration in a networked multi-robot system.

These advances establish a principled pathway for translating formal specification into robust multi-agent cooperative behaviors, with cross-disciplinary impact in robotics, automation, and distributed artificial intelligence systems.