Verifier-Mediated Multi-LLM Coordination for Multi-Robot Path Planning

Large Language Models (LLMs) are increasingly used as high-level planners in embodied multi-robot systems, enabling robots to interpret natural language instructions and coordinate executable actions. Yet, this growing reliance on LLM planners also raises security concerns. Prior work has focused mainly on individual robots, while communication risks in multi-robot collaboration remain insufficiently understood. Existing multi-robot studies are further limited to preliminary analysis under the Decentralized Multi-agent System (DMAS) architecture, so it remains unclear whether these risks persist across other common communication architectures and how attacker access settings shape their propagation. To fill this gap, we formulate two communication attacks corresponding to distinct attacker access settings: the External Entry Point Attack and the Privileged In-System Attack. We evaluate both attacks across DMAS, HMAS-1, and HMAS-2 using three LLMs and five embodied multi-robot tasks. Results show that unsafe information can turn into unsafe actions across all three architectures: DMAS reaches a 96.7% entry endorsement rate and a 100% post endorsement activation rate, HMAS-1 reaches a 97.8% unsafe action success rate, and HMAS-2 triggers 88.3% of task defined unsafe action slots. To mitigate risks from trusted information flow, we introduce the Claim Provenance and Verification (CPV) Gate, which verifies communicated claims before downstream reuse and reduces the violation rate from 70.0% to 36.6%.

Large language models (LLMs) remain limited in multi-agent planning because independently generated plans can create coordination failures such as spatial collisions, resource contention, and temporal deadlocks. We introduce Tensor-Coord, a multilinear algebra framework that represents the joint plan of N agents as a third-order tensor $T \in R^{N \times H \times A}$ over agents, timesteps, and actions. Canonical Polyadic (CP) and Tucker decompositions are used to identify latent coordination structure. The minimal epsilon-approximate CP rank R* defines a computable coordination complexity measure, with $CC(Pi)=(R*-N)/N$. We prove that R*=N is necessary and sufficient for plan independence. The residual $E=T-T_{R*}$ defines a conflict score over agent pairs, timesteps, and actions, localizing failures without domain-specific rules. Tucker factors provide interpretable agent roles, temporal phases, and action clusters that are converted into natural language constraints for iterative LLM replanning. Experiments on multi-robot delivery tasks across Easy (2 agents, 5x5 grid), Medium (3 agents, 5x5 grid), and Hard (4 agents, 5x5 grid) settings show convergence to conflict-free plans in 100% of 2-agent cases within 1.4 iterations on average, 80% of 3-agent cases within 3.2 iterations, and 60% of 4-agent cases within 4.0 iterations. CP rank scaled approximately linearly as $R*(N) = 3.9N + 0.5$, supporting its use as a predictor of coordination complexity.

Multi-robot task planning requires decomposing natural-language instructions into executable actions for heterogeneous robot teams. Conventional Planning Domain Definition Language (PDDL) planners provide rigorous guarantees but struggle to handle ambiguous or long-horizon missions, while large language models (LLMs) can interpret instructions and propose plans but may hallucinate or produce infeasible actions. We present a hierarchical multi-agent LLM-based planner with prompt optimization: an upper layer decomposes tasks and assigns them to lower-layer agents, which generate PDDL problems solved by a classical planner. When plans fail, the system applies TextGrad-inspired textual-gradient updates to optimize each agent's prompt and thereby improve planning accuracy. In addition, meta-prompts are learned and shared across agents within the same layer, enabling efficient prompt optimization in multi-agent settings. On the MAT-THOR benchmark, our planner achieves success rates of 0.95 on compound tasks, 0.84 on complex tasks, and 0.60 on vague tasks, improving over the previous state-of-the-art LaMMA-P by 2, 7, and 15 percentage points respectively. An ablation study shows that the hierarchical structure, prompt optimization, and meta-prompt sharing contribute roughly +59, +37, and +4 percentage points to the overall success rate.