Fast and Adaptive Multi-agent Planning under Collaborative Temporal Logic Tasks via Poset Products

TL;DR

This paper tackles scalable online planning for large fleets of heterogeneous robots under dynamic, temporally constrained tasks specified in syntactically co-safe LTL. It introduces the Poset-prod framework that builds the product of relaxed posets (R-posets) instead of constructing full Büchi automata, dramatically reducing complexity and enabling formulas of hundreds of subtasks and hundreds of agents. An online task-assignment mechanism, Time Bound Contract Net (TBCN), assigns subtasks under partial orders and object interaction constraints, producing valid plans with a polynomial-first-solution guarantee. The approach is validated through extensive simulations and hardware experiments in hospital-like settings, demonstrating fast online replanning, scalability to hundreds of agents, and robust performance under dynamic task releases and object interactions. Overall, the framework provides a practical, verifiable, and scalable solution for adaptive, large-scale multi-agent coordination with complex temporal logic requirements.

Abstract

Efficient coordination and planning is essential for large-scale multi-agent systems that collaborate in a shared dynamic environment. Heuristic search methods or learning-based approaches often lack the guarantee on correctness and performance. Moreover, when the collaborative tasks contain both spatial and temporal requirements, e.g., as Linear Temporal Logic (LTL) formulas, formal methods provide a verifiable framework for task planning. However, since the planning complexity grows exponentially with the number of agents and the length of the task formula, existing studies are mostly limited to small artificial cases. To address this issue, a new planning paradigm is proposed in this work for system-wide temporal task formulas that are released online and continually. It avoids two common bottlenecks in the traditional methods, i.e., (i) the direct translation of the complete task formula to the associated Büchi automaton; and (ii) the synchronized product between the Büchi automaton and the transition models of all agents. Instead, an adaptive planning algorithm is proposed that computes the product of relaxed partially-ordered sets (R-posets) on-the-fly, and assigns these subtasks to the agents subject to the ordering constraints. It is shown that the first valid plan can be derived with a polynomial time and memory complexity w.r.t. the system size and the formula length. Our method can take into account task formulas with a length of more than 400 and a fleet with more than $400$ agents, while most existing methods fail at the formula length of 25 within a reasonable duration. The proposed method is validated on large fleets of service robots in both simulation and hardware experiments.

Figures (9)

• Figure 1: Example of Poset-Prod associated with four formulas $\varphi_{1}= \Diamond D^{\emptyset}_{w7,w7} \land \Diamond(C^\emptyset_{w7,w7} \land \neg M^{\emptyset}_{w7,w7} \land \Diamond M^{\emptyset}_{w7,w7} )$, $\varphi_{2}=\Diamond (C^\emptyset_{w7,w7} \land \neg G^1_{w7,e3} \land \Diamond G^1_{w7, e3}) \land \neg D^\emptyset_{w7,w7} \textsf{U} C^\emptyset_{w7,w7}$ , $\varphi_3=\Diamond( C^\emptyset_{w3,w3}\land\neg T^5_{w3,e2}\land\Diamond D^\emptyset_{w3,w3}\land\Diamond T^5_{w3,e2})$ and $\varphi_{4}=\Diamond(T^{2}_{w1,o1}\land \neg P^{2}_{o1,o1} \land \Diamond (P^{2}_{o1,o1} \land \neg R^{\emptyset}_{o1,o1} \land \Diamond T^{2}_{o1,w1} \land \Diamond R^{\emptyset}_{o1,o1}))$Left:$\mathcal{B}_1, \cdots,\mathcal{B}_4$ are the NBAs of formula $\varphi_1, \cdots,\varphi_4$; Middle:$P_1,\cdots,P_4$ are the R-posets of $\mathcal{B}_1,\cdots,\mathcal{B}_4$; Right:$P_1\otimes P_2=\{P_{f1}, P_{f2}\}$, $P_{f_3}\in P_{f_1}\otimes P_3$ and $P_{f_4}\in P_{f_3}\otimes P_{4}$.
• Figure 2: The bidding process of assigning subtask 4 under the global time bound (when the partial relations in R-poset are satisfied), the time bound for object (when the object is reachable) and local time bounds (when the agents get ready).
• Figure 3: Illustration of computing the product posets. Left: The final R-poset computed from the initial sub-formulas and online sub-formulas (dashed lines); Right: $P_{b_1},\cdots,P_{b_6}$ are the R-posets associated with the initial sub-formulas and $P_{u_1},\cdots,P_{u_5}$ are associated with the online sub-formulas.
• Figure 4: Left: Snapshot of agent trajectories at $40,180,215,400s$ when new tasks are added online. Right: The Gantt graph of task assignment at these time instants, as highlighted in green boxes.
• Figure 5: The computation time (Left) and the execution efficiency $\eta$ (Right) with respect to different number of agents and subtasks.

Theorems & Definitions (8)

• Definition 1
• Definition 2: R-poset
• Definition 3: Language of R-poset
• Definition 4: Product of R-posets
• Theorem 1: Correctness
• proof
• Theorem 2: Completeness
• proof