Time Minimization and Online Synchronization for Multi-agent Systems under Collaborative Temporal Tasks

TL;DR

The paper tackles minimum-time coordination for multi-agent systems under collaborative temporal tasks specified in Linear Temporal Logic. It introduces an anytime synthesis framework that couples partial-order task decomposition (via pruned Büchi automata and posets) with a Branch-and-Bound task assignment, guaranteeing soundness, completeness, and near-optimality within a given time budget. It further adds online synchronization and adaptation mechanisms to handle execution-time uncertainty and agent failures, enabling robust, real-time replanning. The approach is validated through large-scale simulations and hardware experiments, showing fast initial solutions and significant concurrency gains, with scalable performance as team size and task complexity grow. This work advances practical, real-time temporal-task planning for collaborative multi-robot teams and lays groundwork for distributed extensions.

Abstract

Multi-agent systems can be extremely efficient when solving a team-wide task in a concurrent manner. However, without proper synchronization, the correctness of the combined behavior is hard to guarantee, such as to follow a specific ordering of sub-tasks or to perform a simultaneous collaboration. This work addresses the minimum-time task planning problem for multi-agent systems under complex global tasks stated as Linear Temporal Logic (LTL) formulas. These tasks include the temporal and spatial requirements on both independent local actions and direct sub-team collaborations. The proposed solution is an anytime algorithm that combines the partial-ordering analysis of the underlying task automaton for task decomposition, and the branch and bound (BnB) search method for task assignment. Analyses of its soundness, completeness and optimality as the minimal completion time are provided. It is also shown that a feasible and near-optimal solution is quickly reached while the search continues within the time budget. Furthermore, to handle fluctuations in task duration and agent failures during online execution, an adaptation algorithm is proposed to synchronize execution status and re-assign unfinished subtasks dynamically to maintain correctness and optimality. Both algorithms are validated rigorously over large-scale systems via numerical simulations and hardware experiments, against several strong baselines.

Figures (13)

• Figure 1: Comparison of the planning results based on decompositional states in schillinger2018simultaneous (left) and the partial ordering proposed in this work (right). Note that the sub-task $\omega_3$ has to be completed after $\omega_2$, while $\omega_1$ is independent.
• Figure 2: Overall structure of the proposed framework, which consists of three main parts: the computation of the posets, BnB search, and online execution.
• Figure 3: Illustration of the two partial relations contained in the poset. Left: $\omega_1\preceq_{\varphi} \omega_2$ requires that task $\omega_2$ is started after task $\omega_1$. Middle&Right: $\{\omega_3,\omega_4,\omega_5\}\subset\neq_{\varphi}$ requires that there is no time when $\omega_3,\omega_4,\omega_5$ are all executing.
• Figure 4: Left: an illustration of the relation between the accepting language of different posets $L(P_i)$ and the accepting language of the task $L_\varphi$. Right: an example of the poset graph $\mathcal{G}_{P_\varphi}$, where the relations $\preceq_{\varphi}$ and $\neq_{\varphi}$ are marked by black and red arrows, respectively.
• Figure 5: Illustration of the main components in the BnB search, i.e., the node expansion and branching to generate explore new nodes (in green arrow); and the lower and upper bounding to avoid undesired branches (in orange).

Theorems & Definitions (26)

• Definition 1: NBA
• Remark 1
• Remark 2
• Example 1
• Definition 2: Decomposition and Subtasks
• Example 2
• Definition 3: Partial Relations
• Remark 3
• Definition 4: Poset of Subtasks
• Remark 4