Multi-Agent Planning under Local LTL Specifications and Event-Based Synchronization (1610.08380v1)

Abstract: We study the problem of plan synthesis for multi-agent systems, to achieve complex, high-level, long-term goals that are assigned to each agent individually. As the agents might not be capable of satisfying their respective goals by themselves, requests for other agents' collaborations are a part of the task descriptions. We consider that each agent is modeled as a discrete state-transition system and its task specification takes a form of a linear temporal logic formula, which may contain requirements and constraints on the other agent's behavior. A traditional automata-based approach to multi-agent plan synthesis from such specifications builds on centralized team planning and full team synchronization after each agents' discrete step, and thus suffers from extreme computational demands. We aim at reducing the computational complexity by decomposing the plan synthesis problem into finite horizon planning problems that are solved iteratively, upon the run of the agents. As opposed to full synchronization, we introduce an event-based synchronization that allows our approach to efficiently adapt to different time durations of different agents' discrete steps. We discuss the correctness of the solution and find assumptions, under which the proposed iterative algorithm leads to provable eventual satisfaction of the desired specifications.

• The paper introduces an iterative multi-agent planning method that decomposes LTL tasks into finite horizon segments with event-driven updates.
• It constructs dependency classes dynamically and employs product automata to integrate agents’ trace fragments for local satisfaction.
• This approach reduces computational complexity and enables adaptive synchronization, optimizing planning for heterogeneous time durations.

Multi-Agent Planning under Local LTL Specifications and Event-Based Synchronization

Introduction

The paper introduces an iterative approach to multi-agent planning where each agent is assigned specific long-term objectives, expressed via Linear Temporal Logic (LTL) formulas. Traditional centralized methods for plan synthesis often demand full synchronization amongst agents resulting in high computational complexity. Instead, this paper proposes breaking down plan synthesis into finite horizon planning problems, which are solved iteratively as the agents progress. This method introduces event-based synchronization to reduce unnecessary synchronization, allowing for more efficient adaptation to variable time durations of different agent's discrete steps.

Problem Formulation and Approach

In multi-agent systems, each agent has a task specified using LTL, which may include dependencies on other agents. The proposed approach decomposes these tasks by constructing an automaton for each agent, integrating their capabilities as a discrete state-transition system. It builds dependency classes dynamically based on the local interactions required within a given horizon, significantly enhancing the decentralization of plan synthesis.

The key contribution includes the use of a progressive function in automata to evaluate plan success, the creation of product systems that integrate trace fragments across dependencies, and the assumption that at least partial satisfaction of formulas can be realized within each horizon.

Finite Horizon Planning

Each iteration involves partitioning agents into dependency classes where agents influence one another's specifications, constructing an intersection automaton to capture shared language intersections, and forming a product system to synthesize feasible plans from local perspective satisfaction.

A major assumption is that given horizon length is sufficient to mark progress toward satisfaction of high-order specifications, allowing strategic plan recomputation and adaptive synchronization sequences. This ensures system behavior remains compatible and LTL formulas are satisfied locally from each agent's perspective.

Infinite Horizon Replanning

Continual replanning occurs in each iteration. Initially, each step is synchronized, yet further optimization allows synchronization to be triggered by event satisfaction, reducing frequency and computational burden. Compatibility is maintained throughout.

The algorithms provide a reliable path to an infinite plan that eventually completes all specified tasks despite uncertain transition durations. This is achieved by ensuring frequent order changes in agent priorities and rediscovering specification-accepting states.

Complexity Analysis and Assumptions

The complexity of each iteration is linear with respect to the product system size, which scales according to the reached dependency class sizes. The paper assumes satisfiability of formulas within chosen horizons and proposes backtracking solutions and horizon adjustments if Assump. 1 or Assump. 2 fail due to insufficient horizon length.

Practical Implications and Future Work

The approach has potential applications in heterogeneous robot teams where varied transition times may be prevalent. It demonstrates notable reductions in computational overhead by breaking large interconnected systems into dynamic dependency groups, thus enhancing task agility.

Future research may explore optimization criteria or robustness parameters, aiming at performance improvements considering real-world uncertainties, such as perturbed environments or agent failures. Evaluating system dynamics with physical robotic platforms could also validate effectiveness in practical deployments.

Conclusion

The paper successfully introduces a formal method to tackle multi-agent planning leveraging local perspective alignment and efficient computation through finite horizon decomposition and event-based synchronization. Application in practical scenarios presents promising avenues for further decentralization and resource optimization in complex environments.