In this paper, we investigate the problem of linear temporal logic (LTL) path planning for multi-agent systems, introducing the new concept of \emph{ordering constraints}. Specifically, we consider a generic objective function that is defined for the path of each individual agent. The primary objective is to find a global plan for the team of agents, ensuring they collectively meet the specified LTL requirements. Simultaneously, we aim to maintain a pre-determined order in the values of the objective function for each agent, which we refer to as the ordering constraints. This new requirement stems from scenarios like security-aware planning, where relative orders outweigh absolute values in importance. We present an efficient algorithm to solve this problem, supported by proofs of correctness that demonstrate the optimality of our solution. Additionally, we provide a case study in security-aware path planning to illustrate the practicality and effectiveness of our proposed approach.

翻译：本文研究了多智能体系统的线性时序逻辑（LTL）路径规划问题，提出了“顺序约束”这一新概念。具体而言，我们考虑为每个智能体路径定义的一般性目标函数。主要目标是找到团队智能体的全局规划方案，确保它们共同满足指定的LTL要求。同时，我们旨在保持每个智能体目标函数值的预定顺序，即我们所谓的顺序约束。这一新需求源于安全感知规划等场景，其中相对顺序比绝对值更为重要。我们提出了一种高效算法来解决该问题，并通过正确性证明展示了所提方案的最优性。此外，我们还通过安全感知路径规划的案例研究，阐述了所提方法的实用性和有效性。