In this paper, we consider the problem of optimally allocating tasks, expressed as global Linear Temporal Logic (LTL) specifications, to teams of heterogeneous mobile robots. The robots are classified in different types that capture their different capabilities, and each task may require robots of multiple types. The specific robots assigned to each task are immaterial, as long as they are of the desired type. Given a discrete workspace, our goal is to design paths, i.e., sequences of discrete states, for the robots so that the LTL specification is satisfied. To obtain a scalable solution to this complex temporal logic task allocation problem, we propose a hierarchical approach that first allocates specific robots to tasks using the information about the tasks contained in the Nondeterministic Buchi Automaton (NBA) that captures the LTL specification, and then designs low-level executable plans for the robots that respect the high-level assignment. Specifically, we first prune and relax the NBA by removing all negative atomic propositions. This step is motivated by "lazy collision checking" methods in robotics and allows to simplify the planning problem by checking constraint satisfaction only when needed. Then, we extract sequences of subtasks from the relaxed NBA along with their temporal orders, and formulate a Mixed Integer Linear Program (MILP) to allocate these subtasks to the robots. Finally, we define generalized multi-robot path planning problems to obtain low-level executable robot plans that satisfy both the high-level task allocation and the temporal constraints captured by the negative atomic propositions in the original NBA. We show that our method is complete for a subclass of LTL that covers a broad range of tasks and present numerical simulations demonstrating that it can generate paths with lower cost, considerably faster than existing methods.
翻译:在本文中, 我们考虑最佳分配任务的问题, 以全球直线性直线性时空逻辑( LTL) 标准( LTL) 来表达, 给混杂移动机器人的团队分配任务。 机器人被分类为不同类型, 并需要多种类型的机器人。 分配给每个任务的具体机器人并不重要, 只要它们属于想要的类型。 鉴于一个离散的工作空间, 我们的目标是为机器人设计路径, 即离散状态的序列, 使机器人能够满足 LTL 要求。 要找到一个可调整的解决方案, 复杂的时间逻辑任务分配问题, 我们建议一种等级方法, 首先分配特定的机器人, 使用Ndeministic Buchi Automaton( NNBA) 中包含的任务信息, 然后分配特定的机器人任务, 然后设计低层次的 Weblobel 规则。 具体地说, 我们先使用 NBA 宽度的宽度宽度和放松NBA标准, 来消除所有负数原子的主张。 这个步骤的动机是“ 平流性碰撞性比 NBA 水平 水平 ”, 我们只需级的平流的平流的平流的平流的平流的平流路, 最后的平时, 的平流的平时, 平流的平流的平流的平流的平流的平流的平流的平流的平流的平流的平流程序需要的平流的平时,,, 使任务能够使任务能能能的平流的平流法 平流的平流的平流的平流法 平流的平流的平流的平流的平流的平流的平流的平局的平流的平流的平流的平流法 。