Simultaneous Task Allocation and Planning for Multi-Robots under Hierarchical Temporal Logic Specifications

Past research into robotic planning with temporal logic specifications, notably Linear Temporal Logic (LTL), was largely based on singular formulas for individual or groups of robots. But with increasing task complexity, LTL formulas unavoidably grow lengthy, complicating interpretation and specification generation, and straining the computational capacities of the planners. In order to maximize the potential of LTL specifications, we capitalized on the intrinsic structure of tasks and introduced a hierarchical structure to LTL specifications, and designed an algorithm to ascertain whether they are satisfied given an input sequence. Second, we employ a search-based approach to synthesize plans for a multi-robot system, accomplishing simultaneous task allocation and planning. The search space is approximated by loosely interconnected sub-spaces, with each sub-space corresponding to one LTL specification. The search is predominantly confined to a single sub-space, transitioning to another sub-space under certain conditions, determined by the decomposition of automatons. Moreover, multiple heuristics are formulated to expedite the search significantly. A theoretical analysis concerning completeness and optimality is conducted under mild assumptions. When compared with existing methods on service tasks, our method outperforms in terms of execution times with comparable solution quality. Finally, scalability is evaluated by testing a group of 30 robots and achieving reasonable runtimes.