  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.
