Multi-agent control synthesis from global temporal logic tasks with synchronous satisfaction requirements

Abstract

This paper addresses the multi-agent control problem in the context of global temporal logic tasks, considering agents with heterogeneous capabilities. These global tasks involve not only absolute and relative temporal and spatial constraints, but also group behaviors, including task completion times, agent capabilities, and task interdependencies such as the need for synchronous execution. The global tasks are formally formulated into global signal temporal logic (STL) formulae, and a synchronous robustness metric is designed to evaluate the synchronization quality with real values. A mixed-integer linear programming (MILP) encoding method is further proposed to realize task-satisfied motion planning with high synchronicity and minimum control efforts. The encoding method uses a logarithmic number of binary variables to fully capture synchronous robustness, leading to only linear computational complexity. Simulations are conducted to demonstrate the efficiency of the proposed control strategy.