Multiple Subformulae Cooperative Control for Multiagent Systems Under Conflicting Signal Temporal Logic Tasks

This article studies the temporal logic problem for multiagent systems, where each agent is subject to signal temporal logic (STL) tasks with multiple subtasks. In the distributed framework, due to the existence of coupling subtasks, the satisfaction of the conjunction of all subtasks may be conflicting. A two-step distributed model predictive control (DMPC) strategy is proposed to maximize the amount of the satisfied subtasks and minimize the violation degree of those failed subtasks. In step 1, a novel robustness metric of STL is proposed to measure whether each subtask is satisfied or not, and is directly incorporated into the DMPC optimization problem to determine the satisfiability of each subtask. Based on the planning results of step 1, a DMPC optimization problem with a short planning horizon is designed in step 2 to minimize the violation degree of the unsatisfiable subtasks while ensuring the satisfaction of those satisfiable ones. All agents solve their two-step DMPC problems sequentially to realize the satisfaction verification of the coupled subtasks at each time instant. Further, the soundness and feasibility of the two-step DMPC algorithm are formally guaranteed. Simulations and experiments illustrate the effectiveness of the proposed algorithm.