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

Abstract

This paper studies the temporal logic problem for multi-agent systems, where each agent is subject to signal temporal logic (STL) tasks with multiple sub-tasks. In the distributed framework, due to the existence of coupling sub-tasks, the satisfaction of the conjunction of all sub-tasks may be conflicting. A two-step distributed model predictive control (DMPC) strategy is proposed to maximize the amount of the satisfied sub-tasks and minimize the violation degree of those failed sub-tasks. In step one, a novel robustness metric of STL is proposed to measure whether each sub-task is satisfied or not, and is directly incorporated into the DMPC optimization problem to determine the satisfiability of each sub-task. Based on the planning results of step one, a DMPC optimization problem with a short planning horizon is designed in step two to minimize the violation degree of the unsatisfiable sub-tasks 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 sub-tasks 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.