Distributed Predictive Control under Multiple Sub-formula STL Specifications with Temporal Relaxation

In a Multi-Agent System (MAS), where each agent is assigned with local Signal Temporal Logic (STL) tasks, coupled tasks frequently appear, causing STL violations. To address this issue, a Distributed Model Predictive Control (DMPC) algorithm is proposed to loosen the temporal constraints of non-nested STL specifications with multiple sub-formulae. We use temporal relaxation and task postponement of some sub-formulae to handle task conflicts. First, the online reference trajectories of each subtask are generated that the corresponding STL satisfaction constraints are incorporated into the DMPC problem. Then, we use compatibility constraints to implement synchronous cooperative collision avoidance. Based on the online reference trajectories, the temporal relaxation metric of each sub-formula is given, and is optimized in the DMPC optimization problem. As a result, the optimal controller enforcing STL satisfaction and minimal temporal relaxation is found. Finally, simulations demonstrate the effectiveness of the suggested algorithm.