Distributed Receding Horizon Control for Multi-agent Systems with Conflicting Siganl Temporal Logic Tasks

In this paper, a multi-agent cooperative control problem with conflicting temporal logic tasks is studied. Each agent is assigned a temporal logic task which contains a motion task and safety requirements. We consider the cases where the satisfaction of both the motion task and safety requirements may be conflicting due to the limited velocity, so that such a task can not be fulfilled. In order to solve this problem, we give priority to the the safety requirements and the degree of satisfaction of the motion task is slacked. This work proposes a two-stage distributed receding horizon optimization strategy consisting of offline stage and online stage where signal temporal logic (STL) is utilized to formally describe the temporal logic tasks and the receding horizon optimization framework is adopted for cooperative collision avoidance tasks. At offline stage, according to the motion task, a reference robustness evolution curve is presented for each agent by the robust semantics of STL formulas. At online stage, based on the short-term goal region determined by the reference robustness evolution curve, together with the known obstacles' information and agents' real-time information, constraints of both the motion task and safety requirements are constructed in the receding horizon optimization problem for each agent. When conflicting situations happen, the constraint of the motion task is relaxed by a robustness slackness to find a least violating solution. In the proposed framework, the offline stage and the online stage are combined to satisfy the motion task as much as possible and to guarantee the safety requirements. The effectiveness of the framework is verified by simulation results.