Distributed model predictive control for multi-robot systems with conflicting signal temporal logic tasks

In this paper, the control problem of multi-robot systems under temporal logic tasks with limited time and logic constraints is studied, where each robot is required to reach the specified region in a given time and avoid collision all the time. Since the cooperative collision avoidance task of one robot depends on other robots' behaviors, the satisfaction of all the tasks may be conflicting. In this work, a distributed model predictive control (DMPC) strategy is proposed for conflicting temporal logic tasks. First, signal temporal logic (STL) is adopted to formally describe the temporal logic tasks. Based on robust semantics of STL formulas, a reference trajectory for the satisfaction degree of the task is designed to determine the short-term task in the optimization horizon. In the DMPC optimization problem, the compatibility constraints are introduced to redesign the collision avoidance constraints, such that the collision avoidance tasks can be fulfilled using neighbouring robots' predicted information of the last time instant. Then, the terminal constraint is designed by the short-term motion task which enforces each robot to move towards the goal region within the specified time interval. For conflicting tasks, a slack parameter is introduced in the terminal set to relax the motion task of each robot. The recursive feasibility of the DMPC algorithm is guaranteed, and the relaxed temporal logic tasks are fulfilled. In the proposed method, the discrete events including limited time and logic requirements are incorporated into the DMPC optimization problem, such that the motion task can be satisfied as much as possible and safety requirements are fulfilled. The effectiveness of the algorithm is illustrated by simulation and experiment results.