Robust Temporal Logic Task Planning for Multirobot Systems Under Permanent Robot Failures

We investigate the multirobot task planning problem for intricate tasks specified by linear temporal logic (LTL) formulae. While most studies on this topic assume flawless robot performance, it is crucial to recognize that failures can always occur in the real world due to errors or disturbances. Therefore, to enhance the robustness of task planning for multirobot systems (MRSs), one must take the unexpected robot failures into account. In this article, we formulate and solve a new type of failure-aware multirobot task planning problem. Specifically, we aim to find a failure-robust plan that ensures the LTL task can always be accomplished, even if a maximum number of robots fail at any instant during the execution, where a failed robot can no longer contribute to the satisfaction of the LTL task. To achieve this, we extend the mixed-integer linear programming (MILP) approach to the failure-robust setting. To overcome the computational complexity, we identify a fragment of LTL formulae called the free-union-closed LTL, which allows for more scalable synthesis without considering the global combinatorial issue. We provide a systematic method to check this property, as well as several commonly used patterns as instances. We demonstrate the effectiveness of our approach through simulation and real-world experiments, showcasing our failure-robust plans and the efficiency of our simplified algorithm. Our approach offers an optimal and efficient way to achieve robustness in multirobot path planning under unforeseen failure events.