On the Minimal Revision Problem of Specification Automata
This addresses the challenge of ensuring robots can safely and correctly operate by offering practical solutions for task revision in real-world scenarios, though it is incremental in improving existing automata-based planning methods.
The paper tackles the problem of robots providing feedback on unachievable tasks by finding the closest achievable alternative, establishing that the minimal specification revision problem is NP-complete and presenting a polynomial-time heuristic algorithm that often returns optimal solutions.
As robots are being integrated into our daily lives, it becomes necessary to provide guarantees on the safe and provably correct operation. Such guarantees can be provided using automata theoretic task and mission planning where the requirements are expressed as temporal logic specifications. However, in real-life scenarios, it is to be expected that not all user task requirements can be realized by the robot. In such cases, the robot must provide feedback to the user on why it cannot accomplish a given task. Moreover, the robot should indicate what tasks it can accomplish which are as "close" as possible to the initial user intent. This paper establishes that the latter problem, which is referred to as the minimal specification revision problem, is NP complete. A heuristic algorithm is presented that can compute good approximations to the Minimal Revision Problem (MRP) in polynomial time. The experimental study of the algorithm demonstrates that in most problem instances the heuristic algorithm actually returns the optimal solution. Finally, some cases where the algorithm does not return the optimal solution are presented.