Real-world robotic systems must comply with safety requirements in the presence of uncertainty. To define and measure requirement adherence, Signal Temporal Logic (STL) offers a mathematically rigorous and expressive language. However, standard STL cannot account for uncertainty. We address this problem by presenting pacSTL, a framework that combines Probably Approximately Correct (PAC) bounded set predictions with an interval extension of STL through optimization problems on the atomic proposition level. pacSTL provides PAC-bounded robustness intervals on the specification level that can be utilized in monitoring. We demonstrate the effectiveness of this approach through maritime navigation and analyze the efficiency and scalability of pacSTL through simulation and real-world experimentation on model vessels.

Autonomous vehicles have to obey traffic rules. These rules are often formalized using temporal logic, resulting in constraints that are hard to solve using optimization-based motion planners. Reinforcement Learning (RL) is a promising method to find motion plans adhering to temporal logic specifications. However, vanilla RL algorithms are based on random exploration, which is inherently unsafe. To address this issue, we propose a provably safe RL approach that always complies with traffic rules. As a specific application area, we consider vessels on the open sea, which must adhere to the Convention on the International Regulations for Preventing Collisions at Sea (COLREGS). We introduce an efficient verification approach that determines the compliance of actions with respect to the COLREGS formalized using temporal logic. Our action verification is integrated into the RL process so that the agent only selects verified actions. In contrast to agents that only integrate the traffic rule information in the reward function, our provably safe agent always complies with the formalized rules in critical maritime traffic situations and, thus, never causes a collision.