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.

Ensuring safety in cyber-physical systems (CPSs) is a critical challenge, especially when system models are difficult to obtain or cannot be fully trusted due to uncertainty, modeling errors, or environmental disturbances. Traditional model-based approaches rely on precise system dynamics, which may not be available in real-world scenarios. To address this, we propose a data-driven safety verification framework that leverages matrix zonotopes and barrier certificates to verify system safety directly from noisy data. Instead of trusting a single unreliable model, we construct a set of models that capture all possible system dynamics that align with the observed data, ensuring that the true system model is always contained within this set. This model set is compactly represented using matrix zonotopes, enabling efficient computation and propagation of uncertainty. By integrating this representation into a barrier certificate framework, we establish rigorous safety guarantees without requiring an explicit system model. Numerical experiments demonstrate the effectiveness of our approach in verifying safety for dynamical systems with unknown models, showcasing its potential for real-world CPS applications.

The deployment of Large Language Models (LLMs) in robotic systems presents unique safety challenges, particularly in unpredictable environments. Although LLMs, leveraging zero-shot learning, enhance human-robot interaction and decision-making capabilities, their inherent probabilistic nature and lack of formal guarantees raise significant concerns for safety-critical applications. Traditional model-based verification approaches often rely on precise system models, which are difficult to obtain for real-world robotic systems and may not be fully trusted due to modeling inaccuracies, unmodeled dynamics, or environmental uncertainties. To address these challenges, this paper introduces a safety assurance framework for LLM-controlled robots based on data-driven reachability analysis, a formal verification technique that ensures all possible system trajectories remain within safe operational limits. Our framework specifically investigates the problem of instructing an LLM to navigate the robot to a specified goal and assesses its ability to generate low-level control actions that successfully guide the robot safely toward that goal. By leveraging historical data to construct reachable sets of states for the robot-LLM system, our approach provides rigorous safety guarantees against unsafe behaviors without relying on explicit analytical models. We validate the framework through experimental case studies in autonomous navigation and task planning, demonstrating its effectiveness in mitigating risks associated with LLM-generated commands. This work advances the integration of formal methods into LLM-based robotics, offering a principled and practical approach to ensuring safety in next-generation autonomous systems.

In this work, we present a transformer-based framework for predicting future pedestrian states based on clustered historical trajectory data. In previous studies, researchers propose enhancing pedestrian trajectory predictions by using manually crafted labels to categorize pedestrian behaviors and intentions. However, these approaches often only capture a limited range of pedestrian behaviors and introduce human bias into the predictions. To alleviate the dependency on manually crafted labels, we utilize a transformer encoder coupled with hierarchical density-based clustering to automatically identify diverse behavior patterns, and use these clusters in data-driven reachability analysis. By using a transformer-based approach, we seek to enhance the representation of pedestrian trajectories and uncover characteristics or features that are subsequently used to group trajectories into different "behavior" clusters. We show that these behavior clusters can be used with data-driven reachability analysis, yielding an end-to-end data-driven approach to predicting the future motion of pedestrians. We train and evaluate our approach on a real pedestrian dataset, showcasing its effectiveness in forecasting pedestrian movements.