Notably, modern tools for the verification of hybrid automata are designed formodels thatrarely haveoverhundred discrete states [7],while arbitrary meshes grow exponentially as the granularity increases.

Decision trees have gained popularity as interpretable surrogate models for learning-based control policies.

Verifying closed-loop vision-based control systems remains a fundamental challenge due to the high dimensionality of images and the difficulty of modeling visual environments. While generative models are increasingly used as camera surrogates in verification, their reliance on stochastic latent variables introduces unnecessary overapproximation error. To address this bottleneck, we propose a Deterministic World Model (DWM) that maps system states directly to generative images, effectively eliminating uninterpretable latent variables to ensure precise input bounds. The DWM is trained with a dual-objective loss function that combines pixel-level reconstruction accuracy with a control difference loss to maintain behavioral consistency with the real system. We integrate DWM into a verification pipeline utilizing Star-based reachabil-ity analysis (StarV) and employ conformal prediction to derive rigorous statistical bounds on the trajectory deviation between the world model and the actual vision-based system. Experiments on standard benchmarks show that our approach yields significantly tighter reachable sets and better verification performance than a latent-variable baseline.

Explaining unsolvability of planning problems is of significant research interest in Explainable AI Planning. AI planning literature has reported several research efforts on generating explanations of solutions to planning problems. However, explaining the unsolvability of planning problems remains a largely open and understudied problem. A widely practiced approach to plan generation and automated problem solving, in general, is to decompose tasks into sub-problems that help progressively converge towards the goal. In this paper, we propose to adopt the same philosophy of sub-problem identification as a mechanism for analyzing and explaining unsolvability of planning problems in hybrid systems. In particular, for a given unsolvable planning problem, we propose to identify common waypoints, which are universal obstacles to plan existence; in other words, they appear on every plan from the source to the planning goal. This work envisions such waypoints as sub-problems of the planning problem and the unreachability of any of these waypoints as an explanation for the unsolvability of the original planning problem. We propose a novel method of waypoint identification by casting the problem as an instance of the longest common subsequence problem, a widely popular problem in computer science, typically considered as an illustrative example for the dynamic programming paradigm. Once the waypoints are identified, we perform symbolic reachability analysis on them to identify the earliest unreachable waypoint and report it as the explanation of unsolvability. We present experimental results on unsolvable planning problems in hybrid domains.

As perception-based controllers for autonomous systems become increasingly popular in the real world, it is important that we can formally verify their safety and performance despite perceptual uncertainty. Unfortunately, the verification of such systems remains challenging, largely due to the complexity of the controllers, which are often nonlinear, nonconvex, learning-based, and/or black-box. Prior works propose verification algorithms that are based on approximate reachability methods, but they often restrict the class of controllers and systems that can be handled or result in overly conservative analyses. Hamilton-Jacobi (HJ) reachability analysis is a popular formal verification tool for general nonlinear systems that can compute optimal reachable sets under worst-case system uncertainties; however, its application to perception-based systems is currently underexplored. In this work, we propose RoVer-CoRe, a framework for the Robust Verification of Controllers via HJ Reachability. To the best of our knowledge, RoVer-CoRe is the first HJ reachability-based framework for the verification of perception-based systems under perceptual uncertainty. Our key insight is to concatenate the system controller, observation function, and the state estimation modules to obtain an equivalent closed-loop system that is readily compatible with existing reachability frameworks. Within RoVer-CoRe, we propose novel methods for formal safety verification and robust controller design. We demonstrate the efficacy of the framework in case studies involving aircraft taxiing and NN-based rover navigation. Code is available at the link in the footnote.

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.

Abstract-- Predicting the motion of surrounding vehicles is key to safe autonomous driving, especially in unstructured environments without prior information. This paper proposes a novel online method to accurately predict the occupancy sets of surrounding vehicles based solely on motion observations. The approach is divided into two stages: first, an Extended Kalman Filter and a Linear Programming (LP) problem are used to estimate a compact zonotopic set of control actions; then, a reachability analysis propagates this set to predict future occupancy. The effectiveness of the method has been validated through simulations in an urban environment, showing accurate and compact predictions without relying on prior assumptions or prior training data. I. INTRODUCTION Autonomous driving has generated great research interests given the expected benefits, such as reducing accidents, optimizing traffic efficiency and energy management [1]. However, ensuring safety remains a major challenge, particularly in urban environments, where multiple agents interact dynamically [2].Predicting the motion of surrounding vehicles (SVs) is critical to designing safe motion planning and control strategies for autonomous vehicles.