Bridging Model Predictive Control and Deep Learning for Scalable Reachability Analysis

Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which is computationally prohibitive due to the curse of dimensionality. Recent learning-based methods have sought to address this challenge by approximating reachability solutions using neural networks trained with PDE residual error. However, these approaches often suffer from unstable training dynamics and suboptimal solutions due to the weak learning signal provided by the residual loss. In this work, we propose a novel approach that leverages model predictive control (MPC) techniques to guide and accelerate the reachability learning process. Observing that HJ reachability is inherently rooted in optimal control, we utilize MPC to generate approximate reachability solutions at key collocation points, which are then used to tactically guide the neural network training by ensuring compliance with these approximations. Moreover, we iteratively refine the MPC generated solutions using the learned reachability solution, mitigating convergence to local optima. Case studies on a 2D vertical drone, a 13D quadrotor, a 7D F1Tenth car, and a 40D publisher-subscriber system demonstrate that bridging MPC with deep learning yields significant improvements in the robustness and accuracy of reachable sets, as well as corresponding safety assurances, compared to existing methods.

AED: Automatic Discovery of Effective and Diverse Vulnerabilities for Autonomous Driving Policy with Large Language Models

Assessing the safety of autonomous driving policy is of great importance, and reinforcement learning (RL) has emerged as a powerful method for discovering critical vulnerabilities in driving policies. However, existing RL-based approaches often struggle to identify vulnerabilities that are both effective-meaning the autonomous vehicle is genuinely responsible for the accidents-and diverse-meaning they span various failure types. To address these challenges, we propose AED, a framework that uses large language models (LLMs) to automatically discover effective and diverse vulnerabilities in autonomous driving policies. We first utilize an LLM to automatically design reward functions for RL training. Then we let the LLM consider a diverse set of accident types and train adversarial policies for different accident types in parallel. Finally, we use preference-based learning to filter ineffective accidents and enhance the effectiveness of each vulnerability. Experiments across multiple simulated traffic scenarios and tested policies show that AED uncovers a broader range of vulnerabilities and achieves higher attack success rates compared with expert-designed rewards, thereby reducing the need for manual reward engineering and improving the diversity and effectiveness of vulnerability discovery.