Bridging Model Predictive Control and Deep Learning for Scalable Reachability Analysis

2025-05-04

AI Summary

Hamilton–Jacobi (HJ) reachability analysis for safety verification of high-dimensional robotic systems suffers from the curse of dimensionality, while existing learning-based methods exhibit training instability and suboptimal solutions due to reliance on PDE residual losses. Method: We propose an MPC-guided neural network training paradigm. It leverages high-confidence approximate solutions generated by model predictive control (MPC) at critical collocation points as strong supervision—replacing weak residual-based supervision—and incorporates an iterative co-optimization mechanism that dynamically updates MPC reference trajectories to escape local optima. Technically, the approach integrates HJ PDE modeling, residual-informed neural training, and real-time MPC feedback. Results: Experiments across 2D–40D benchmark systems demonstrate substantial improvements in reachable set accuracy and robustness, effectively mitigating the curse of dimensionality. The method establishes a scalable, highly reliable framework for safety verification of high-dimensional dynamical systems.

Technology Category

• Intelligent Robots: Learning & Optimization for ROB
• Natural Language Processing: Safety and Robustness
• Search and Optimization: Learning to Search

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• Overcoming computational limits in HJ reachability analysis
• Improving neural network training stability for reachability solutions
• Integrating MPC with deep learning for accurate safety assurances

Innovation

• Combines MPC with deep learning for reachability
• Uses MPC to guide neural network training
• Iteratively refines MPC solutions with learned data