Hao Wang, Max Cohen, Zeyuan Feng, Donggeon David Oh, Oswin So, Songyuan Zhang, Javier Borquez, Chuchu Fan 等 12 位作者
原文摘要
Safety is a central concern in modern autonomous systems. Safety certificates---functions whose existence guarantees that a system meets its safety specification---have long been used as a principled tool for rigorously reasoning about safety. Methods for synthesizing such certificates are scattered across research areas, with little guidance on when to use a particular approach. This tutorial provides a holistic treatment of safety certificate synthesis centered on two widely used families: Hamilton--Jacobi (HJ) reachability analysis and control barrier functions (CBFs). For each family of methods, we first introduce its general formulation, along with classical and learning-based tools for certificate synthesis. Next, we introduce two benchmark problems consisting of vehicle systems of differing complexity to assess the certificate quality of different synthesis methods and their effectiveness in safety-critical control. We use these benchmarks to compare various methods and provide practical guidance for selecting an approach.
Zeyuan Feng, Ali Fuat Sahin, Santiago Thorup, Somil Bansal
原文摘要
Hamilton-Jacobi (HJ) reachability provides a principled framework for synthesizing safety certificates and robust controllers for safety-critical robotic systems. However, applying reachability analysis to high-dimensional nonlinear systems remains challenging: classical grid-based solvers suffer from the curse of dimensionality, continuous-time neural solvers require accurate spatial value gradients, and reinforcement-learning-based approaches often suffer from weak boundary anchoring and non-stationary adversarial policy optimization. We propose a discrete-time neural reachability framework for control-disturbance-affine systems that learns backward reachable tubes (BRTs) and backward reach-avoid tubes (BRATs) through Bellman-Isaacs value propagation. Our key idea is to combine equation-driven self-supervision with structured policy learning: rather than computing explicit PDE-gradients, we exploit the bang-bang structure of optimal safety interventions to construct approximate teacher actions from gradient-free value probes, converting adversarial actor learning into supervised policy learning. To stabilize long-horizon value propagation, we leverage the learned actor to train the value function backward from the terminal boundary using a windowed temporal curriculum, where each window is used as the boundary condition for the next window. Across benchmark problems up to 80 dimensions, our method learns accurate reachability value functions while improving stability over existing learning-based solvers. We further demonstrate observation-space scalability on F1-tenth racing with over 16,000-dimensional egocentric inputs. The learned safety filter generalizes zero-shot to unseen tracks and transfers to a physical RC car, achieving real-time robust collision avoidance.
Yusuf Umut Ciftci, Joonwon Kang, Ajay Suresha Sathya, Somil Bansal
原文摘要
Imitation learning typically treats every demonstration state as equally important, optimizing a behavior-cloning objective uniformly across the dataset. Yet not all states are created equal: in a small number of critical states, even a slight deviation from the expert action can lead to a failure, while in many other states such errors are recoverable and inconsequential. We formalize state criticality in imitation learning as the worst-case degradation in downstream value induced by a bounded perturbation of the expert action at a given state. We then propose SCRIM, a practical State CRIticality Measure that estimates this quantity by training an adversarial disturbance policy and a value critic around a fixed imitation policy. SCRIM assigns each demonstration state a score reflecting how vulnerable the task outcome is to small, policy-relevant action errors. We show that these scores can be used to reweight behavior-cloning losses, improving imitation at consequential states and increasing overall task performance. We further show that SCRIM enables data curation by selecting compact, high-value subsets of demonstrations that preserve performance while substantially reducing the amount of training data. We evaluate SCRIM across various simulated and real-world robotic manipulation tasks, and demonstrate that SCRIM improves policy training, enables efficient data selection, and provides interpretable insights into which moments in a demonstration are most critical for task success. Project website: https://sia-lab-git.github.io/SCRIM/