Hamilton Jacobi Reachability

Hamilton-Jacobi (HJ) reachability analysis is a formal verification method used to determine the set of states a dynamical system can reach under various conditions, primarily focusing on ensuring safety and guaranteeing task completion. Current research emphasizes improving the scalability and efficiency of HJ reachability, particularly for high-dimensional systems, often employing deep learning techniques and algorithms like Control Barrier Functions (CBFs) to approximate solutions or guide reinforcement learning. This work has significant implications for robotics and autonomous systems, enabling the design of provably safe controllers for complex tasks in challenging environments, such as autonomous driving and legged locomotion.