DeepReach, a reachability toolbox that leverages recent advances in neural PDE solvers to tractably solve high-dimensional reachability problems. The computational requirements of DeepReach do not scale directly with the state dimension, but rather with the complexity of the underlying reachable tube. DeepReach achieves comparable results to the state-of-the-art reachability methods, does not require any explicit supervision for the PDE solution, can easily handle external disturbances, adversarial inputs, and system constraints, and also provides a safety controller for the system.

Existing methods provide safety assurances under the assumption that once deployed, the system or its environment does not evolve. Online, however, an autonomous system might experience changes in system dynamics, control authority, external disturbances, and/or the surrounding environment, requiring updated safety assurances, which can be timeconsuming and often intractable to perform online. Assuming system and environment changes can be parameterized, we leverage recent advances in high-dimensional reachability analysis to compute parameter-conditioned reachable sets -- a family of reachable set parameterized by the uncertain system and environment factors. Online, as these factors change, the system can query the corresponding safety function from this family to ensure system safety, enabling a real-time update of the safety assurances.

Contact-rich robotic systems, such as legged robots and manipulators, are often represented as hybrid systems. However, designing stabilizing controllers for these systems is often challenging because of the discontinuous state changes upon contact (also referred to as state resets). In this work, we generalize the HJ reachability framework to account for the discontinuous state changes originating from state resets, which has remained a challenge until now. We apply our approach for computing region-of-attractions and stabilizing controllers for several underactuated walking robots and demonstrate that the obtained controllers can leverage the state resets and contacts for enhancing the system stability.

The tutorial covered the theoretical foundations as well as computational tools for Hamilton-Jacobi (HJ) reachability analysis. The tutorial facilitated the application of HJ reachability to a variety of research domains such as model validation, human-robot interaction, and bio-engineering; it also started a platform for collaboration between these different fields.