DeepReach: A Deep Learning Approach to High-Dimensional Reachability

Hamilton-Jacobi (HJ) reachability approach to approximately solve high-dimensional analysis is a verification method for autonomous systems that reachability problems. What sets DeepReach apart is its computes both the safe configurations and the corresponding ability to compute BRTs (and BRATs) as well as the corresponding safe controller for the system. In reachability analysis, one safety controller for general nonlinear dynamical computes the Backward Reachable Tube (BRT) of a dynamical systems in the presence of disturbances and state and input system. This is the set of states such that the trajectories constraints. DeepReach is rooted in HJ reachability analysis; that start from this set will eventually reach some given target however, instead of solving the value function PDE over a set despite the worst case disturbance (or an exogenous, grid, DeepReach draws inspiration from the recent progress adversarial input more generally). As an example, for an in solving PDEs using deep learning, and represents the aerial vehicle, the disturbance could be wind or another value function as a deep neural network (DNN) to learn adversarial aircraft flying nearby, and the target set could a parameterized approximation of the value function. Thus, be the destination of the vehicle. The BRT provides both the computation and memory requirements for obtaining the the set of states from which the aerial vehicle can safely value function do not scale with the grid resolution, but reach its destination and a robust controller for the vehicle.