Reusable Neural Reachability via Local Refinement

This research paper introduces a reusable neural reachability framework for obstacle avoidance under translation-invariant dynamics. By formulating the problem using an avoid-side travel cost Hamilton-Jacobi approach, the authors prove that the value function can be reused across translated obstacles, providing exact collision certificates outside the avoid set and conservative inner certificates within clutter. A blockwise composition framework is proposed to merge subsets of obstacles, reducing conservatism while maintaining monotonicity under merging. The method is illustrated on a Dubins car navigating a repeated clutter field.