Description
This thesis uses Hamilton-Jacobi (HJ) reachability analysis to robustly guarantee safety for systems with uncertainty. In the presence of uncertainty there must be a balance between conservativeness as it pertains to safety and performance as it pertains to other system objectives, and we also account for this through reachability analysis. In addition, this thesis also explores methods for modifying the analysis as more data is collected from the robotics system, which ultimately allows for improved performance. This is referred to here as learning-based reachability analysis. The thesis concludes with a new HJ reachability formulation that enhances the learning-based analysis. The myriad of ideas presented throughout the thesis are demonstrated on various examples.