Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachability

Autonomous systems like aircraft and assistive robots often operate in\nscenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi\nreachability can provide guaranteed safe sets and controllers for such systems.\nHowever, often these same scenarios have unknown or uncertain environments,\nsystem dynamics, or predictions of other agents. As the system is operating, it\nmay learn new knowledge about these uncertainties and should therefore update\nits safety analysis accordingly. However, work to learn and update safety\nanalysis is limited to small systems of about two dimensions due to the\ncomputational complexity of the analysis. In this paper we synthesize several\ntechniques to speed up computation: decomposition, warm-starting, and adaptive\ngrids. Using this new framework we can update safe sets by one or more orders\nof magnitude faster than prior work, making this technique practical for many\nrealistic systems. We demonstrate our results on simulated 2D and 10D\nnear-hover quadcopters operating in a windy environment.\n