Removing Leaking Corners to Reduce Dimensionality in Hamilton-Jacobi Reachability

Abstract

Hamilton-Jacobi (HJ) reachability provides a flexible framework for the verification of safety in robotic systems: it accounts for nonlinear system dynamics and provides safety-preserving controllers. However, computational scalability limits its direct application to systems of less than five continuous state dimensions. To alleviate this computational burden, system decomposition methods have been proposed; however, safety guarantees are lost in situations involving “leaking corners which arise when there are conflicting controls between subsystems. In this paper, a coupled HJ formulation is presented, which addresses leaking corners and guarantees safety, while incorporating dimensionality reduction. We demonstrate our method in two examples, one of which is a vehicle obstacle avoidance problem with a 5D car model, whose HJ computation was previously considered to be intractable.