The Maximal Hitting-Time Stochastic Reachability Problem

The maximal hitting-time stochastic reachability problem focuses on finding the maximum likelihood of reaching a time-varying target at some optimal time within a finite time horizon, while remaining inside a time-varying set of safe states. This problem is motivated by target capture problems in which maximizing the likelihood of capture is more important than the particular time of capture. We employ a target tube framework, which admits time-varying target and constraint sets. We show that solution of the maximal hitting-time problem relies upon the solution of the terminal hitting-time problem, for which efficient computational methods exist for linear dynamics and convex and compact target and constraint sets. We demonstrate our method on a 2-dimensional point mass system, and a quadrotor stochastic target capture problem.