Optimal Path-Planning With Random Breakdowns

Abstract

We propose a model for path-planning based on a single performance metric that accurately accounts for the the potential (spatially inhomogeneous) cost of breakdowns and repairs. These random breakdowns happen at a known (also spatially inhomogeneous) rate and can be one of two types: total, which halt all movement until an in-place repair is completed, or partial, after which movement continues in a damaged state. We use the framework of piecewise-deterministic Markov processes to describe the optimal policy for all starting locations. We also introduce an efficient numerical method that uses hybrid value-policy iterations to solve the resulting system of Hamilton-Jacobi-Bellman PDEs. Our method is illustrated through a series of computational experiments that highlight the dependence of optimal policies on the rate and type of breakdowns, with one of them based on Martian terrain data near Jezero Crater.