Optimal Path-Planning with Random Breakdowns

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