Optimal Path-Planning with Random Breakdowns
| Autor: | Alexander Vladimirsky, Marissa Gee |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematical optimization
Control and Optimization Series (mathematics) Computer science Numerical analysis Markov process Terrain Type (model theory) symbols.namesake Control and Systems Engineering Optimization and Control (math.OC) symbols FOS: Mathematics State (computer science) Motion planning Mathematics - Optimization and Control Performance metric 93C30 (Primary) 49L12 65N22 60J28 93C85 (Secondary) |
| DOI: | 10.48550/arxiv.2109.06910 |
| Popis: | 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 (or system faults) happen at a known, spatially inhomogeneous rate. Our model includes breakdowns of two types: total, which halt all movement until an in-place repair is completed, and partial, after which movement continues in a damaged state toward a repair depot. 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. Comment: 6 pages, 4 figures, published in Control Systems Letters and presented at American Control Conference 2022. Revised to fix typos in equations (19) and (20) |
| Databáze: | OpenAIRE |
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