On the topology of discrete planning with uncertainty
type: Item
instance of: scholarly article
zbMATH Open document ID: 1278.68300
author: Michael Erdmann
publication date: 2012-09-14T00:00:00Z
Mathematics Subject Classification ID: 68T37
Mathematics Subject Classification ID: 68T40
Mathematics Subject Classification ID: 55U05
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 6082693
zbMATH Keywords: topology
zbMATH Keywords: graph
zbMATH Keywords: complex
zbMATH Keywords: strategy
zbMATH Keywords: robotics
zbMATH Keywords: planning
zbMATH Keywords: uncertainty
MaRDI profile type: Publication
title: On the topology of discrete planning with uncertainty
review text: The article is devoted to the investigation of the topology of planning with uncertainty in discrete spaces. It is closely related to mathematical basics of robotics. The article consists of the following chapters and subsections:NEWLINENEWLINE1. Planning with uncertainty in roboticsNEWLINENEWLINE 1.1. Discrete modelingNEWLINENEWLINE 1.2. UncertaintyNEWLINENEWLINE 1.3. PlannersNEWLINENEWLINE 1.4. Collections of plansNEWLINENEWLINE 1.5. Topology of plansNEWLINENEWLINE 1.6. Chapter outlineNEWLINENEWLINE 2. Nondeterministic graphs and strategy complexesNEWLINENEWLINE 2.1. Nondeterministic graphsNEWLINENEWLINE 2.2. Simplicial complexesNEWLINENEWLINE 2.3. Strategy complexes arising from nondeterministic graphsNEWLINENEWLINE 3. Topological characteristics of goal attainabilityNEWLINENEWLINE 4. Stochastic graphs and strategy complexesNEWLINENEWLINE 5. Topological characterization of full controllabilityNEWLINENEWLINE 6. Sources and dual complexesNEWLINENEWLINE 6.1. Modeling system capabilitiesNEWLINENEWLINE 6.2. System designNEWLINENEWLINE 6.3. Inferring adversarial capabilitiesNEWLINENEWLINE 7. Unions and quotientsNEWLINENEWLINE 7.1. Graph unionsNEWLINENEWLINE 7.2. Collapsing fully controllable subgraphsNEWLINENEWLINE 8. Topology of prescribed motionsNEWLINENEWLINE 8.1. Links and sourcesNEWLINENEWLINE 8.2. Quillen filter lemmaNEWLINENEWLINE 8.3. Two link-based homotopy equivalencesNEWLINENEWLINE 9. Essential actionsNEWLINENEWLINE 10. Decision treesNEWLINENEWLINE 11. Category connectionsNEWLINENEWLINE 11.1. Each graph as a categoryNEWLINENEWLINE 11.2. All graphs as a categoryNEWLINENEWLINE11.3. Functoriality of stability complexesNEWLINENEWLINE 11.4. Functoriality of source complexesNEWLINENEWLINE 11.5. A planner's classifying spaceNEWLINENEWLINE 12. DiscussionNEWLINENEWLINE 12.1. Uncertainty, geometry, and topologyNEWLINENEWLINE 12.2. Higher-order interactionsNEWLINENEWLINE 12.3. Computational complexityNEWLINENEWLINE 12.4. Complex structure and future workNEWLINENEWLINET…
reviewed by: Andreiy Kondrat'yev
description: scientific article; zbMATH DE number 6082693