On the topology of discrete planning with uncertainty (Q2912387)

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 workNEWLINENEWLINEThe article may be classified as an intermediate project report and is valuable for software designers working in mathematical modeling of various robotics problems.NEWLINENEWLINEFor the entire collection see [Zbl 1245.55001].