On the Topology of Discrete Planning with Uncertainty

Michael Erdmann
Advances in Applied and Computational Topology, Afra Zomorodian, ed., American Mathematical Society, 2012, pp. 147-194.


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Abstract
This chapter explores the topology of planning with uncertainty in discrete spaces. The chapter defines the strategy complex of a finite discrete graph as the collection of all plans for accomplishing all tasks specified by goal states in the graph. Transitions in the graph may be nondeterministic or stochastic. One key result is that a system can attain any state in its graph despite control uncertainty if and only if its strategy complex is homotopic to a sphere of dimension two less than the number of states in the graph.

Keywords
topology, graph, complex, strategy, robotics, planning, uncertainty

Notes
Sponsor: DARPA
Grant ID: Providence, RI

Text Reference
Michael Erdmann, "On the Topology of Discrete Planning with Uncertainty," Advances in Applied and Computational Topology, Afra Zomorodian, ed., American Mathematical Society, 2012, pp. 147-194.

BibTeX Reference
@incollection{Erdmann_2012_7202,
   author = "Michael Erdmann",
   editor = "Afra Zomorodian",
   title = "On the Topology of Discrete Planning with Uncertainty",
   booktitle = "Advances in Applied and Computational Topology",
   pages = "147-194",
   publisher = "American Mathematical Society",
   address = "Providence, RI",
   month = "July",
   year = "2012",
}