On the Topology of Plans
Workshop Paper, 8th International Workshop on the Algorithmic Foundations of Robotics (WAFR '08), pp. 267 - 282, December, 2008
Abstract
This paper explores a topological perspective of planning. A series of examples and theorems establishes a fundamental coupling between tasks on graphs and simplicial complexes. Planning under uncertainty is one application. The paper introduces strategy and loopback complexes. The paper's main theorem shows that tasks specified by goal states in nondeterministic graphs have guaranteed solutions if and only if their loopback complexes are homotopic to spheres.
BibTeX
@workshop{Erdmann-2008-10143,author = {Michael Erdmann},
title = {On the Topology of Plans},
booktitle = {Proceedings of 8th International Workshop on the Algorithmic Foundations of Robotics (WAFR '08)},
year = {2008},
month = {December},
pages = {267 - 282},
}
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