On the Topology of Plans

Michael Erdmann
Eighth International Workshop on the Algorithmic Foundations of Robotics, 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.

Notes

Text Reference
Michael Erdmann, "On the Topology of Plans," Eighth International Workshop on the Algorithmic Foundations of Robotics, December, 2008.

BibTeX Reference
@inproceedings{Erdmann_2008_6820,
   author = "Michael Erdmann",
   title = "On the Topology of Plans",
   booktitle = "Eighth International Workshop on the Algorithmic Foundations of Robotics",
   month = "December",
   year = "2008",
}