Exact Cellular Decompositions in Terms of Critical Points of Morse Functions

Howie Choset, Ercan Acar, Alfred Rizzi, and Jon Luntz
Proceedings of IEEE International Conference on Robotics and Automation (ICRA '00), April, 2000, pp. 2270 - 2277.


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Abstract
Exact cellular decompositions are structures that globally encode the topology of a robot's free space, while locally describing the free space geometry. These structures have been widely used for path planning between two points, but can be used for mapping and coverage of robot free spaces. In this paper, we define exact cellular decompositions where critical points of Morse functions indicate the location of cell boundaries. Morse functions are those whose critical points are non-degenerate. Between critical points, the structure of a space is effectively the same, so simple control strategies to achieve tasks, such as coverage, are feasible within each cell. In this paper, we derive a general framework for defining decompositions in terms of critical points and then give examples, each corresponding to a different task. All of the results in this paper are derived in an m-dimensional Euclidean space, but the examples depicted in the figures are 2D and 3D for ease of presentation.

Notes
Associated Lab(s) / Group(s): Biorobotics
Associated Project(s): Coverage Path Planning in the Plane: Exact Cellular Decompositions and Bridge Inspection with Serpentine Robots

Text Reference
Howie Choset, Ercan Acar, Alfred Rizzi, and Jon Luntz, "Exact Cellular Decompositions in Terms of Critical Points of Morse Functions," Proceedings of IEEE International Conference on Robotics and Automation (ICRA '00), April, 2000, pp. 2270 - 2277.

BibTeX Reference
@inproceedings{Choset_2000_3386,
   author = "Howie Choset and Ercan Acar and Alfred Rizzi and Jon Luntz",
   title = "Exact Cellular Decompositions in Terms of Critical Points of Morse Functions",
   booktitle = "Proceedings of IEEE International Conference on Robotics and Automation (ICRA '00)",
   pages = "2270 - 2277",
   month = "April",
   year = "2000",
   volume = "3",
}