Exact Cellular Decompositions in Terms of Critical Points of Morse Functions

Exact cellular decompositions are structures that globally encode the topology of a robot's free space, while locally describing the free space's 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 dene 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 e ectively 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 de ning decompositions in terms of critical points and then give examples, each corresponding to a di erent task. All of the results in this paper are derived in an m-dimensional Euclidean space, but the examples depicted in the gures are two- and threedimensional for e...

• Type: Conference
• Year: 2000
• Where: ICRA
• Authors: Howie Choset, Ercan U. Acar, Alfred A. Rizzi, Jonathan E. Luntz
• Keywords: Critical Points, Exact Cellular Decompositions, Free Spaces, ICRA 2000, Robotics