6.3 Cell Decompositions

Section 6.2.2 introduced the vertical cell decomposition to solve the motion planning problem when is polygonal. It is important to understand, however, that this is just one choice among many for the decomposition. Some of these choices may not be preferable in 2D; however, they might generalize better to higher dimensions. Therefore, other cell decompositions are covered in this section, to provide a smoother transition from vertical cell decomposition to cylindrical algebraic decomposition in Section 6.4, which solves the motion planning problem in any dimension for any semi-algebraic model. Along the way, a cylindrical decomposition will appear in Section 6.3.4 for the special case of a line-segment robot in .

- 6.3.1 General Definitions

- 6.3.2 2D Decompositions

- 6.3.3 3D Vertical Decomposition
- 6.3.4 A Decomposition for a Line-Segment Robot

Steven M LaValle 2020-08-14