5.1 Distance and Volume in C-Space

Virtually all sampling-based planning algorithms require a function
that measures the distance between two points in . In most cases,
this results in a *metric space*, which is introduced in Section
5.1.1. Useful examples for motion planning are given in
Section 5.1.2. It will also be important in many of
these algorithms to define the volume of a subset of . This
requires a *measure space*, which is introduced in Section
5.1.3. Section 5.1.4 introduces invariant
measures, which should be used whenever possible.

- 5.1.1 Metric Spaces

- 5.1.2 Important Metric Spaces for Motion Planning

- 5.1.3 Basic Measure Theory Definitions
- 5.1.4 Using the Correct Measure

Steven M LaValle 2012-04-20