14.2 Reachability and Completeness

This section provides preliminary concepts for sampling-based planning
algorithms. In Chapter 5, sampling over was of
fundamental importance. The most important consideration was that a
sequence of samples should be *dense* so
that samples get arbitrarily close to any point in
. Planning
under differential constraints is complicated by the specification of
solutions by an action trajectory instead of a path through
.
For sampling-based algorithms to be resolution complete, sampling and
searching performed on the space of action trajectories must somehow
lead to a dense set in
.

- 14.2.1 Reachable Sets

- 14.2.2 The Discrete-Time Model
- 14.2.2.1 Reachability graph
- 14.2.2.2 Resolution completeness for
- 14.2.2.3 Resolution completeness for

- 14.2.3 Motion Primitives

Steven M LaValle 2012-04-20