Once again, any of the
planning methods described in Chapters 5 and
6 can be adapted here, but the methods are slightly
complicated by the fact that is a complex. To use sampling-based
methods, a dense sequence should be generated over . For example,
if random sampling is used, then an -cube can be chosen at random,
followed by a random point in the cube. The local planning method
(LPM) must take into account the
connectivity of the cube complex, which requires recognizing when
branches occur in the topological graph. Combinatorial methods must
also take into account this connectivity. For example, a sweeping
technique can be applied to produce a vertical cell decomposition, but
the sweep-line (or sweep-plane) must sweep across the various
-cells of the complex.

Steven M LaValle
2012-04-20