The general motion planning problem has been proven to
be computationally very difficult. But we still would
like to plan motions for robots (or molecules).
Therefore we have to look for practical solutions.
Our view of motion planning is the following: Almost
no motion planning problem is as difficult as the
complexity bounds are implying. Most of them are
actually quite easy. The approaches we divise in our
laboratory attempt to exploit the structure present in
the problem to make the computation of the solution
more efficient. Basically, use the information from
the problem instance. Use the information you obtain
as you start solving the problem. Use all the
information you can get to reduce the amout of
configuration space you have to search. It works, see
for yourself:
