We present a general and modular algorithmic framework for path planning of
robots. Our framework combines geometric methods for exact and complete
analysis of low-dimensional configuration spaces, together with practical,
considerably simpler sampling-based approaches that are appropriate for higher
dimensions. In order to facilitate the transfer of advanced geometric
algorithms into practical use, we suggest taking samples that are entire
low-dimensional manifolds of the configuration space that capture the
connectivity of the configuration space much better than isolated point
samples.