  Sampling-based planning methods often become inefficient due to narrow
passages. Narrow passages induce a higher runtime, because the chance to sample
them becomes vanishingly small. In recent work, we showed that narrow passages
can be approached by relaxing the problem using admissible lower-dimensional
projections of the state space. Those relaxations often increase the volume of
narrow passages under projection. Solving the relaxed problem is often
efficient and produces an admissible heuristic we can exploit. However, given a
base path, i.e. a solution to a relaxed problem, there are currently no
tailored methods to efficiently exploit the base path. To efficiently exploit
the base path and thereby its admissible heuristic, we develop section
patterns, which are solution strategies to efficiently exploit base paths in
particular around narrow passages. To coordinate section patterns, we develop
the pattern dance algorithm, which efficiently coordinates section patterns to
reactively traverse narrow passages. We combine the pattern dance algorithm
with previously developed multilevel planning algorithms and benchmark them on
challenging planning problems like the Bugtrap, the double L-shape, an egress
problem and on four pregrasp scenarios for a 37 degrees of freedom shadow hand
mounted on a KUKA LWR robot. Our results confirm that section patterns are
useful to efficiently solve high-dimensional narrow passage motion planning
problems.
