  The past decade has amply demonstrated the remarkable functionality that can
be realized by learning complex input/output relationships. Algorithmically,
one of the most important and opaque relationships is that between a problem's
structure and an effective solution method. Here, we quantitatively connect the
structure of a planning problem to the performance of a given sampling-based
motion planning (SBMP) algorithm. We demonstrate that the geometric
relationships of motion planning problems can be well captured by graph neural
networks (GNNs) to predict SBMP runtime. By using an algorithm portfolio we
show that GNN predictions of runtime on particular problems can be leveraged to
accelerate online motion planning in both navigation and manipulation tasks.
Moreover, the problem-to-runtime map can be inverted to identify subproblems
easier to solve by particular SBMPs. We provide a motivating example of how
this knowledge may be used to improve integrated task and motion planning on
simulated examples. These successes rely on the relational structure of GNNs to
capture scalable generalization from low-dimensional navigation tasks to high
degree-of-freedom manipulation tasks in 3d environments.
