  This paper investigates the feasibility of using Graph Neural Networks (GNNs)
for classical motion planning problems. We propose guiding both continuous and
discrete planning algorithms using GNNs' ability to robustly encode the
topology of the planning space using a property called permutation invariance.
We present two techniques, GNNs over dense fixed graphs for low-dimensional
problems and sampling-based GNNs for high-dimensional problems. We examine the
ability of a GNN to tackle planning problems such as identifying critical nodes
or learning the sampling distribution in Rapidly-exploring Random Trees (RRT).
Experiments with critical sampling, a pendulum and a six DoF robot arm show
GNNs improve on traditional analytic methods as well as learning approaches
using fully-connected or convolutional neural networks.
