  Swept Volume (SV), the volume displaced by an object when it is moving along
a trajectory, is considered a useful metric for motion planning. First, SV has
been used to identify collisions along a trajectory, because it directly
measures the amount of space required for an object to move. Second, in
sampling-based motion planning, SV is an ideal distance metric, because it
correlates to the likelihood of success of the expensive local planning step
between two sampled configurations. However, in both of these applications,
traditional SV algorithms are too computationally expensive for efficient
motion planning. In this work, we train Deep Neural Networks (DNNs) to learn
the size of SV for specific robot geometries. Results for two robots, a 6
degree of freedom (DOF) rigid body and a 7 DOF fixed-based manipulator,
indicate that the network estimations are very close to the true size of SV and
is more than 1500 times faster than a state of the art SV estimation algorithm.
