  This paper presents c2g-HOF networks which learn to generate cost-to-go
functions for manipulator motion planning. The c2g-HOF architecture consists of
a cost-to-go function over the configuration space represented as a neural
network (c2g-network) as well as a Higher Order Function (HOF) network which
outputs the weights of the c2g-network for a given input workspace. Both
networks are trained end-to-end in a supervised fashion using costs computed
from traditional motion planners. Once trained, c2g-HOF can generate a smooth
and continuous cost-to-go function directly from workspace sensor inputs
(represented as a point cloud in 3D or an image in 2D). At inference time, the
weights of the c2g-network are computed very efficiently and near-optimal
trajectories are generated by simply following the gradient of the cost-to-go
function. We compare c2g-HOF with traditional planning algorithms for various
robots and planning scenarios. The experimental results indicate that planning
with c2g-HOF is significantly faster than other motion planning algorithms,
resulting in orders of magnitude improvement when including collision checking.
Furthermore, despite being trained from sparsely sampled trajectories in
configuration space, c2g-HOF generalizes to generate smoother, and often lower
cost, trajectories. We demonstrate cost-to-go based planning on a 7 DoF
manipulator arm where motion planning in a complex workspace requires only 0.13
seconds for the entire trajectory.
