  Planning collision-free motions for robots with many degrees of freedom is
challenging in environments with complex obstacle geometries. Recent work
introduced the idea of speeding up the planning by encoding prior experience of
successful motion plans in a neural network. However, this "neural motion
planning" did not scale to complex robots in unseen 3D environments as needed
for real-world applications. Here, we introduce "basis point set", well-known
in computer vision, to neural motion planning as a modern compact environment
encoding enabling efficient supervised training networks that generalize well
over diverse 3D worlds. Combined with a new elaborate training scheme, we reach
a planning success rate of 100%. We use the network to predict an educated
initial guess for an optimization-based planner (OMP), which quickly converges
to a feasible solution, massively outperforming random multi-starts when tested
on previously unseen environments. For the DLR humanoid Agile Justin with 19DoF
and in challenging obstacle environments, optimal paths can be generated in
200ms using only a single CPU core. We also show a first successful real-world
experiment based on a high-resolution world model from an integrated 3D sensor.
