  Fast inverse kinematics (IK) is a central component in robotic motion
planning. For complex robots, IK methods are often based on root search and
non-linear optimization algorithms. These algorithms can be massively sped up
using a neural network to predict a good initial guess, which can then be
refined in a few numerical iterations. Besides previous work on learning-based
IK, we present a learning approach for the fundamentally more complex problem
of IK with collision avoidance. We do this in diverse and previously unseen
environments. From a detailed analysis of the IK learning problem, we derive a
network and unsupervised learning architecture that removes the need for a
sample data generation step. Using the trained network's prediction as an
initial guess for a two-stage Jacobian-based solver allows for fast and
accurate computation of the collision-free IK. For the humanoid robot, Agile
Justin (19 DoF), the collision-free IK is solved in less than 10 milliseconds
(on a single CPU core) and with an accuracy of 10^-4 m and 10^-3 rad based on a
high-resolution world model generated from the robot's integrated 3D sensor.
Our method massively outperforms a random multi-start baseline in a benchmark
with the 19 DoF humanoid and challenging 3D environments. It requires ten times
less training time than a supervised training method while achieving comparable
results.
