  The need for rapid and reliable robot deployment is on the rise. Imitation
Learning (IL) has become popular for producing motion planning policies from a
set of demonstrations. However, many methods in IL are not guaranteed to
produce stable policies. The generated policy may not converge to the robot
target, reducing reliability, and may collide with its environment, reducing
the safety of the system. Stable Estimator of Dynamic Systems (SEDS) produces
stable policies by constraining the Lyapunov stability criteria during
learning, but the Lyapunov candidate function had to be manually selected. In
this work, we propose a novel method for learning a Lyapunov function and a
policy using a single neural network model. The method can be equipped with an
obstacle avoidance module for convex object pairs to guarantee no collisions.
We demonstrated our method is capable of finding policies in several simulation
environments and transfer to a real-world scenario.
