  The objective function used in trajectory optimization is often non-convex
and can have an infinite set of local optima. In such cases, there are diverse
solutions to perform a given task. Although there are a few methods to find
multiple solutions for motion planning, they are limited to generating a finite
set of solutions. To address this issue, we presents an optimization method
that learns an infinite set of solutions in trajectory optimization. In our
framework, diverse solutions are obtained by learning latent representations of
solutions. Our approach can be interpreted as training a deep generative model
of collision-free trajectories for motion planning. The experimental results
indicate that the trained model represents an infinite set of homotopic
solutions for motion planning problems.
