  We present a framework for visual action planning of complex manipulation
tasks with high-dimensional state spaces, focusing on manipulation of
deformable objects. We propose a Latent Space Roadmap (LSR) for task planning
which is a graph-based structure globally capturing the system dynamics in a
low-dimensional latent space. Our framework consists of three parts: (1) a
Mapping Module (MM) that maps observations given in the form of images into a
structured latent space extracting the respective states as well as generates
observations from the latent states, (2) the LSR which builds and connects
clusters containing similar states in order to find the latent plans between
start and goal states extracted by MM, and (3) the Action Proposal Module that
complements the latent plan found by the LSR with the corresponding actions. We
present a thorough investigation of our framework on simulated box stacking and
rope/box manipulation tasks, and a folding task executed on a real robot.
