  In recent decades, advancements in motion learning have enabled robots to
acquire new skills and adapt to unseen conditions in both structured and
unstructured environments. In practice, motion learning methods capture
relevant patterns and adjust them to new conditions such as dynamic obstacle
avoidance or variable targets. In this paper, we investigate the robot motion
learning paradigm from a Riemannian manifold perspective. We argue that
Riemannian manifolds may be learned via human demonstrations in which geodesics
are natural motion skills. The geodesics are generated using a learned
Riemannian metric produced by our novel variational autoencoder (VAE), which is
especially intended to recover full-pose end-effector states and joint space
configurations. In addition, we propose a technique for facilitating on-the-fly
end-effector/multiple-limb obstacle avoidance by reshaping the learned manifold
using an obstacle-aware ambient metric. The motion generated using these
geodesics may naturally result in multiple-solution tasks that have not been
explicitly demonstrated previously. We extensively tested our approach in task
space and joint space scenarios using a 7-DoF robotic manipulator. We
demonstrate that our method is capable of learning and generating motion skills
based on complicated motion patterns demonstrated by a human operator.
Additionally, we assess several obstacle avoidance strategies and generate
trajectories in multiple-mode settings.
