  Robots can rapidly acquire new skills from demonstrations. However, during
generalisation of skills or transitioning across fundamentally different
skills, it is unclear whether the robot has the necessary knowledge to perform
the task. Failing to detect missing information often leads to abrupt movements
or to collisions with the environment. Active learning can quantify the
uncertainty of performing the task and, in general, locate regions of missing
information. We introduce a novel algorithm for active learning and demonstrate
its utility for generating smooth trajectories. Our approach is based on deep
generative models and metric learning in latent spaces. It relies on the
Jacobian of the likelihood to detect non-smooth transitions in the latent
space, i.e., transitions that lead to abrupt changes in the movement of the
robot. When non-smooth transitions are detected, our algorithm asks for an
additional demonstration from that specific region. The newly acquired
knowledge modifies the data manifold and allows for learning a latent
representation for generating smooth movements. We demonstrate the efficacy of
our approach on generalising elementary skills, transitioning across different
skills, and implicitly avoiding collisions with the environment. For our
experiments, we use a simulated pendulum where we observe its motion from
images and a 7-DoF anthropomorphic arm.
