  In this paper we present a framework to learn skills from human
demonstrations in the form of geometric nullspaces, which can be executed using
a robot. We collect data of human demonstrations, fit geometric nullspaces to
them, and also infer their corresponding geometric constraint models. These
geometric constraints provide a powerful mathematical model as well as an
intuitive representation of the skill in terms of the involved objects. To
execute the skill using a robot, we combine this geometric skill description
with the robot's kinematics and other environmental constraints, from which
poses can be sampled for the robot's execution. The result of our framework is
a system that takes the human demonstrations as input, learns the underlying
skill model, and executes the learnt skill with different robots in different
dynamic environments. We evaluate our approach on a simulated industrial robot,
and execute the final task on the iCub humanoid robot.
