  This paper proposes a combined optimization and learning method for
impact-friendly, non-prehensile catching of objects at non-zero velocity.
Through a constrained Quadratic Programming problem, the method generates
optimal trajectories up to the contact point between the robot and the object
to minimize their relative velocity and reduce the impact forces. Next, the
generated trajectories are updated by Kernelized Movement Primitives, which are
based on human catching demonstrations to ensure a smooth transition around the
catching point. In addition, the learned human variable stiffness (HVS) is sent
to the robot's Cartesian impedance controller to absorb the post-impact forces
and stabilize the catching position. Three experiments are conducted to compare
our method with and without HVS against a fixed-position impedance controller
(FP-IC). The results showed that the proposed methods outperform the FP-IC
while adding HVS yields better results for absorbing the post-impact forces.
