  Programming a robot manipulator should be as intuitive as possible. To
achieve that, the paradigm of teaching motion skills by providing few
demonstrations has become widely popular in recent years. Probabilistic
versions thereof take into account the uncertainty given by the distribution of
the training data. However, precise execution of start-, via-, and end-poses at
given times can not always be guaranteed. This limits the technology transfer
to industrial application. To address this problem, we propose a novel
constrained formulation of the Expectation Maximization algorithm for learning
Gaussian Mixture Models (GMM) on Riemannian Manifolds. Our approach applies to
probabilistic imitation learning and extends also to the well-established
TP-GMM framework with Task-Parameterization. It allows to prescribe
end-effector poses at defined execution times, for instance for precise pick &
place scenarios. The probabilistic approach is compared with state-of-the-art
learning-from-demonstration methods using the KUKA LBR iiwa robot. The reader
is encouraged to watch the accompanying video available at
https://youtu.be/JMI1YxtN9C0
