  Small variance asymptotics is emerging as a useful technique for inference in
large scale Bayesian non-parametric mixture models. This paper analyses the
online learning of robot manipulation tasks with Bayesian non-parametric
mixture models under small variance asymptotics. The analysis yields a scalable
online sequence clustering (SOSC) algorithm that is non-parametric in the
number of clusters and the subspace dimension of each cluster. SOSC groups the
new datapoint in its low dimensional subspace by online inference in a
non-parametric mixture of probabilistic principal component analyzers (MPPCA)
based on Dirichlet process, and captures the state transition and state
duration information online in a hidden semi-Markov model (HSMM) based on
hierarchical Dirichlet process. A task-parameterized formulation of our
approach autonomously adapts the model to changing environmental situations
during manipulation. We apply the algorithm in a teleoperation setting to
recognize the intention of the operator and remotely adjust the movement of the
robot using the learned model. The generative model is used to synthesize both
time-independent and time-dependent behaviours by relying on the principles of
shared and autonomous control. Experiments with the Baxter robot yield
parsimonious clusters that adapt online with new demonstrations and assist the
operator in performing remote manipulation tasks.
