Probabilistic decomposition of sequential force interaction tasks into movement primitives

Learning sequential force interaction tasks from kinesthetic demonstrations is a promising approach to transfer human manipulation abilities to a robot. In this paper we propose a novel concept to decompose such demonstrations into a set of Movement Primitives (MPs). The decomposition is based on a probability distribution we call Directional Normal Distribution (DND). To capture the sequential properties of the manipulation task, we model the demonstrations with a Hidden Markov Model (HMM). Here, we employ mixtures of DNDs as the HMM's output emissions. The combination of HMMs and mixtures of DNDs allows to infer the MP's composition, i.e., its coordinate frames, control variables and target coordinates from the demonstration data. In addition, it permits to determine an appropriate number of MPs that explains the demonstrations best. We evaluate the approach on kinesthetic demonstrations of a light bulb unscrewing task. Decomposing the task leads to intuitive and meaningful MPs that reflect the natural structure of the task.