This paper describes a syntactic approach to imitation learning that captures important task structures in the form of probabilistic activity grammars from a reasonably small number of samples under noisy conditions. We show that these learned grammars can be recursively applied to help recognize unforeseen, more complicated tasks that share underlying structures. The grammars enforce an observation to be consistent with the previously observed behaviors which can correct unexpected, out-of-context actions due to errors of the observer and/or demonstrator. To achieve this goal, our method (1) actively searches for frequently occurring action symbols that are subsets of input samples to uncover the hierarchical structure of the demonstration, and (2) considers the uncertainties of input symbols due to imperfect low-level detectors.

We evaluate the proposed method using both synthetic data and two sets of real-world humanoid robot experiments. In our Towers of Hanoi experiment, the robot learns the important constraints of the puzzle after observing demonstrators solving it. In our Dance Imitation experiment, the robot learns 3 types of dances from human demonstrations. The results suggest that under reasonable amount of noise, our method is capable of capturing the reusable task structures and generalizing them to cope with recursions.