Inducing Probabilistic Context-Free Grammars for the Sequencing of Movement Primitives

Movement Primitives are a well studied and widely applied concept in modern robotics. Composing primitives out of an existing library, however, has shown to be a challenging problem. We propose the use of probabilistic context-free grammars to sequence a series of primitives to generate complex robot policies from a given library of primitives. The rule-based nature of formal grammars allows an intuitive encoding of hierarchically and recursively structured tasks. This hierarchical concept strongly connects with the way robot policies can be learned, organized, and re-used. However, the induction of context-free grammars has proven to be a complicated and yet unsolved challenge. In this work, we exploit the physical nature of robot movement primitives to restrict and efficiently search the grammar space. The grammar is learned applying a Markov Chain Monte Carlo optimization over the posteriors of the grammars given the observations. The proposal distribution is defined as a mixture over the probabilities of the operators connecting the search space. Restrictions to these operators guarantee continuous sequences while reducing the grammar space. We validate our method on a redundant 7 degree-of-freedom lightweight robotic arm on tasks that require the generation of complex sequences consisting of simple movement primitives.

I. Introduction

Movement primitives (MPs) are a well established concept in robotics. MPs are used to represent atomic, elementary movements and are, therefore, appropriate for tasks consisting of a single stroke-based or rhythmic movement [1]. They have been used in a large variety of applications, e.g., table tennis [2], pancake flipping [3] and hockey [1]. However, for more complex tasks a single MP is often not sufficient. Such task require sequences of MPs for feasible solutions.