# The Motion Grammar

Motion Grammars model robot policies as context-free grammars. This is a
useful intermediate representation that enables a variety of policy
generation, analysis, and software synthesis techniques.

## The Motion Grammar for Physical Human-Robot Games

We demonstrate the motion grammar through the physical human-robot games
of Yamakuzushi and Chess and analyze the theoretical capabilities and
guarantees of this approach.

## Software Synthesis from Mathematical Models

We synthesize software for speed-controlled robot walking from the
mathematical system model using supervisory control of a context-free Motion
Grammar. First, we use Human-Inspired control to identify parameters for
fixed speed walking and for transitions between fixed speeds, guaranteeing
dynamic stability. Next, we build a Motion Grammar representing the
discrete-time control for this set of speeds. Then, we synthesize C code from
this grammar and generate supervisors online to achieve desired walking
speeds, guaranteeing correctness of discrete computation. Finally, we
demonstrate this approach on the Aldebaran NAO, showing stable walking
transitions with dynamically selected speeds.

## Linguistic Task Transfer

We pose a learning-from-demonstration scenario as grammatical inference.
First, we perform a visual analysis to extract a task description from human
demonstration, then we transfer the results to a simulated robot.

## The Motion Grammar Calculus

To produce correctly operating robotic systems, we need a way to modify
the system dynamics to achieve the desired behavior. To help automate the
derivation of correctly operating controlled systems, we introduce the Motion
Grammar Calculus, a set of rewrite rules for Context-Free Hybrid Systems
based on the Motion Grammar.