# 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.