  Our goal is to enable robots to \emph{time} their motion in a way that is
purposefully expressive of their internal states, making them more transparent
to people. We start by investigating what types of states motion timing is
capable of expressing, focusing on robot manipulation and keeping the path
constant while systematically varying the timing. We find that users naturally
pick up on certain properties of the robot (like confidence), of the motion
(like naturalness), or of the task (like the weight of the object that the
robot is carrying). We then conduct a hypothesis-driven experiment to tease out
the directions and magnitudes of these effects, and use our findings to develop
candidate mathematical models for how users make these inferences from the
timing. We find a strong correlation between the models and real user data,
suggesting that robots can leverage these models to autonomously optimize the
timing of their motion to be expressive.
