This video demonstrates Pi's new "arm tracking" behavior which allows
the arms to move up and down in sync with the up and down movements of
the ball. This allows Pi to anticipate a hand off from the person
holding the ball. It could also be used to reach for the ball if it
was resting on a chair or some other object.

How does Pi's arm tracking work? The arm tracking algorithm depends
on head tracking wherein the yellow ball is kept in the center of the
field of view. Then the forward facing sonar module (the one with the
green blinking light that looks like Pi's eyes) measures the distance
to the ball by continually pinging it with a sonar pulse about 20
times per second. Combining this distance with the tilt angle of Pi's
head and the geometry of Pi's body and limbs, a bit of high school
three-dimensional geometry gives the x, y, z coordinates of the ball
in Pi's head-centered coordinate system. I then use some more math to
translate these coordinates into a frame of reference centered at Pi's
shoulder joint. From these new coordinates, I can compute the angle
of the arms required to point at the ball. All of these calculations
are continually updated so that the arms can follow the movement of
the ball.

As to how Pi knows when to grasp the ball, there is an infrared sensor
embedded in Pi's right hand that faces Pi's left hand. With the arms
open, the sensor measures a large gap between the hands. When the
ball is placed between the hands, it cuts into the beam and Pi knows
something is there and therefore begins closing his arms. The inside
of Pi's hands are lined with force sensors that detect contact with
the ball. Squeezing continues until a certain force level is
obtained, thereby assuring a good grip on the ball. Once he has a
firm hold on the ball, Pi lifts his arms upward so as to be able to
carry the ball or hand it off.