In theory, designing a robot that continuously juggles a single ball should not be difficult. Calibrating the machine would be a pain but once you got the thing running, it should continue to juggle the ball until some variable intervenes. In a perfect world, this would occur elegantly, but here on Earth things just don't come off so beautifully. However, through some smart design and precise math, researchers at the Swiss Federal Institute of Technology in Zurich have created the Blind Juggler, so named because it juggles a ball continuously, even when variables are introduced, without the use of sensors.
The two constants that a robot of this nature needs to maintain its juggle are the height at which the ball bounces and the location at which it hits the robot's paddle. But keeping those elements constant is easier said than done. To work around the location issue, Blind Juggler's designers created a paddle that is slightly concave, so if the ball starts to stray from the center of the paddle, the slight slope nudges it back toward the center on the next bounce.
But the real elegance is in the deceleration of the paddle as it moves upward to strike the ball. Working essentially from the principal of mechanical feedback, the paddle decelerates very precisely before reaching the pinnacle of its upstroke and moving back down again. If the ball is bouncing too low, it reaches the paddle earlier on the upstroke, and thus is hit with more force, sending the ball higher. If it's bouncing too high, the ball reaches the paddle later in the deceleration phase, giving it less of a boost on the next bounce.
Constantly self-correcting, the robot can maintain its juggle even when variables are introduced, as evidenced by the researcher moving the robot around in the video below.
not to be ignorant but the plain math is much easier to program than "sensor" feeds
they need one of a size to fit on a desk... alongside those clacker-sphere things and the magnetic dolphins...