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Jascha van Pommeren created the Unibot, a robot that pivots on a single wheel.
Video after the jump.
“The Unibot is a self balancing unicycle robot. This robot combines the principles of the famous wheeled inverted pendulum and inertia wheel pendulum. A well known application of the wheeled inverted pendulum is the Segway. Take one wheel off the Segway and add an other one perpendicular to and above the remaining wheel and the Unibot is born! The wheel on the ground is used to establish the stabilization in the y-z-plane. The wheel in the air is used to balance the robot in the x-z-plane. ”
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October 8th, 2007
[...] Unibot - 3D Stabilization [Hacked Gadgets] [...]
October 8th, 2007
Nifty.
December 4th, 2008
Pretty cool!
Now what you need to add is a third wheel, with a vertical axis, to provide directional control.
Scale it up, and add a platform to stand on.
Kind of awkward with those spinning wheels, but some clever packaging — maybe multiple smaller, or higher speed and smaller, wheels might be used for the non-contact rotating masses.