Robotic unicycle

The problem of creating a robotic unicycle that "rides itself" whilst balancing itself in three dimensions is an interesting problem in robotics and control theory.

Note: the term "unicycle" is also sometimes used in robotics to mean a two-wheeled vehicle moving in a two-dimensional world: this article is about normal one-wheeled cycles, albeit with robotic riders.

A physically realisable unicycle, in this sense, is a nonholonomic system. This is a system in which a return to the original internal (wheel) configuration does not guarantee return to the original system (unicycle) position. In other words, the system outcome is path-dependent.

The theoretical work on the unicycle problem is complemented by work on the construction of actual mechanically ridden unicycles. (need reference here: the work was Japanese/Russian, I believe)

The difficulty of this problem can be compared to that of constructing a one-wheeled Segway.

In 2003, Bombardier announced a conceptual design for just such a product, the EMBRIO, intended as a sports vehicle. It is unclear whether Bombardier intends to create a working prototype of this vehicle.

This is a stub article: more is needed to be written on this subject that is both amusing and mathematically interesting (and potentially a laboratory for some important problems).

See also:

• Lyapunov-Malkin theorem
• Inverted pendulum
• Segway

Trivia:

• Pixar's 1987 animated film "Red's Dream" depicts a computer-animated unicycle riding itself. It is unclear to what degree this provided motivation for the research described above.

References:

• S. V. Ulyanov et. al. Soft computing for the intelligent robust control of a robotic unicycle with a new physical measure for mechanical controllability. Soft Computing Volume 2 Issue 2 (1998) pp 73-88.
• Zenkov, DV, AM Bloch, and JE Marsden [1999] Stabilization of the Unicycle with Rider. Proc. CDC 38, 3470-3471 (pdf format available here)
• Zenkov, DV, AM Bloch, NE Leonard and JE Marsden, Matching and Stabilization of Low-dimensional Nonholonomic Systems. Proc. CDC, 39, (2000), 1289-1295. (pdf format available here)
• Sheng, Zaiquan; Yamafuji, Kazuo: Realization of a Human Riding a Unicycle by a Robot. Proceedings of the 1995 IEEE International Conference on Robotics and Automation, Vol. 2 (c1995), pp 1319 - 1326

External links

• Robot unicycle model (Japanese language text)
• http://www.ifr.mavt.ethz.ch/movic98/proceedings/78c.pdf another paper
• An interesting post from the Unicycling mailing list
• Bombardier Recreation Products EMBRIO one-wheeled recreational vehicle concept design