A self-balancing unicycle is a unicycle electric vehicle that assists the rider in staying upright by using an electric motor and gyroscopes controlled by a computer that is fed data from accelerometers and other sensors. As of 2015, several models were commercially available. They are commonly referred to as Electric Unicycles and EUCs.
- 1 Control theory of the self-balancing unicycle
- 2 Legal status
- 3 Human-ridable self-balancing unicycles and commercialization
- 4 Similar vehicles
- 5 Fictional self-balancing unicycles
- 6 OpenSource technology
- 7 See also
- 8 References
- 9 Further reading
- 10 External links
Control theory of the self-balancing unicycle
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Creating a self-powered unicycle that balances itself in three dimensions is a robotics and control theory problem. A self-balancing unicycle can be considered as a non-linear control system similar to that of a two-dimensional inverted pendulum with a unicycle cart at its base. There are many higher-order effects involved in modelling the full system. Rotation of the drive wheel itself can provide control in only one dimension, forwards and backwards. Control in other dimensions generally requires other actuators, such as auxiliary pendulums, reaction wheels, or control moment gyroscopes attached to the main unicycle pendulum.
Laws in some places do not address powered unicycles, but there are some provisions regarding electric mobility devices for the disabled.
Human-ridable self-balancing unicycles and commercialization
Single-axis self-balancing ridable unicycles
Single-axis unicycles are self-balancing only in the forwards-backwards direction, so a rider must balance them from side to side, such as Trevor Blackwell's Eunicycle or the RYNO Motors Micro-Cycle.[better source needed] In 2008, Focus Designs released the first commercially available self-balancing unicycle.[better source needed] In 2011, Inventist marketed an 11 kg stand-up, seatless version called the Solowheel that has a weight, size and carry handles that make it usable by last mile commuters.[better source needed] Late in 2015, the Ford Motor Company patented a "self-propelled unicycle engagable with vehicle", intended for last-mile commuters.
The RIOT wheel is a ridable single-axis self-balancing unicycle with an unusually low centre of gravity, with its rider in front of, rather than on top of its single wheel, balanced by a counterweight within the wheel.
True two-axis self-balancing ridable unicycles
A two-axis self-balancing unicycle balances itself side to side, in addition to the forward and backward axis.
- In 2003, Bombardier announced a conceptual design for such a device used as a sport vehicle, the Embrio. It is unclear whether Bombardier ever intends to create a working prototype of this vehicle.
- Aleksander Polutnik's Enicycle (2006) is probably the first two-axis balancing human-ridable unicycle.
A number of vehicles share characteristics of self-balancing unicycles:
- The Segway is a vehicle which is capable of automatically balancing itself in the forwards-and-backwards direction, but is a dicycle with two parallel wheels, similar to the later self-balancing two-wheeled board rather than being capable of balancing from side to side.
- In 2006, researchers at Carnegie Mellon University developed a 2-dimensional inverted pendulum that balances on a ball rather than a wheel.
- Two-wheeled self-balancing (mobile) robots 
- The Uno, a vehicle that superficially resembles a self-balancing unicycle but is actually a dicycle with its two wheels very close together
- The Honda U3-X looks like a self-balancing unicycle, but balances on a powered Omni wheeI rather than on a single wheel
Fictional self-balancing unicycles
- A self-balancing unicycle was described in 1969 in The Man From R.O.B.O.T., a short story by science fiction author Harry Harrison.
- Fenton Crackshell, a Disney character, is depicted wearing a robotic unicycle suit as Gizmoduck.
- Demolishor, a Decepticon from the 2009 Transformers sequel, whose robot mode is a gigantic robotic unicycle.
- The "tumblebugs" in The Roads Must Roll
- The protagonist in the Flash browser game, Little Wheel.
- Thor, fictional inventor of the wheel and the comb, of the comic strip B.C..
- Securitrons from Fallout: New Vegas.
The community developed some OpenSource technology for electric unicycles:
- Android app
- Shell to be 3D printed
Please see more information on the EGG Electric Unicycle project page.
The community gathers on the online forum Electric Unicycle.
- Charles F. Taylor working prototypes 1939-1964
- Control moment gyroscope
- Inertia wheel pendulum
- Inverted pendulum
- Outline of cycling
- Self-balancing two-wheeled board
- Self-balancing scooter
- Segway PT
- List of land vehicles types by number of wheels
- Rice, Vincent (26 January 2012). "Version 2.0 of Focus Designs Self-Balancing Unicycle now ready for primetime". GizMag. Retrieved 25 September 2014.
- "ElectricUnicycleReviews.com :: Self balancing electric micro unicycle reviews :: Airwheel, Firewheel, Gotway, Inmotion, IPS, Legway, Ninebot One, Rockwheel, Solowheel :: All Reviews By Brand". electricunicyclereviews.com. Retrieved 2015-12-27.
- http://rynomotors.com/ Micro-Cycle — archived RYNO Motors 'blog page
- "Slide 3 Slide 3", Self-Balancing Unicycle | Focus Designs, Inc. | The SBU is the coolest light electric vehicle on the market. The gyro-stabilized SBU contains full-frontal nerdity!, Focusdesigns.com, 2013-04-17, retrieved 2013-04-26
- "Home - SOLOWHEEL".
- Solowheel: self-balancing last mile transport for the upstanding commuter.
- Last Mille Club, unicycle archive
- Kaiman, Jonathan (May 30, 2015), "For Solowheel maker, a patent rights nightmare in China", The Los Angeles Times
- Read, Richard (December 29, 2015). "Ford Patent Could Transform Your Car Into A Unicycle". The Car Connection. Internet Brns Automotive Group. Retrieved 10 September 2016.
- Carnegie Mellon Press Release, August 6, 2006 – "Ballbot"
- Ruan, Jian-Wei Zhao; Xiao-Gang (1 September 2011). "Modelling and Control of a Flexible Two-Wheeled Self-Balancing Mobile Robot". 3 (3): 330–355. doi:10.1504/IJSCC.2011.042438 – via ACM Digital Library.
- Flexible two-wheeled self-balancing mobile robot, 9th IFAC Symposium on Robot Control (2009)
- Wu, Junfeng; Zhang, Wanying; Wang, Shengda (26 November 2012). "A Two-Wheeled Self-Balancing Robot with the Fuzzy PD Control Method". 2012: 1–13. doi:10.1155/2012/469491.
- "SELF-BALANCING MOBILE ROBOT TILTER".
- "What is a Swegway?". Swegwayshq.com.
- ANALOG — Science Fiction/Science Fact, Vol. LXXXIII, No. 5, July 1969, pp. 120-151. Illustrations by Peter Skirka.
- "Little Wheel - game at". Fastgames.com. Retrieved 2013-04-26.
- 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  The Lyapunov-Malkin Theorem and Stabilization of the Unicycle with Rider. Systems and Control Letters, Volume 45, Number 4, 5 April 2002, pp. 293–302(10) (postscript 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
- A. Schoonwinkel, "Design and test of a computer stabilized unicycle," Ph.D. dissertation, Stanford University, California, 1987.
- Johnson, R.C. Unicycles and bifurcations, American J. of Physics, volume 66, no.7, 589-92
|Wikimedia Commons has media related to Solowheel.|
- Bombardier Recreation Products EMBRIO one-wheeled recreational vehicle concept design
- The loonycycle, which superficially resembles a simple robotic unicycle, but uses side-thrusting fans for lateral balance
- Rosie the Robot - a Question of Balance Ken Perlin's page on robotic unicycles, with designs and java applet examples.
- The Unibot: a working robotic unicycle built for a university engineering project (with movies)
- Robotic Unicycle: Ongoing project
- Micycle (reports, papers, photographs and movies)
- "Unicycle riding robot unveiled". BBC News. 24 September 2008. Retrieved 2008-11-24.