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The problem of creating a self-balancing unicycle, a self-powered unicycle that balances itself in three dimensions, is an interesting problem in robotics and control theory.

The theoretical work on the unicycle problem is complemented by work on the construction of actual mechanically ridden unicycles.

Control theory of the self-balancing unicycle[]

To first order, 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: however, 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 (i.e., 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.

Early work[]

A number of academic papers have been published that either investigate the problem theoretically, or document laboratory-scale prototypes. A number of student and amateur engineering projects have implemented similar designs. Self-riding self-balancing unicycles are necessarily two-axis balancing devices.

Human-ridable self-balancing unicycles[]

Single-axis self-balancing ridable unicycles[]

A number of self-balancing unicycles have been created which are self-balancing only in the forwards-backwards direction, and still need a human being to balance them from side to side. Trevor Blackwell's Eunicycle is an example of a human-ridable single-axis self-balancing unicycle. Focus Designs advertise a similar device commercially.[1] The R.I.O.T. 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 both forwards and backwards and also side to side. Aleksander Polutnik's Enicycle is probably the first two-axis balancing human-ridable unicycle.

Conceptual designs[]

  • 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.

Similar-looking vehicles that are not true unicycles[]

A number of vehicles are almost 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 rather than being capable of balancing from side to side.
  • In 2006, Carnegie Mellon developed a 2-dimensional inverted pendulum that balances on a ball rather than a wheel.[2]
  • The Uno (vehicle), 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 wheel rather than on a single wheel

Fictional self-balancing unicycles[]

Fenton Crackshell, a Disney character, is depicted wearing a robotic unicycle suit. Demolishor, a Decepticon from the 2009 Transformers sequel, whose robot mode is a gigantic robotic unicycle.

See also[]

  • Inverted pendulum
  • Inertia wheel pendulum
  • Control moment gyroscope


Further reading[]


  • 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 [2001] 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


External links[]