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 Edit
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 Edit
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 Edit
Single-axis self-balancing ridable unicycles Edit
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. 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 Edit
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 Edit
- 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 Edit
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.
- 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 Edit
- 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
- The Enicycle, a true 2-axis self-balancing unicycle
- Gizmodo article: Self-Balancing eniCycle is Like a Segway for the Circus
- Honda unveils U3-X – a battery-powered unicycle
- The R.I.O.T Wheel
- Le Monorue
- Hack A Day: Motorized unicycles
- Hack A Day: Commercial self-balancing unicycle
- 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.
- Pixar - Red's Dream, a short CGI movie depicting a unicycle riding itself
- The Unibot: a working robotic unicycle built for a university engineering project (with movies)
- Home made unicycle: Radio controlled unicycle robot (with movies)
- Lego Unicycle (RCX): with very simple software (movie and links to controller software)
- Robotic Unicycle: Ongoing project
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