Self-stabilizing Autonomous Bicycle

For [Gunnar]’s diploma thesis, he wanted to build an autonomous bicycle. There’s an obvious problem with this idea, though: how, exactly does a robotic bicycle stand upright? His solution to balancing the bicycle was a reaction wheel that keeps the bicycle upright at all times.

A bicycle is basically an inverted pendulum; something we’ve seen controlled in a number of projects. To balance his driver-less bike, [Gunnar] used a stabilizing wheel and an IMU to make sure the bicycle is always in the upright position. The bike measure the tilt and angular velocity of itself, along with the speed of the stabilizing wheel. To correct a tilt to the left, the stabilizing wheel spins clockwise, and corrects a rightward tilt by spinning counterclockwise.

While [Gunnar]’s solution of a bike wheel used as a gyroscope is clever – it uses common bicycle wheel, hugely reducing costs if someone wants to replicate this project – there’s not a whole lot of ground clearance. The size of the stabilizing wheel could probably be reduced by replacing the 7.4 kg steel wheel with a Tungsten, Osmium, or Lead disk, possibly becoming so small it could fit inside the frame. Still, though, a very nice build that is sure to turn a few heads.


52 thoughts on “Self-stabilizing Autonomous Bicycle

    1. I have a R/C motorcylce that stands about 12 inches tall, in which you steer by shifting the weight of the “driver” (a model of a person that shifts left to right under proportional remote control). Shifting the weight tilts the bike which turns the front wheel (just like riding a bicycle with “no hands” by shifting weight). It works great while moving reasonably fast, but at slow speed it is very easy to tip over (just like a real bicycle with no hands).

      Using that R/C model proves to me that the same should work on a full-sized R/C bicycle even with no driver model, by connecting a steering motor to the front neck under the handlebars. What would be more fun is to ride that bike using GPS and autonomous steering. If you are going fast enough, I do not think you need the reaction wheel, unless you want the bike to balance when it is NOT moving forward (is that really needed?) ;-)

      1. Thanks for your request.This project is the first step and more challenging part for building a selfdriving bicycle.The University of Berlin has got several experiences with autonomous cars,but would like to test this on a bicycle aswell.The first step for this is to stabilize while the bike does not move.Next step will be controlling the steerage, so it will be balanced while the bike moves forward.Check out for motivation:
        Bicycle Robot
        C1 from

    2. Any bike you own already has this feature – above a certain treshold speed, bikes are stable, and if no one’s sitting on them they can ride indefinitely (well, at least they won’t fall over above the treshold speed).

      1. PS this is also the reason you can ride without hands – steering actually is not necessary as long as you’re cycling fast enough: your bike is stable from a control-theoretical point of view.

      2. And your bicycle is not self-stable when you are riding it without hands. The rider is a critical component of the servo loop, using vestibular feedback to control weight shifting from side to side to compensate for systemic dynamic instability mentioned in my previous post.

      3. In other words, the wheels provide gyroscopic filtering of high-frequency instability, resulting in a low-frequency precession instability that is within human reaction time, allowing manual course correction to counteract the force of gravity and maintain an upright attitude while “driving” a bicycle.

      4. Bicycle stability is not well understood, so it is not surprising that a few misconceptions have been voiced. The paper “A bicycle can be self-stable without gyroscopic or caster effects”,
        Science 15 April 2011: 332(6027), 339-342, turns the subject on its head by challenging some deeply held beliefs: [].

        Tulcod: Conventional bicycles are not unconditionally stable “above a threshold speed”. The eigenvalues tell the truth, and for a conventional bicycle they specify a stability speed range, above – or below-which the bicycle loses stability.

        Rob: Precession is neither an explanation for stability nor instability. It is, in this case, one component of a complex mechanical system. A theoretical frictionless bicycle coasting in a vacuum could remain upright forever if started within its range of unconditionally stable parameters. By the way, as the title of the paper I cited states, gyroscopic effects are not necessary for “bicycle” stability (provided your definition of bicycle is sufficiently inclusive).

      5. ken: That is why I said “gyroscopic precession forces applied to the two wheels by the force of gravity”. I was tempted to mention that you could be stable outside gravitational influences (if such a place could be found and you chose a suitable reference for the relativistic “up” direction in which to frame your definition of “stability”).

      6. But even outside the forces of gravity, to achieve total long-term stability you would also have to to free of the influences of solar winds and micrometeorite impacts.

        Regarding your linked paper, it is definitely interesting, and now has me challenging beliefs I held since I learned about bicycle gyroscopic stability in a Physics course at the university. After reading in that paper that a bicycle is stable even with no significant gyroscopic forces and even with no “trail”, I now believe that bicycles are held upright by sheer strength of human willpower beyond the understanding of mere Physical science. ;-)

      7. Actually, I was just kidding about changing my beliefs. The “bicycle” used in that paper and videos shows significant “trail” by artifically putting weight forward of the front wheel, in a way that is NOT found on a traditional bicycle, and you obviously see that placing the weight forward of the front wheel makes it steer into the turn compensating for tipping. A normal bicycle a similar property by pushing the front wheel axis forward of the handlebars by tilting the steering axis and by using a curved front fork. Even so, it is only partial compensation and will not keep the bike stable at slow speeds.

        Also, regarding your claim about a bike being stable in a vacuum — are you sure about that? You also need no gravity or other external forces causing a reduction of forward velocity (wheel friction alone would reduce the speed until gravity pulls it over).

      8. Rob – The frictionless bike is stable in a gravitational field. That’s really the point. Frictionless precession is energy conserving, so the bike resumes its ideal speed once it recovers from a disturbance.

        Also, I admire your insight about the Cornell/TU Delft “bike”. The best the authors, who are bona fide bike physics fanatics, have to offer is that the eigenvalues are positive. If you are really sure about your insight, you ought to contact them … but do some reading first.

  1. I’m guessing this is inspired by the Gyrobike, a well-known product sold to help teach kids to ride bikes as an alternative to training wheels. It mounts a gyro in one of the bike’s existing wheels to make the bike self-balance to some extent (a little more elegant than this solution). Here’s a link:

    1. Bikes with wheels smaller than 20-inches are extremely unstable even at higher speeds due to the lack of gyroscopic stability from those tiny wheels. Those tiny wheels also encourage slower riding where they are especially unstable. In that case, additional gyroscopic stabilization from a power-hungry add-on gyrobike wheel would make those tiny wheels less of a problem for beginners, but a much better solution is to learn to ride with a 20-inch wheel and a little “push-off” from a parent to get up to a stable speed before trying to steer.

    1. That video is a neat example of gyroscopic precession forces acting on a single wheel to make if fall slowly to the ground. That is exacly the force that you compensate for when you turn steer by turning the handlebars and/or shifting your weight.

    1. This diploma thesis is about balancing a standing bicycle”. Also not clear if autonomous meant to apply to balancing the bike aid only, or the intent is to have an entirely autonomous one track vehicle. In any event a simple toe guard would keep your little piggies attached.

  2. What’s the use of a bike like this? If a better design idea exists, the gyrowheel? This bike is, at best, a bad bar joke: “Did you hear the one of the three wheeled bike…only one [wheel] worked”, Did you hear the one of one training wheel bicycle? The rider was 20 years old. Heard of the cyclist who had an accident on his bicycle, his body was entwined within the three wheels of his bike. Sometimes when it looks better on paper, it’s better to be a cartoonists. Think Rube Goldberg.

      1. Did you hear the one about the guy who got his toes caught in the spokes of the reaction wheel? ;-)

        Yeah, I did…took up running and found he was better at it, than riding a gyrobike…that is to say, was better off in the first place.

    1. Thanks for your request.This project is the first step and more challenging part for building a selfdriving bicycle.The University of Berlin has got several experiences with autonomous cars,but would like to test this on a bicycle aswell.The first step for this is to stabilize while the bike does not move.Next step will be controlling the steerage, so it will be balanced while the bike moves forward.Check out for motivation:

      Bicycle Robot


      C1 from Litmotors

  3. most self stabilized bikes are stable while they are moving – but the idea of this project is to have a bike like an autonomous car which drives by itself – imagine as a robot that can transport stuff –

    another motivation is the C1 from litmotors as a gyrocar. you’v got a car which is a on track vehicle . but you need something to be stabilized when you’ve got to stop —
    imagine the safety of a car but dynamic of a motorbike

  4. What was the use of this device? To be the basis of a diploma thesis for a *autonomous* bicycle,not transport —–( the utilization of this principle is best left as a exercise for the astute ) :-D

  5. Very cool build however while the replacement of the wheel with lead or tungsten is a great idea, just one made of osmium would cost over half a million since the stuff is pretty damn pricy. And since bikes get stolen all the time you’d want a pretty big bike lock on that thing.
    but none-the-less a good demonstration of physics in practise :D

    1. cost by side osmium is like the real life version of adamantium how the heck do you want to machine that stuff into a wheel?
      oh and by the way did i mention that it reacts with oxygen /air and most of its compounds are insanely toxic?

  6. @Brian Benchoff

    Osmium would be a poor choice as a replacement material for the wheel, 7.4 kg of osmium is ~$100,000; not exactly what I might call a hobbyist budget.

    Also, denser materials only do so much. Rotational inertia goes as mR^2. So a lead wheel is 87% as big as the steel one.

  7. I understand building something for no reason other than the builder wanted to. Now that I’m aware of the concept of autonomous two wheel vehicle in a bicycle configuration, I left with pondering possible practical or even not so practical applications. Seems as a Segway like two wheel autonomous vehicle would be able to operate in more environments.

  8. why replace the steel wheel with an exotic metal disk? Wouldn’t one be able to achieve the desired gyroscopic forces with a slightly smaller steel disc, simply because it would fill in the open area of the spokes?

  9. Why a wheel at all. A sliding weight should work.
    I like the 1911 touring car I saw in an old (XXyears ago column)Popular Mechanics. Driver and mechanic, club seating for 6. All on TWO wheels, gyro stabilized. A century ago!

  10. Cite: “bike wheel used as a gyroscope”. This is inexact, the wheel is used as a reaction wheel instead.
    The reaction wheel produces a momentum by just accelerating its rotation around its axle.
    On the other hand in a gyroscope the rotation of the wheel is constant, however the wheel needs to be gimballed so that the rotation axle is itself rotated to produce a momentum.

  11. Autonomous Bicycle stabilized by an accelerated reaction wheel and
    modelled as an inverted pendulum:

    This diploma thesis is about balancing a standing bicycle. Stabilizing this one-track vehicle was modelled on the basis of an inverted pendulum which also served as preliminary study on controlling algorithms and on the applicability of electronic equipment utilized in the later campaign.
    Measured state variables being crucial for the controlling are listed below:

    – Inclination angle of the pendulum / bicycle
    – Angular speed of the pendulum / bicycle
    – Speed of rotation of the wheel

    Rotation of the reaction wheel is measured by an optical incremental encoder which is attached to the shaft of the Faulhaber DC-Motor. The supply voltage to the DC-Motor controls the speed of rotation of the wheel. It is provided by a 24V lead battery. An H-Bridge regulates the turning direction and the required voltage by a pulse width modulation. The motor equation gives information about the current, which is proportional to the torque. The Torque of the reaction wheel minimizes any angular pitch which is measured by the inertial measurement unit CHR-6d. Good stabilization results were achieved with a Classical Riccati Controller.

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