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It Takes Two Neurons to Ride a Bicycle (2004)

paradise.caltech.edu

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Re: It Takes Two Neurons to Ride a Bicycle (2004)

#61

Post by kevin_thibedeau »

GoToRO wrote: post #52

There are no secrets to riding a bike: 1. Do no try to go straight. Move the handlebars violently left and right when you feel you are falling left or right. 2. Going slow is hard. Go fast. The wheels spinning will behave as stabilizers, making it easier to stay on the bike. 3. Moving your body will make you fall at first if you do not counteract by moving the handlebar. Start by going downhill, without pedaling.

> The wheels spinning will behave as stabilizers, making it easier to stay on the bike.

Bicycle wheels do not have enough mass to impact handling through gyroscopic inertia. They do not act as stabilizers.

Motorcycle wheels do, and consequently they require more effort to lean at higher speeds as well as require additional lean when accelerating into a curve.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#62

Post by aidenn0 »

dahart wrote: post #51

> There is not a direct or fixed correspondence, but as a general rule, during stable riding, a higher clockwise torque on the handlebars will cause the bicycle to start leaning more to the left It's counter-steering! I was glad to read that counter-steering is accounted for and works in their physics simulation like it does in the real world. I don't have a source handy, but I believe that there is a fixed correspon…

The fixed correspondence between leaning and turning is easy to derive on your own:

Draw a picture of a leaning bike from behind. Add a horizontal line for the ground. Assume the entire bike/human system is leaning an equal amount, so put the center-of-mass somewhere in the leaning line.

If the bicycle is maintaining a constant amount of lean, then the extended line of the force applied by the ground to the bike must pass through the center of mass (i.e. in this case the angle of the force vector is the same as the angle of lean).

Now decompose the force vector into vertical and horizontal components. The vertical portion when riding on the ground (i.e. not jumping the bike), neglecting aerodynamic effects, is fixed to be the gravitational force, so it will be constant regardless of the direction of lean.

This means that the horizontal portion of the force will be equal to the the gravitational force times the tangent of the lean-angle. This also means that when the tangent of the lean-angle exceeds the coefficient of friction between the tires and pavement, you will crash.

The turn-radius can then be calculated by treating the horizontal force as the centripetal acceleration, and is indeed related to speed (faster speeds mean a larger turn radius).

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#63

Post by andrewflnr »

lucb1e wrote: post #50
chestervonwinch wrote: post #31

Earlier quoted context omitted.

1) Sometimes it's actually helpful to use greek letters when a convention is used. For example: capitals for matrices (A), lowercase for column vectors (a), and Greek for scalars (α). 2) I agree with the gist of your point, but I'm guessing you're being down-voted because you come off as sort of flippant. Anyhow, I've long thought that mathematics should have hover-text to help remove the mental overhead of translati…

> Obviously, using variables names like `velocity_of_thing` is much too verbose in mathematics That is not obvious to me. Perhaps in a purely mathematical paper with dozens of formulas, but that's not my field of study. In any paper I read of any discipline, I never came across any paper filled with enough formulas that it would make sense to compress at the cost of clarity. I fully agree, though, on following conven…

It's like programming languages: people want loud syntax for things that are new, but short syntax for familiar concepts.

Math is heavily optimized for peope already familiar with the topic at hand. In many cases, that's the only way you have a chance of understanding the paper at all. So long names would just be noise to the main audience of the paper.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#64

Post by dahart »

aidenn0 wrote: post #62
dahart wrote: post #51

> There is not a direct or fixed correspondence, but as a general rule, during stable riding, a higher clockwise torque on the handlebars will cause the bicycle to start leaning more to the left It's counter-steering! I was glad to read that counter-steering is accounted for and works in their physics simulation like it does in the real world. I don't have a source handy, but I believe that there is a fixed correspon…

The fixed correspondence between leaning and turning is easy to derive on your own: Draw a picture of a leaning bike from behind. Add a horizontal line for the ground. Assume the entire bike/human system is leaning an equal amount, so put the center-of-mass somewhere in the leaning line. If the bicycle is maintaining a constant amount of lean, then the extended line of the force applied by the ground to the bike must…

Yeah, that's a useful breakdown, thank you!

Does this help to explain the fixed correspondence between steer and direction of turn? (For example, to someone who doesn't believe counter-steering is a thing.) The physics of the lean seems easier to decompose than the physics of counter-steering.

I am interested in finding a way to describe counter-steering so that it's obvious, similar to the way you described the horizontal force vs coefficient of friction.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#65

Post by hexane360 »

dahart wrote: post #49
hathawsh wrote: post #8

Does a Raspberry Pi have enough computing power to run these two neurons in the real world? Could I attach motors and sensors to a real bike and have it drive itself? That would be amazing.

Fun fact: PID controllers are embedded into the wiring of today's brushless hobby motors, the kind used for drones, for example. The last motor I dissected had a tiny little ATMEL 8-bit 1Mhz chip shrinkwrapped into the wires that controls the phase of the magnets that drive the motor, to make sure it matches the spin rate and make sure it doesn't skip or get out of phase. ATMEL published a whitepaper on the PID contr…

Not surprising, given that we had mechanical PID controllers working with extreme accuracy (steering a ship in severe weather) in 1922.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#66

Post by hexane360 »

GoToRO wrote: post #52

There are no secrets to riding a bike: 1. Do no try to go straight. Move the handlebars violently left and right when you feel you are falling left or right. 2. Going slow is hard. Go fast. The wheels spinning will behave as stabilizers, making it easier to stay on the bike. 3. Moving your body will make you fall at first if you do not counteract by moving the handlebar. Start by going downhill, without pedaling.

2. is the correct outcome but not the correct explanation. The real explanation is that turning inputs have a greater effect on balance at high speed. Turning input directly relates to turning radius, which, when combined with the square of tangential velocity, gives centripetal acceleration. This centripetal acceleration is used to counteract an imbalance of the body/bike system.

Basically, the faster you go, the easier it is to influence your balance on the bike. If you go fast enough you can get too much influence, which is how speed wobbles happen.

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#67

Post by 21 »

goialoq wrote: post #43
hathawsh wrote: post #8

Does a Raspberry Pi have enough computing power to run these two neurons in the real world? Could I attach motors and sensors to a real bike and have it drive itself? That would be amazing.

No, because the model described in the paper only works for an extremely simplified toy simulation of a bicycle, not a real bicycle riding on a real road that is not a spherical cow.

https://www.youtube.com/watch?v=mT3vfSQePcs

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#68

Post by 21 »

GoToRO wrote: post #52

There are no secrets to riding a bike: 1. Do no try to go straight. Move the handlebars violently left and right when you feel you are falling left or right. 2. Going slow is hard. Go fast. The wheels spinning will behave as stabilizers, making it easier to stay on the bike. 3. Moving your body will make you fall at first if you do not counteract by moving the handlebar. Start by going downhill, without pedaling.

I don't think I've ever heard about somebody which knew how to ride a bike after just reading some text :)

Re: It Takes Two Neurons to Ride a Bicycle (2004)

#69

Post by einstok »

dahart wrote: post #64
aidenn0 wrote: post #62

Earlier quoted context omitted.

The fixed correspondence between leaning and turning is easy to derive on your own: Draw a picture of a leaning bike from behind. Add a horizontal line for the ground. Assume the entire bike/human system is leaning an equal amount, so put the center-of-mass somewhere in the leaning line. If the bicycle is maintaining a constant amount of lean, then the extended line of the force applied by the ground to the bike must…

Yeah, that's a useful breakdown, thank you! Does this help to explain the fixed correspondence between steer and direction of turn? (For example, to someone who doesn't believe counter-steering is a thing.) The physics of the lean seems easier to decompose than the physics of counter-steering. I am interested in finding a way to describe counter-steering so that it's obvious, similar to the way you described the hori…

If you are going straight at a constant speed and you turn the handlebars clockwise your front wheel is going to go to the right. The center of mass will want to continue forward due to the momentum of the bike. Now your bike is leaning left.
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