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Unread 01-15-2018, 10:40 AM
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Skid Drive Longitudinal Slip Percent

I am attempting to use encoders for localization of a skid steer robot. Among others, I am using the paper Experimental Comparison of Skid Steering Vs. Explicit Steering for a Wheeled Mobile Robot to do this.

The paper states:


What I do not understand is why the formula isn't simply i=(1-R/r)*100, where R is the radius of the wheel. I must be understanding this wrong because I have seen this same formula in multiple papers; it doesn't make sense to base the formula off of dynamic variables when it can be based off of static ones. Can someone enlighten me?
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Unread 01-15-2018, 11:01 AM
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Re: Skid Drive Longitudinal Slip Percent

This is a ALL new to me, but if the equation is what you are thinking it should be, the i value would be 0... always.

The idea is that if the V value is larger than that of a "non slipping" wheel, then V/omega is larger than R, and you gain a slip percentage.
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Unread 01-15-2018, 11:56 AM
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Re: Skid Drive Longitudinal Slip Percent

I don't understand why you think the slip percentage has anything to do with the radius of the wheel. What is R and r in your proposed equation?

As for explaining the original equation:
It's a way of describing the slip percentage in terms of things that could be known, not really a way of keeping slipping to a minimum.

Let v (small v) be the linear speed of some point at the edge of the wheel. I like to think of it as the point where the wheel contacts the ground. From physics, v = rw, or wheel radius times angular speed of the wheel.

Thus the important part of the equation is V/v. Because our wheels are fixed, V (big V) is the speed of the robot. If V is 0 and v is nonzero, our wheels are moving but the robot isn't, and our slip will be 100% e.g. the wheels are just spinning. If V = v, then the speed of the robot is the same as that of the wheels.
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Unread 01-16-2018, 11:20 AM
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Re: Skid Drive Longitudinal Slip Percent

Quote:
Originally Posted by AndrewGazelka View Post
I am attempting to use encoders for localization of a skid steer robot. Among others, I am using the paper Experimental Comparison of Skid Steering Vs. Explicit Steering for a Wheeled Mobile Robot to do this.

The paper states:


What I do not understand is why the formula isn't simply i=(1-R/r)*100, where R is the radius of the wheel. I must be understanding this wrong because I have seen this same formula in multiple papers; it doesn't make sense to base the formula off of dynamic variables when it can be based off of static ones. Can someone enlighten me?
It looks like you got a very reasonable answer above. If it still does not make sense, I would recommend checking out a book on Vehicle Dynamics like Gillespie or Wong as they will have additional info. Wong is probably better for this application as he has some additional examples and text on skid steer dynamics.

Thanks for the tip to this paper, I am pretty excited to read through it and see what the author has to say.

Based off the project you are doing, you might want to look into some of the setups from 2009. The slick surface had many teams making their own "follower" wheels to help measure slip and create homemade traction control and launch control algorithms.
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Unread 01-16-2018, 12:48 PM
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Re: Skid Drive Longitudinal Slip Percent

Our team has done some analysis and found that, so long as linear accelerations are low enough to avoid slipping the wheels, wheel scrub in a FRC differential drive is well-approximated by using an "effective trackwidth" somewhat larger than the robot's geometrical trackwidth, with everything else treated as if there is no wheel slip of any sort. The "effective trackwidth" does not appear to depend on either linear or angular velocity of the robot.

To measure the "effective trackwidth," simply turn the robot in place by driving the wheels a known distance, and measure the resulting angular displacement.
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Unread 01-16-2018, 02:45 PM
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Re: Skid Drive Longitudinal Slip Percent

A possible explanation as to why the longitudinal slippage depends on torque is because the wheel and substrate deform as torque is applied. To take an extreme example, check out this top-fuel drag racer wheel:

https://i.imgur.com/tlkJh1Y.gifv

The wheel sits there at one resting radius, as soon as torque is applied you can see the wall of the tire ripple and reduce the effective radius of the tire.
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