What is the friction coefficient value used in the Magic Tire Model in ADT Stanley Controller for an Autonomous Vehicle (Highway)?

I am simulating ADT Stanley Controller for an Autonomous Vehicle (Highway), and I would like to know what value is used for the friction coeffcient (μ) in the implementation of ADT Stanley Controller for an Autonomous Vehicle (Highway). Can anybody help please?

Best, Kanat.

[Torsten]

The question is too specific to be answered in this forum.

You should ask your question here in the "Discussions" part:

https://uk.mathworks.com/matlabcentral/fileexchange/88977-vehicle-path-tracking-using-stanley-controller

[Kanat]

thanks Mr. Torsten!

Answer 1

[Matthew]

Kanat,

This example implements the "Combined Slip Wheel 2DOF" block with a default built-in tire model parameter set. The parameter values are obfuscated and can't be edited for the built-in model options. However, you can adjust the friction scale factors via the "Friction" constant block at the top level of the Simulink model. It is 1 by default.

This value is assigned to the LMUX (lam_mux) and LMUY (lam_muy) friction scale factors. A value less than 1 will decrease the peak friction, and a value greater than 1 will increase the peak friction.

Please be aware these are scaling factors for the friction, not the friction coefficient.

Matt

[Kanat]

@Matthew, yes, I saw those scaling factors, but I expect to see values for the peak friction, mu, such as 0.8 or 0.5, so they could not be seen in the built-in tire model? If I want to set a friction coefficient mu = 0.8, how can I do that?

I want that value for my friction coefficient estimation algorithm, and I want to see that my estimation is converging to the actual friction coefficient value.

Thanks!

[Matthew]

@Kanat, unfortunately, the parameter values for those built-in tire models are obfuscated.

In any event, the Magic Formula tire model does not have a global peak friction cofficient value. The longitudinal and lateral friction coefficients are dependant on normal load, inflation pressure, and inclination angle. In the longitudinal direction, the peak friction cofficient is determined using parameters PDX1, PDX2, PDX3, PPX3, and PPX4.

If you have the Extended Tire Features for Vehicle Dynamics Blockset support package installed, you could plot the tire model's behavior to determine the approximate peak friction coefficient at specific conditions. For example:

tm = tireModel.builtin("Mid-size passenger car 235/45R18");
plot(tm,"Direction","kappa","Fz",[2000,4000,6000],"gamma",0);

This should help give an approximation for this tire model.

I should also advise that the tire will not always be operating at this peak friction coefficient. At slip values more or less than the slip of peak force (most of the time), the tire's force coefficient (Fx/Fz and Fy/Fz) will be much less than the peak cofficient of friction.

If you're interested in the cofficient at all times, and not just the peak cofficient of friction, you might consider intercepting the Fx, Fy, and Fz out port signals of the tire block location in "stanleyHighway/Powertrain & Driveline/Brakes and Wheels" in that example and calculate the Fx/Fz and Fy/Fz values throughout the simulation.

[Kanat]

@Matthew, thanks for your explanation. Now, it makes sense.