Coaxial Swerve Derivation with Paired Modules

[Ether]

Originally Posted by Oblarg

If I'm guessing correctly, the cusp is due to the transition between traction-limited and motor-limited.

Correct.

I wonder why there is a slight decrease in acceleration while traction-limited as the speed increases, though?

Yes, that's the one I was expecting to get questioned about.

See if you can figure it out with the following hint: Notice that Krv is set to a non-zero value.

[Oblarg]

Originally Posted by Ether

Correct.



Yes, that's the one I was expecting to get questioned about.

See if you can figure it out with the following hint: Notice that Krv is set to a non-zero value.

Ah. The rolling friction losses are being applied (incorrectly, I'd think) even when the wheels are slipping.

[Ether]

Originally Posted by Oblarg

Ah. The rolling friction losses are being applied (incorrectly, I'd think) even when the wheels are slipping.

It's not incorrect if you look closely at what Krv is supposed to be. It's supposed to be rolling resistance force proportional to vehicle speed (not wheel speed).

[Oblarg]

Originally Posted by Ether

It's not incorrect if you look closely at what Krv is supposed to be. It's supposed to be rolling resistance force proportional to vehicle speed (not wheel speed).

Yes; I meant incorrect compared to what is actually physically happening.

I imagine even if you corrected it to be wheel speed it would not be quite right, since it's supposed to be accounting for rolling friction losses, and clearly the physics are pretty different when you're slipping the wheels from when you're rolling.

[Ether]

Originally Posted by Oblarg

Yes; I meant incorrect compared to what is actually physically happening.

What is actually physically happening is quite complex, and the model provides 3 parameters to attempt to model it: Kf, Kro, and Krv.

You can set the values of these parameters to whatever you believe best reflects the physics.

Wind resistance depends on vehicle speed, not wheel speed. The force required to plow through the carpet arguably depends more on vehicle speed than wheel speed. You can use Krv to attempt to account for those effects.

the physics are pretty different when you're slipping the wheels from when you're rolling.

That is true, and the friction model used attempts to account for these differences. Friction models are notoriously tricky. In this model, I used a "standard" static/kinetic friction model... so when the wheels are slipping, the torque on the wheels is constant at uk*normal_force*radius, and the wheels will be spinning at whatever speed that corresponds to on their torque vs speed curve, at the voltage derated for resistance losses in the circuit. When the vehicle speed finally catches up to wheel speed, the friction model transitions to static friction.

[Oblarg]

Originally Posted by Ether

Wind resistance depends on vehicle speed, not wheel speed. The force required to plow through the carpet arguably depends more on vehicle speed than wheel speed. You can use Krv to attempt to account for those effects.

I'd naively think that when you're slipping the wheels you wouldn't have much of an effect from vehicle speed at all; in the reference frame of the wheel, the only thing vehicle speed does is decrease the effective rotational speed of the wheel (almost negligibly at those speeds, at that). It's not clear what effect that would actually have on the force generated by the wheel.

[Ether]

Originally Posted by Oblarg

I'd naively think that when you're slipping the wheels you wouldn't have much of an effect from vehicle speed at all; in the reference frame of the wheel, the only thing vehicle speed does is decrease the effective rotational speed of the wheel (almost negligibly at those speeds, at that). It's not clear what effect that would actually have on the force generated by the wheel.

As I stated in the previous post, the force exerted on the wheel by kinetic friction with the carpet is modeled to be constant (independent of relative slip speed) when the wheel is slipping.

But the acceleration of the vehicle depends on the net external force on the vehicle, not just the kinetic friction force of the carpet acting on the wheel.

Krv allows you to account for that. A robot with a large "shot-blocking shield" for example could generate windage force. The carpet could generate speed-dependent force to plow through it.

I'm not claiming that 0.5 is a "typical" value for Krv. AFAIK, nobody yet has empirical data to establish a typical value. But if there is a vehicle-speed-dependent force resisting the robot motion, Krv is there in an attempt to model it. The model is a teaching tool - it allows you to see what effect a vehicle-speed-dependent resisting force has on robot acceleration.

I'd be willing to bet that if someone ever runs some precision tests of robot acceleration with wheels slipping over a sufficient speed range, it will show a decrease in acceleration with speed as shown in the plot (i.e., Krv>0).

I've attached a plot showing the effect of changing Krv to 0 (notice the flat line when the wheels are slipping), and of changing μ_s to 2 (not realistic I know, but it shows what the 6CIM would do if not traction limited).

[Oblarg]

Originally Posted by Ether

The carpet could generate speed-dependent force to plow through it.

This is where I'm not following. If the wheels are slipping, then the wheels are never "plowing through carpet" in that direction; they're plowing in the opposite direction, but plowing less as speed increases. I do not think it is obvious that this will necessarily decrease the acceleration of the robot, or that the robot-speed model that you use to calculate the drag of moving through carpet when rolling is at all valid in that situation.

I need to go to bed, but I'll draw some pictures tomorrow to explain my confusion.