Rolling Resistance - proportional to speed?

Hi all you physics people.... we are building a high-speed robotic camera dolly here in LA for a film, and are trying to make sure we calculate our torque requirements correctly.

The maximum torque required to propel a wheeled vehicle up an incline at a given acceleration is fairly easy to understand. But how in the heck do you figure the rolling resistance of the wheels into that basic equation?

I do know the basic equations to calculate the rolling resistance force, based on a coefficient at 3 mph... but does this stay the same no matter what the speed?

I've read conflicting accounts that the rolling resistance force is linearly proportional to speed... but then have also heard and seen in numerous bicycle charts, that it is a relative constant???

It makes a HUGE difference if is linearly proportional, and we will need huge motors.

Really need to figure this out as we have a lot of wheels on the dolly that are guide wheels and drive wheels that do not support the load, but are spring loaded with lots of force.

We are using this formula for our basic torque calculation :

Where:
T= torque at the drivewheel
a=desired acceleration
g=acceleration of gravity
θ= incline of ramp
m=mass of vehicle
R=radius of drive wheel

Many thanks to you all!