How much Torque is needed to do Skid Steering

[vsming]

Hello, I need help in figuring out how much weight can Lynxmotion A4WD1 (http://www.lynxmotion.com/p-657-a4wd1-combo-kit-for-autonomous.aspx) carry
if it is equipped with four GHM-04 motors (http://www.lynxmotion.com/p-96-gear-head-motor-72vdc-501-175rpm-6mm-shaft.aspx)
but still be able to "smoothly" perform Skid Steering (a.k.a. Tank Steering)
such as Spin (In Place Pivot) and Hard Turn (Circular Pivot) according to http://www.beam-wiki.org/wiki/Steering_Techniques

The Lynxmotion A4WD1 is equipped with four 4.75" (0.12065 m) RC truck tires (http://www.lynxmotion.com/p-108-off-road-robot-tire-475d-x-2375w-pair.aspx)
and its total mass is around 2.1kg (wheels + chassis + electronics).

Below are some of GHM-04 motor's specs (worst-case scenario):
Rated Voltage          = 7.2 V
Rated Torque/Load   = 1.0000 kgf-cm = 0.0981 Nm
Stall Torque             = 7.1000 kgf-cm = 0.6963 Nm
Speed at Rated Load = 131.4 RPM = 2.19 RPS
Efficiency at Rated Load = 40% to 45%

I would like the A4WD1 to carry a payload of at least 4.9kg (giving a total mass of 7kg),
and I estimate its expected efficiency to be 30%,
because GHM-04's efficiency is already around 40%, so (40% * 75% = 30%)

Using RobotShop's calculator in http://www.robotshop.ca/dc-motor-selection.html
with the given input (7kg, four 0.0603m radius tire, 30% efficiency)
to produce the desired torque of 0.0981 Nm (GHM-04's rated torque),
and using the RMF equation in http://www.societyofrobots.com/mechanics_dynamics.shtml
I obtain the following performance:

Under an incline of (0       degree ), A4WD1 can accelerate (0.2788 m/s^2) to a velocity of (0.8299 m/s)
Under an incline of (1       degree ), A4WD1 can accelerate (0.1075 m/s^2) to a velocity of (0.8299 m/s)
Under an incline of (1.628 degrees), A4WD1 can accelerate (0        m/s^2)

Which are obtained by rearranging the Torque relation in http://www.robotshop.ca/drive-motor-tutorial.html
to solve for acceleration as a function of incline angle (units omitted below):

T = (100/e)*(a + g*sin@)*M*R/N
0.0981 = (100/30) * (a + 9.81*sin@) * 7 * 0.0603 / 4
0.0981 = (a + 9.81*sin@) * 0.35175
0.2788 = a + 9.81*sin@
a = 0.2788 - 9.81*sin@

And using this acceleration into the RMF equation in http://www.societyofrobots.com/mechanics_dynamics.shtml
to solve for velocity (units omitted below):

Torque * RPS >= Mass * Acceleration * Velocity * (100/efficiency%) / (2*PI) / #Wheels
Where:
   Acceleration = a + 9.81*sin@ = 0.2788 - 9.81*sin@ + 9.81*sin@ = 0.2788
Gives:
Torque * RPS  >= Mass * 0.2788 * Velocity * (100/efficiency%) / (2*PI) / #Wheels
0.0981 * 2.19 >= 7    * 0.2788 * Velocity * (100/30) / (2*PI) / 4
0.2148           >= Velocity * 0.2588
0.8299           >= Velocity

This seems to suggest that A4WD1 is able to carry a total mass of 7kg,
and still achieve an acceleration of 0.2788 m/s^2 (at best)
without overheating the four GHM-04 motors under its 0.0981 Nm rated torque/load.

However, I believe this calculation is only valid when A4WD1 is "travelling in straight lines"
and I am unsure of how to calculate for the case when A4WD1 needs to perform Skid Steering
such as Spin (In Place Pivot) and Hard Turn (Circular Pivot).

I am sincerely hoping for some advice on how to calculate the amount of Torque needed to do Skid Steering...
because based on my experience, 4 Wheeled Robots are unable to "turn smoothly"
where the main cause seems to be due to friction, according to both websites below:
http://www.ikalogic.com/tut_mech_1.php
http://www.gizmology.net/tracked.htm
But I am unsure of how to take friction into account, and am sincerely hoping for detailed guidance on this...

[madsci1016]

The short answer is 'alot'.

I'm not a mechanical math kind of guy, I tend to follow my gut; so someone else will have to help you with math. But I can help you with experience with that platform.

I am building a robot using the same chassis, and the 12V version of the motors running at 14.4V, since I was using Li-Ion batteries.
 
SAGAR Autonomous Robot Waypoint Mission Interface and Vehicle Video

I have voltage and current monitoring on my robot. If you watch the video in HD, you can see the two blue bar indicators on the left side for 'Voltage' and 'Current'. Running straight, the four motors draw around .5 - .7 Amps. Making turn you see the current jump up to 2-3 Amps. That's a big jump. In place rotating is the worse. My motorcontroller is programmed to enter a 'constant current' mode if the current draw hits 3 Amps, until the speed requested falls below the current speed at 3 Amps. This was to protect my H-bridge, which was only rated for 4 Amps load.

Rotating in place almost always hit 3 Amps, and I could never rotate in place as fast as my motors could travel straight without getting limited.

[vsming]

Thanks madsci1016 for your reply

May I ask if you remember which 12V motor your SAGAR robot was using in http://lynxmotion.com/c-11-spur-gear-motors.aspx ?
Because the current "default" 12V motor for purchasing A4WD1 is the GHM-01,
which has a lower torque compared to the 7.2V GHM-04 (I want to get this motor, because it can equip wheel encoders),
but the 12V GHM-13 (most expensive) has the largest torque in Lynxmotion's website (but it can't equip wheel encoders).

May I also ask how heavy was your SAGAR robot?
Because I can't see it carrying any PC or anything.

I actually plan to buy the A4WD1 and let it carry a Mini-ITX PC (< 3kg) + Stereo Camera (< 1kg) + Batteries (< 1kg) to do SLAM research.
Do you think the A4WD1 is able to "carry" such a heavy payload (4.9kg max) but still be able to move "reasonably" well?
Or do you know of any other robot kit/platform that might be able to carry such a heavy load?

Thanks in advance for any advice that you will give

[madsci1016]

At the time of the video, I was suing these motors. Less torque, but faster speed.

I never weighed SAGAR, but it is relatively light. It's power source is 65 Watt Hours worth of Lithium Ion cells, and it's brain is a AVR based Axon Microcontroller.

I'd guess you would be able to move 'reasonably' well. I've seen videos of the same platform around the internet with some bigger payloads.

It also depends on the floor. Carpet is very had to turn on, but the standard laboratory floor is pretty slick and easy to turn on. 

[vsming]

Thanks madsci1016

May I ask if you remember any links showing A4WD1 carrying those heavier payloads?
I did actually tried to surf the Web before to look for projects using A4WD1 to see how heavy it could carry,
but I'm not sure why I couldn't find such links...

I guess I was always bad at surfing  

It would definately help a lot if I could see other people using the A4WD1 to carry heavy payloads