Determine steering angle given radius and wheelbase

After installing the Wheel Angle Sensor, we need to know the actual angle that the tractor’s front wheels have when fully steering to one side. With the actual steering angle we can then adjust the “counts per degree” until the angle value in AOG matches the actual steering angle.
I first tried to measure the actual steering angle directly on the front wheel but it was difficult and not accurate. Therefore I thought about a different approach:

  1. mount steel bar on the hitch in the center of the tractor like a scribing iron
  2. drive a circle at max steering angle
  3. measure radius
  4. calculate steering angle using formula

I did this today and the tractor drives curves smoothly now. Let me know if there is any error in my thoughts or in the formula.

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Everything looks good!

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I was wondering how others have got their settings for a four wheel drive. I’ve adjusted the counts/degree till it tracks straight but struggle with uturns.

Trying to get my simple mind around this wheel angle calculation, after reading through the thread “WAS with Ackerman steering” and looking at your drawing and caluclation Andi, correct me if I am wrong, that the angle being calculated is for a virtual wheel between the two actual wheels, in center of tractor? The R is the radius length to center of rear tractor tires. Once calculated turn tractor wheel full one way and adjust count per degree until AOG reads calculated degrees, then adjust Ackerman % until the degrees are equal in the other direction.

exactly. the angle is for a virtual wheel as if the tractor were a bicycle. assuming that AOG also works with the “bicycle simplification”, this approach should be better than using one of the two actual wheel angles.

Correct, the R is the radius length to center of rear tractor tires. but since it’s easier to mount the scribing iron on the hitch, I actually measured the small “r”. the small r is radius length from scribing iron on the hitch to center of the circle you drive. for the formula you just need:

  • r (measured after “scribing” the circle)
  • L (wheelbase)
  • d (distance from rear axis to scribing iron).

the R is just there to better understand the calculation

the procedure after calculating is exactly what I did.

How well does Agopengps deal with slip angles caused by draft forces? (The difference between the direction a wheel is pointed in and the direction it actually moves)

I’m used to using a Trimble ez pilot, which has a calibration feature for working out the equivalent setting and I found it worked well when there is zero draft, such as fert spreading, but pulling a drill or a cultivator it needs a different setting to work well. You can at least rerun the calibration while pulling some implements in the field and it will work out the setting for those conditions.

Hi,
I was thinking about that. Actualy there is a small error, where the WAS is positioned on the wheel knockle this value is not the actual heading of the traktor. The angle is a little less if the WAS is mounted on the right wheel when you turn left. If you turn right it is then bigger.
It is why some have trouble to turn in the uturns, going straight or almost straight the error is very small. We don’t notice the problem, but when the angle is greater, the error is bigger and the PID can handle it. Or the PID calculate the turns just perfect turning in one direction but then in the other it makes a mess. AOG has ackerman fix don’t know if this is the solution to solve this??
But what I suggest is to make a calibration form in AOG, so AOG knows each value of the wheels and the wheel angles; the max WAS value to left and right position, the center position and calculate a count per degree for the left and right, this automatically by driving straight for a couple of meters and take an average for the zero angle(wheels straight).
make a couple of turns to the full left, with the gps we can map the circles we made and again take an average of that to know the radius when turning max left. Also the value of WAS in full left position. So we have a count per degree in left direction. And do the same to the right.

Now when turning left we calculate with the left count per degree and convert Alfa( the heading AOG wants the traktor to go) to Beta the wheel angle sensor itself.
just to make simple again ; because the WAS is mounted on the wheel knockle doesn’t mean that this is where the traktor goes.
and making a good calibration form, everybody should have the perfect counts per degrees in both direction. And with this the PID will be easier to adjust for everyone.

after this; if the steeringPID is well tuned, we can make an other PID system to control Alfa, this with the error we have from track to track.
example: if the GPS and AOG calculate we are 2cm to the left, give Alfa a certain degree in function of the speed, wheelbase, hitchlenght, tool lenght, sidehill and heading. and control with PID how much overshoot / reactiveness we want.

I know the second PID is not easy to code or to tune and certainly not if the steering PID is not working properly.
So this is my Idea to make good steering calculation and make the traktor drive better in traight lines and in the Uturns.

Hope you understand me a bit, and thanks for reading this :smiley:

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Not well at all at the moment, many of us are having problems with tracking near / next to the line for this reason. Brian is working on including some integral to help combat this problem…