Auto Steer: There is more to driving a nice straight line down the field than one first thinks. Yes, one needs to judge the distance to the last pass, but just as important is the angle of approach and the rate of convergence/divergence to the last pass. When we drive manually, we combine all these visual cues and make a quick calculation as to how much we should move the steering wheel. We do it without even thinking – it becomes so automatic. It’s not perfect, but one can get pretty good at judging the distance and the angle to the last pass. Can we mechanize the control of driving a farm tractor? The distance to the last pass can be done with a positioning system like GPS, but how do we measure the angle? And we don’t have all day to do this, it must be done quickly, it must be done now – without delay. A delay in a control system becomes the juggernaut Eventually, we used GPS for the position, even though it’s accuracy and delay were questionable. Later we will see how the plant row can be used to improve the accuracy. An electronic gyro would be used to acquire the angle, but it was not without challenge. Electronic gyros put out a voltage that is proportional to the turning rate. One must integrate this to get an angle. And there is drift in the output with age and temperature. Corrections and compensations must be done in real time. Also, the vibration of the tractor, if close to the sample rate of the gyro, could result in egregious angle errors.
In Engineering we are taught that a control system with the least error in tracking is one with critical damping. So, if we are driving and we are off the desired line, we want to get back to where we belong as quickly as possible and this will result in some over-shoot. There will be a little loop in the corrective action taken. When doing the auto-steering trials; I soon learned that farmers wanted to forego this optimum response. They did not want to see any little loops or squiggles – they wanted a perfectly straight line no matter how long it took or the resulting accumulated overlap error. They wanted a controlled correction that was over-damped.
There were three things used in determining the steering correction: the offset, the angle and the tractor’s rate of turn. Let’s look at each of these more carefully.
The Offset: This is the perpendicular distance of the center of the tractor, to the desired track line. It is shown in Fig 1 as the offset. The desired track line is set by the driver doing a strike line across the field. From this strike line a set of parallel lines is calculated one implement width apart. The desired track line is the parallel line closest to the tractor’s position. When the positioning systems coordinate (GPS) is received on the tractor a calculation is made using a point to line formula, yielding the offset. GPS is accurate to ten feet, but it can be improved by using differential GPS, DGPS to get to within about a foot. This can be made even better with Real Time Correction, RTK GPS, to get to inches, especially if we are using relative measurements within minutes of each other. However, all positioning systems do not report the current position of the tractor, they report where the tractor was a moment ago, a fraction of a second ago. This just adds to the difficulty of steering.
The Angle: The tractor is shown on its course line to the * on the desired track line as shown in Fig 1. The angle j is the angle between the actual course line and the desired course line. Some call it the angle of attack. When we have a large offset, we need a large angle of attach, but as we get closer to the desired line, we want to make the angle smaller and smaller so that we don’t overshoot the line. One could think that driving is actually just aiming a few hundred yards down onto the desired line.
Rate of Turn: The tractor could be turning, so the turning will determine what the angle will be in the future. So it is another factor in determining the steering correction. An electronic gyro is used to determine the rate of turn, such as degrees per second. The gyro we used put out a voltage from zero to five volts, with the mid voltage of about 2.5 volts being no turn. A voltage higher than this was a left turn, and one lower than this was a right turn. We called this no turn voltage zero_w. It was not exactly 2.5 volts. It was initially calculated by averaging 32 readings when the tractor was standing still. When the tractor was moving, a reading from the gyro minus zero_w gave the turn-rate. Digital integration of the turn-rate gave the angle j. Angle j is acquired and adjusted by taking the inverse tangent of the difference of past offsets over the distance traveled. The correction to the steering = offset – angle – turn-rate.. This correction was a pulse applied to a hydraulic valve that put a squirt of oil into the steering ram.
