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Self-Run Agricultural Equipment Steered by GPS

Automatic farming vehicles are no new thing, but controlling those vehicles remotely has only been tried relatively successfully. Such equipment have necessitated large and unwieldy extra equipment, while other needed clear, sunny weather for cameras to have visibility to see the markers in the fields. Now that GPS units are cheaper, it’s much easier to make a machine that can be controlled remotely.

GPS isn’t new to vehicles, even agricultural ones. Techniques like meter-level code-differential have been utilized as well as automatic control of land vehicles and control that is driver-assisted.

The next phase is precision. CDGPS units can be accurate within centimeters for position and within a tenth of an inch for altitude.

The system’s ability is strengthened by pseudo-satellite Beacons. CDGPS is perfect for identifying systems because it can measure more than one state. It is also great for estimating states, and automatic control. People have tried CDGPS in many vehicles, like a golf, cart, a model airplane, and a Boeing 737.

However, this article is not about planes or golf carts, but about controlling a tractor with a CDGPS. The unit would be the sole sensor for positioning. There  has been a system already created for a tractor. It was tested with a model then on a tractor of actual size.

The reason this system was developed was to show that such precise positioning control was possible with only a CDGPS unit.

Hardware Used

A John Deere Model 7800 was the vehicle used for the test. Four GPS antennas (single-frequency) were put on the roof. An additional rack for equipment was installed on the interior. To sense the angle of the front-wheels, an Orhman electro-hydraulic steering unit (modified for this occasion) was installed. To enable communication between the steering and the computer, a Motorola MC68HC11 microprocessor board was used.

Computer commands were changed to pulse widthmodulated signals by the microprocessor, then communicated through circuits to the motor for steering. This same microprocessor took signals from a feedback potentiometer – the one sensor on the test tractor that wasn’t a GPS – which was mounted to the front, right wheel. The angle potentiometer was 8-bit and delivered the measurements at 20 Hz.


The tractor positioning CDGPS system was exactly the same as the one for the Integrity Beacon Landing System (IBLS). Altitude was measured at 10 Hz by four antennas and six channels of a Trimble Vector receiver. At 4 Hz, code and carrier phase was measured by a TANS receiver with nine channels and one antennae. Those readings could be used to ascertain the position of the tractor. The computer used was a PC by Industrial Computer Source Pentium that ran LYNX as its operating system. It collected the data, determined the position and used a Stanford-created software to control the computations.

As a reference point, there is a  Dolch computer outfitted with one antennae and a Trimble TANS receiver with nine channels that makes phased measurements, as well as a Trimble 4000ST receiver that corrects RTCM code differentials. Transmission occurred at 4800 bits per second via Pacific Crest modems located at the reference headquarters – a location 800 meters away from the tractor being tested.

The Test Tractor

In order to have a realistic test, there had to be a variety of changes and even minor problems. A farmer could have a basic or very complicated farming vehicle. No one tractor is the go-to tractor for farming. High-tech tractors are sometimes too much for the task, particularly when designing for controlling a vehicle necessitates a basic, mostly linear, plant system.

The Kinematic Kind

A kinematic model for a vehicle is both simple and useful. It is a model that utilizes geometric mathematics instead of the physics of force and inertia. You must take for granted that your vehicle’s wheels will not slip laterally, that it will move forward at a constant rate, one forward wheel actualizing with a small angle, then the math of movement is easy to calculate. These equations were created with the intention of making control and estimation easy. This vector is the error in heading, how far off the front wheel is from it’s ideal route, and at what angle the wheel works best at.

At first, testing the calibration helped programmers make two spread sheets: one for looking up what the potentiometer steering output was against the angle of the front wheel, and one that showed the angle that the computer told the wheel to be at against the angle it really was at. To make sure the potentiometer was correctly reading the angles, many tests were run with the tractor making turns to establish the heading rate, measured dY/dt, at a variety of potentiometer readings. Every time, the tractor went in a circle with the front-wheel at the same angle, the speed steady. Meanwhile, GPS data got collected. This way, a correlation was shown between potentiometer measurements and steady-state headings.

The commanded wheel rate of the angle is easier to calibrate. The computer kept the steering slews commanded continuously, though the actuator authority did change in level. Then information about the angle of the wheel was recorded by the computer. After all this, the computer calculated at what rate the wheel angle changed according to every steering slew.

What it Looked Like on a Closed Loop

The first test-run was a tractor on a closed-loop heading. The programmer made it so a farmer could tell the tractor what heading he wanted by typing it. Once the farmer typed the command, it would be communicated. The electro-hydraulic actuator received the command and thus kept track of whatever heading was commanded. At first, only closed-loop tests were conducted to ensure that the kinematic model was verified. These first runs gave a good understanding of things that might effect the tractor.

How the Controller was Designed

The command center was made as a hybrid so that it would be quick in delivering several commands in steps. If the tractor showed huge problems with its wheel’s angle or its heading, then command were given two at a time (“bam-bam”) instead of linearly. These problems or change usually happened after a big step command regarding heading. If the tractor showed to be near zero, an LQR controller (Linear Quadratic Regulator) was utilized.

The “bam-bam” commands take into account the phase-plane technique. Unique from linear programs, “bam-bam” programs make good on actuator authority to eliminate problems efficiently, just as the farmer would if he were steering. For instance, when a command is sent to increase the heading by 90 degrees, the “bam-bam” approach to communicating the message is to give three commands all together: turn a hard right, hold the wheel there, then straighten out to  go the desired direction. However, the linear commands would have the tractor turn a hard right and slowly turn back to straight.

One problem with the “bam-bam” commands is when the errors of state are near zero, commands vacillate, commanding a hard turn left, and then a hard turn right, and so on. Therefore, when only slight changes were needed, linear commands were given.

The Results: Heading

When testing commands regarding heading, the test tractor drove on uneven land at a consistent pace: 9/10 of a mile per second. The man at the “helm” used the computer to give the tractor heading commands at the start and several throughout the test. On the tractor side, the commands were accounted correctly, regardless of the bumpiness of the terrain. During the span of a minute, the average error was only 3/100 of a degree. The standard deviation was 76/100 of a degree. The results from different tests were expected to have zero sensor noise and 1/10 degree of a standard deviation, therefore the actual standard deviation was assuredly less than one degree.

For a 90 degree turn, the time for the controller to rise was about seven seconds. It took 10 seconds or less to settle. At the finish of heading responses, there was four degrees overshoot that happened.

The Results: Closed-loop

On the path to fully automatic farm vehicles, straight-lines come after closed-loops. The tests were done to be like tracking a row. For straight-lines, the tractor’s exact location, heading and wheel angle were all communicated to the control computer.

Designing Link Trackers

Just like the closed-loop test, a hybrid of many kinds of controller methods was used for line tracking. First, it was necessary to maneuver the tractor to the desired piece of land and lined up on a row. To do this, a program similar to the closed-loop system was used. After that was accomplished, precision techniques utilizing LQR started in.

The Results: Line Tracking

The tests were done on the same land as the closed-loop tests. The tractor was set in first gear at 33/100 of a second. The computer told the tractor to drive along four parallel 50m lines, 3m apart. The control program was charged with U-turns, tracking the lines and ensuring the tractor stayed on the lines. The tractor was maneuvered near a known and surveyed area and so as to initialize CDGPS integer cycle ambiguities.

A ten centimeter bias occurred in both trials since the GPS carrier phase integer cycle ambiguity resolution was low-tech. To do away with this, two receivers could be used. There is discussion of doing this in the future.

The land mapping displays CDGPS as opposed to “true” measurements. This shows how the control system and the effects of terrain affect the test. On straight-lines, the standard of deviation was more than 2.5 centimeters. The tractor didn’t go off position more than ten centimeters, and the average deviation wasn’t even one centimeter on each test.

In Conclusion:

These experiments are the first on the path to remotely controlling land vehicles cheaply, safely and precisely. The results give us a lot of hope for a few reasons. 1) A tractor was controlled with only a GPS for both heading and positioning. The only non-GPS unit was the steering potentiometer. 2) A tractor could go on a straight path that was decided beforehand. 3) GPS was enough to get a tractor to follow straight lines very well.

In all eight tests, the standard deviation wasn’t even 2.5 centimeters. This experiment represents a huge shift from automatically controlling a tractor, to an automatic tractor that also tows some farming equipment. The whole setup would be more difficult to manage since it has more physical variables to deal with. Another hurdle to jump in this industry will be taking a tractor along a path that is curved. This whole test endeavored to be very precise in its control. In the same way, slight modifications can refine the method to control even more intricate tractor system. We expect more testing and research to investigate this more.



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