Auto steering isn’t a new concept when it comes to farming, but the implementation hasn’t been great since all the sensors that were utilized had serious shortcomings. Some needed difficult-to-set-up equipment outside of the vehicle to guide it and others needed clear visibility and good makers on the fields for their camera guidance to function properly. Now that GPS receivers are less expensive, manufacturers can utilize this affordable sensor for navigation, and even auto-steering.
GPS is already a common tool for many system, including agricultural. Systems that are accurate to less than a meter are used for geographic data collection, aids for drivers and auto-steering.
Now, even more precise systems that use CDGPS can be accurate within centimeters in addition to also being extremely accurate about vehicle dynamics.
The accuracy is heightened with the use of Integrity Beacons. These CDGPS systems can measure, precisely, several states so that it can identify systems, estimate states and automatically control vehicles. Such systems have been employed in many different ways such as a Boeing aircraft, a golf cart and a model airplane.
The point of this article is to look at using a CDGPS on a tractor as the sole positioning and dynamic meter. After developing an automation system, the software was simulated with a simple vehicle, then tested on a tractor.
The test intended to show if a CDGPS could sufficiently act as the only positional and dynamic meter.
The tractor was a John Deere Model 7800. On top of the truck, the testers attached four GPS antennas. They put a rack for equipment in the cab. An Orthman eltro-hydraulic steering unit, modified for the needs, controlled the front wheels. The software utilized a Motorola MC68HC11 microprocessor to relay information to the steering unit.
It was the microprocessor’s job to turn commands into pulse-width modulated signals that the steering system got via the power circuitry. In addition to this, the microprocessor collected feedback data from the (notably the one non-GPS sensor) potentiometer on the front, right, wheel. It was an 8-bit wheel angle potentiometer that sent its data back via a serial link at 20 Hz.
The GPS Equipment
The hardware used was exactly the same kind of CDGPS-based unit used by the Integrity Beacon Landing System. A Trimble Vector that boasted six-channels and had four antennas measured the dynamics of the vehicle and sent out the data at 10Hz. A Trimble TANS with nine channels and one antenna measured carrier phases and code phases and sent out the data at 4Hz. A LYNX operating system on a PC (Industrial Computer Source Pentium) received the data and GPS position, and then computed the signals with software from Stanford.
At the reference station, there was a Trimble TANS receiver making measurements of the carrier phases, a Dolch computer, and a Trimble 4000ST receive that made corrections to the RTCM code differentials. Data communication happened at 4800 bits per second via Pacific Crest radio modems. The reference station was about 800 meters away from where the test tractor was.
Setting Up the Vehicle
A good test would emulate real-world movements of a tractor. Textbook examples go from simple to complicated, but there isn’t a standard model. High-tech models with a variety of complication aren’t always the best option since designing controllers necessitates a straight-forward formula of plant dynamics.
This model is based on geometry, as opposed to physics. It assumes that the wheels don’t slip, the vehicle moves forward consistently, steering through a front wheel which has a small angle. If all the variables are consistent, then inertia and force can be derived. This model was made to be easy for the controller. Its vector is made up of position (lateral) difference from intended path, error in direction and the angle of the wheel.
Calibrating the Steering
At first, a couple of tables were made by calibration tests so customers could use them as a reference. One which showed what the steering potentiometer was reading against what a good wheel angle should be. The second showed what the computer was telling the wheel to turn to, versus what angle it actually turned to. Many tests were performed to get the heading rate according to the potentiometer reading. The tests had a tractor circling a track at a constant speed and angle. GPS tracked the data. Putting the data from all these tests together, they were able to deduce what a steady-state heading would look like according to the potentiometer.
Calibrating the angle rate of the commanded wheel was easier. The computer told the actuator to drive at a variety of levels. Data was collected on the wheel angle. After analyzation, it was simple to deduce the time it took for the change of angle for each command.
Results for Closed-Loop Heading
The first time a controller was made for and put on a tractor for testing, it did closed-loop heading. The software enabled an operator to type in a heading he or she wanted. Then, the desired heading would be communicated to the electro-hydraulic actuator to turn appropriately. At first, the test were closed-loop to ensure the model of the kinematic vehicle. These first tests gave the industry a good feeling for other things that might disturb the tractor.
Design of the Heading Controller
To handle quick responses to great heading step commands, the designers made a hybrid controller. They made it non-linear, with two commands following in quick succession, to quickly respond to big problems in steering, angle or heading. Big changes usually happened after big step commands. A vehicle whose state was near zero allowed the Linear Quadratic Regulator controller to take command
Double quick succession commands, or “bang-bang” commands, is the standard non-linear design. This design allows the auto-steering to self-corrects similar to how a human driver would. If the desired change is an increase of 90 degrees, the quick succession commands would make a hard right, hold, then straighten to get in line with the intended heading. This is opposed to the linear commands that would make a hard right then slowly straightening toward the target heading.
The one negative thing about quick succession commands is that when the changes are small, the controller jiggles between commands of hard rights and lefts. So small change commands were reserved for a linear controller.
The test had the tractor driving .9 meters per second on bumpy land. The operator put in for the first heading, and then several commands, in sequence, after. Regardless of the bumpiness, the tractor performed according to how it was commanded. In one minute’s time, the average error was a mere .03 degrees off in heading. It’s standard deviation was .76 degrees. In other tests, the sensor noise was zero with one degree standard deviation, so an accurate standard deviation would definitely be less than one degree.
Response time for a 90 degree change in heading was seven seconds, and the time it took to fully complete the command was ten seconds. Four degrees of overshoot occurred at the completion of the heading step response.
Results of Tracking the Closed-loop
After this performance, next was the need to track a straight line. A set of tests was created to be like tracking a row. This was accomplished by collecting heading and wheel-angle data and communicating the data back to the control system.
Design of the controller
The controller for this test was also a hybrid. The first task was getting the vehicle to the field and lined up with the row. To do this, a control mode was created based on the closed-loop controller of the previous test. When the vehicle was lined up on the row, a linear controller took command.
Results of Line Tracking Experiment
These tests were done on the same plot of land as the closed-loop tests. The vehicle was set before the test (manually) at .33 meters per second (in first gear). The command was to drive along four swaths, running parallel to each other, along the field. The swaths were 50 m long and 3 m apart. Everything was automatic: steering to get on the row, driving down the row, and the u-turns. The CDGPS was set by a manual drive to set the position estimate.
Because of this method, a consistent bias of about 10 centimeters appeared as a difference in the two trials. To eliminate this bias, a more sophisticated method of cycle ambiguity resolution would be required such as two-frequency receivers or pseudolites. This is something to look into in further experimentation.
The CDGPS did not show actual positioning, so the errors are errors in the control and how the vehicle was disturbed. In fact, the tractor drove along the rows with a standard deviation of less than 2.5 centimeters. The position, laterally was never off by greater than 10 centimeters, and the average error, in every test, was less than 1 centimeter.
These experiment are the the beginning of the path to reliable and inexpensive automation for land vehicles. The results are exciting because:
- A tractor was auto-steered using GPS only
- A constant gain controller (one that based on the simplest of vehicle models) guided the tractor
- GPS was shown to be able to guide along straight paths accurately and effectively.
Among all eight tests, the standard deviation was less than 2 1/2 centimeters. The next big step would be the transition between auto-steering a tractor by itself to auto-steering a tractor hauling some form of heavy equipment. This will be much more complicated as there are many more variables of movement to consider. Auto-steering on a curve is also a future challenge. It is possible that the methods tested here, with a bit more sophistication, could handle a tractor plus implement combo. There is more testing going on to research this.