This paper presents the system identification of a new model for the farm tractor’s yaw dynamics in order to improve automatic control at higher speeds and understand controller limitations from neglecting these dynamics. As speed increases, higher order models are required to maintain accurate lateral control of the vehicle. Neglecting these dynamics can cause the controller to become unstable at the bandwidths required for accurate control at higher speeds. The yaw dynamic model, which is found to be dominated by a second order response, is identified for multiple speeds to determine the effect of velocity on the model. The second order yaw dynamics cannot be represented by the traditional bicycle model. An analytical derivation shows that the model characteristics can, however, be captured by a model consisting of a significant (non-negligible) relaxation length in the front tire. Experimental results are presented showing that the new yaw dynamic model can provide lateral control of the tractor to within 4 cm (1σ) at speeds up to 8 m/s. These results are shown to be an improvement, at high speeds, over controllers based on models (such as a kinematic model) previously used for control of farm equipment.

Issue Section:
Technical Papers
Keywords:
farming, vehicles, dynamics, identification
Topics:
Dynamic models, Dynamics (Mechanics), Relaxation (Physics), Tires, Vehicles, Yaw
1.
Cohen
,
C. E.
, et al.,
1995
, “
Autolanding a 737 Using GPS Integrity Beacons
,”
Navigation
,
42
, pp.
467
–
486
.
2.
Cohen
,
C. E.
,
Parkinson
,
B. W.
, and
McNally
,
B. D.
,
1994
, “
Flight Tests of Attitude Determination Using GPS Compared Against an Inertial Navigation Unit
,”
Navigation
,
41
, pp.
83
–
97
.
3.
Lachapelle
,
G.
, et al.,
1994
, “
GPS Systems Integration and Field Approaches in Precision Farming
,”
Navigation
,
41
, pp.
323
–
335
.
4.
O’Connor, M. L., et al., 1996, “Automatic Steering of Farm Vehicles Using GPS,” 3rd Int. Conf. on Precision Agriculture, Minneapolis, MN, June.
5.
Bell, T., et al., 1998, “Automated Tractor Row and Contour Control on Sloped Terrain Using Carrier-Phase Differential GPS,” 4th Int. Conf. on Precision Agriculture, St. Paul, MN, June.
6.
Nieminen, T., Mononen, J., and Sampo, M., 1994, “Unmanned Tractors for Agriculture Applications”, XII CIGR World Congress and AgEng ’94 Conf. on Agricultural Engineering, Milan, Italy, Sept.
7.
Owen
,
G. M.
,
1982
, “
A Tractor Handling Study
,”
Veh. Syst. Dyn.
,
11
, pp.
215
–
240
.
8.
Crolla, D. A., 1983, “The Steering Behavior of Off-Road Vehicles,” Proc. of 8th IAVSD-Symp. Cambridge, MA, August.
9.
Owen
,
R. H.
, and
Bernard
,
J. E.
,
1982
, “
Directional Dynamics of a Tractor-Loader-Backhoe
,”
Veh. Syst. Dyn.
,
11
, pp.
251
–
265
.
10.
Ito
,
H.
,
Oida
,
M.
, and
Yamazaki
,
M.
,
1995
, “
Measurement of Forces Acting on 4WD- 4WS Tractor Tires During Steady-State Circular Turning in a Rice Field
,”
J. Terramech.
,
32
, pp.
263
–
283
.
11.
Stombaugh, T. S., Benson, E. R., and Hummel, J. W., 1998, “Automatic Guidance of Agricultural Vehicles at High Field Speeds,” Proc. of 1998 ASAE Annual Int. Meeting, Orlando, FL, July, Paper No. 983110.
12.
Cordesses, et al., 1999, “CP-DGPS Based Combine Harvester Control without Orientation Sensor,” Proc. of 1999 ION-GPS Meeting, Nashville, TN, Sept.
13.
Carious, C., Cordesses, L., and Thuilot, B., 2001, “CP-DGPS Farm Tractor Control Along Curved Path,” Proc. of 3rd European Conf. on Precision Agriculture, G. Greneir and S. Blackmore, eds., Agro Montpellier, pp. 1–6.
14.
Elkaim, G., et al., 1997, “System Identification and Robust Control of Farm Vehicles Using CDGPS,” Proc. of ION-GPS ’97, Sept.
15.
Rekow
,
A.
, et al.,
1999
, “
System Identification and Adaptive Steering of Tractors Utilizing Differential Global Positioning System
,”
J. Guid. Control Dyn.
22
, (
5
) Sept/Oct, p.
671
–
674
.
16.
Bevly, D. M., Rekow, A., and Parkinson, B., 1999, “Comparison of an INS vs. Carrier Phase DGPS Attitude in the Control of Off-Road Vehicles,” Proc. of ION Annual Meeting, Cambridge, MA, June.
17.
Ljung, L., 1987, System Identification: Theory For the User, PTR Prentice-Hall, Inc., Englewood Cliffs, NJ.
18.
Dixon, J. C., 1996, Tires, Suspension, and Handling, Second Edition, SAE Warrendale, PA.
19.
Guldner
, et al.,
1996
“
Analysis of Automatic Steering Control for Highway Vehicles with Look-Down Lateral Reference Systems
,”
Veh. Syst. Dyn.
,
26
(
4
), pp.
243
–
269
.
20.
Garrott, W. R., Monk, M. W., and Chrstos, J.P., 1988, “Vehicle Inertial Parameters–Measured Values and Approximations,” SAE Passenger Car Meeting and Exposition, Detroit, MI, SAE Paper No. 881767.
21.
Loeb, J., Guenther, D., and Chen, H., 1990, “Lateral Stiffness, Cornering Stiffness, and Relaxation Length of the Pneumatic Tire,” SAE Int. Congress and Exposition, Detroit, MI, SAE Paper No. 900129.
22.
Gillespie, T., 1992, Fundamentals of Vehicle Dynamics, Society of Automotive Engineers, Inc, Warrendale, PA.
23.
Bevly, D. M., 2001, High Speed, Dead Reckoning, and Towed Implement Control for Automatically Steered Farm Tractors Using GPS, Ph.D. Dissertation, Stanford University.
24.
Bevly, D. M., Rekow, A., and Parkinson, B., 1999, “Evaluation of a Blended Dead- Reckoning and Carrier Phase Differential GPS System for control of an Off-Road Vehicle,” Proc. of 1999 ION-GPS Meeting, Nashville, TN, Sept., pp. 2061–2069.
25.
Franklin, G., Powell, D., and Workman, M., 1988, Digital Control of Dynamic Systems, 3rd Ed., Addison-Wesley, Menlo Park, CA.
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