Slope Gradient and Vehicle Attitude Definition Based on Pitch and Roll Angle Measurements: A Simplified Approach

R. N. Barbosa1, *, J. B. Wilkerson2, H. P. Denton3, D. C. Yoder2
1 Biological and Agricultural Engineering Department, Louisiana State University Agricultural Center, Baton Rouge, Louisiana, EUA, USA
2 Biosystems Engineering and Soil Science Department, University of Tennessee, Knoxville, Tennessee, EUA, USA
3 Plant Sciences Department, University of Tennessee, Knoxville, Tennessee, EUA, USA

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open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the BAE Department, Louisiana State University Agricultural Center, 119 E. B. Doran Bldg., Baton Rouge, LA 70803, USA; Tel: (+1) (225) 578-1065; Fax: (+1) (225) 578-3492; E-mail:


Simplified models relating pitch and roll angle measurements of a roving vehicle to terrain slope and vehicle attitude were developed. The simplified models are based on previously published models by Rowe and Spencer [1] and Yang et al. [2]. These simplified models are easier to implement using microcontroller technology reducing the number of trigonometric function calculations, improving program execution and simplicity. Simulated and field tests were conducted comparing published and simplified models. In a simulated test, agreement between models showed coefficient of correlation (r) results of 0.999 (p<0.05). Mean absolute deviation between models was less than 0.12° for slope gradient, and 0.51° for vehicle attitude. In a field test models were programmed in a microcontroller, a clinometer was used to obtain pitch and roll measurements of a roving ATV. Terrain slope results derived from pitch and roll measurements were compared to results derived from high accuracy GPS readings. Slope gradient results showed high coefficient of correlation, low absolute error and high model efficiency. Slope aspect results showed correct aspect classification more than 85% of the time.

Keywords: Slope measurement, vehicle attitude, euler angles, modeling, soil slope.