The growing demand for automation in the mining industry, particularly for the autonomous operation of articulated dump trucks (ADTs), has drawn increased attention to accurate vehicle modeling. The importance of such models lies in their use in model predictive control (MPC), model-based estimation methods, and vehicle simulation. While dynamic modeling offers a viable solution for these purposes, it is associated with complex setup and parametrization and may require recalibration in changing operating environments. As a result, kinematic models have dominated ADT modeling, especially in MPCs, at the expense of reduced prediction accuracy. In this work, we propose an approach using Gaussian Process Regression (GPR) to learn the sideslip angle of the vehicle, which is identified as the primary contributor to the reduced accuracy of kinematic models. The learned GPR function is augmented into the kinematic model to form a gray-box model that aims to reduce the gap to dynamic models. We show that the gray-box model can predict the sideslip angle and, consequently, the vehicle's lateral velocity, thereby improving the MPC's prediction performance. The resulting gray-box MPC is compared against two white-box MPCs in a simulation environment. The results indicate an improvement in terms of maximum lateral tracking error from over 2 m to 0.56 m.
Figures & tables
Fig. 1 : ADTs with equipment in a mining field. Image from [ 10 ] .
Fig. 2 : Kinematic configuration of an ADT with front sideslip based on [ 11 ] .
Fig. 3 : Reference trajectory from [ 11 ] .
Fig. 4 : Articulation angle ϕ profile for creating the test track.
Fig. 5 : Measurement (dynamic model) vs. GPR model prediction for sideslip angle α on the test data.
Fig. 6 : Box plot of the absolute sideslip angle α prediction error by the GPR model.
Fig. 7 : Lateral velocity at the front axle vy comparison between the dynamic model and the gray-box model on the test data.
Fig. 8 : Lateral velocity error and absolute lateral velocity error percentage comparison between the dynamic model and the gray-box model on the test data.
Parameter
Symbol
Value
Vehicle lengths
l1,l2
1.36,3.65m
Speed constants
Tv,kv
1.25s , 1
Steering constants
Tω,kω
0.5s , 1
Weight matrix
Q
diag([100,100,0,0,0,0])
Weight matrix
R
diag([1,1])
Further parameters
Td,Ts,Nc
0.5s , 0.3s , 20
TABLE I : MPC parameters
Fig. 9 : Lateral error between the reference trajectory and the front axle for the three MPCs.
Fig. 10 : Absolute lateral error between the reference trajectory and the front axle for the three MPCs.
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