Trajectory-Following and Off-Tracking Minimization of Long Combination Vehicles: A Comparison Between Nonlinear and Linear Model Predictive Control

Preprint, 2020

Vehicle models are commonly linearized in vehicle motion planning and trajectory-tracking control to achieve driving automation. The linearization is performed either for specific operating conditions, limiting the generality of the designed function, or for the current operating condition, which requires on-line linearization. The latter is commonly used in model predictive control (MPC) and is only valid for a short prediction horizon because the accuracy of the linear model diminishes with increasing distance from the linearization point especially for long combination vehicles (LCVs) where the vehicle model is highly nonlinear. The accuracy of the linear prediction model can be increased if the linearization is performed for all the discrete steps of an initial guess reference trajectory. In this paper, we compared the linear and nonlinear motion prediction models of a LCV. We designed a nonlinear MPC (NMPC) for trajectory-following and off-tracking minimization of the LCV. The used prediction model allowed coupled longitudinal and lateral dynamics together with the possibility of a combined steering, propulsion and braking control of those vehicles. We showed that the control actions calculated by a linear time-varying MPC (LTV-MPC) are relatively close to those obtained by the NMPC if the guess linearization trajectory is sufficiently close to the nonlinear solution. We discussed how those guess trajectories can be obtained allowing off-line fixed time-varying model linearization that is beneficial for real-time implementation of MPC in LCVs with long prediction horizons. The long prediction horizons are necessary for motion planning and trajectory-following of LCVs to maintain stability and tracking quality, e.g., by reducing the speed prior to reaching a curve, and by generating control actions within the actuators limits.