Stochastic model predictive braking control for heavy-duty commercial vehicles during uncertain brake pressure and road profile conditions

Abstract When heavy-duty commercial vehicles (HDCVs) must engage in emergency braking, uncertain conditions such as the brake pressure and road profile variations will inevitably affect braking control. To minimize these uncertainties, we propose a combined longitudinal and lateral controller method based on stochastic model predictive control (SMPC) that is achieved via Chebyshev–Cantelli inequality. In our method, SMPC calculates braking control inputs based on a finite time prediction that is achieved by solving stochastic programming elements, including chance constraints. To accomplish this, SMPC explicitly describes the probabilistic uncertainties to be used when designing a robust control strategy. The main contribution of this paper is the proposal of a braking control formulation that is robust against probabilistic friction circle uncertainty effects. More specifically, the use of Chebyshev–Cantelli inequality suppresses road profile influences, which have characteristics that are different from the Gaussian distribution, thereby improving both braking robustness and control performance against statistical disturbances. Additionally, since the Kalman filtering (KF) algorithm is used to obtain the expectation and covariance used for calculating deterministic transformed chance constraints, the SMPC is reformulated as a KF embedded deterministic MPC. Herein, the effectiveness of our proposed method is verified via a MATLAB/Simulink and TruckSim co-simulation.