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.

Heavy-duty commercial vehicles (HDCVs) have specific characteristics different from passenger cars. This paper deals with one of the characteristics of HDCV, propagation delay by air of an air-brake system. It is related to the braking performance of the vehicle. Thus, it is necessary to reflect it appropriately in the control model. In this paper, we propose the model predictive braking controller with the model of HDCV, including the air-brake system. The effectiveness of the proposed method is demonstrated via numerical simulations with the full dynamics vehicle model and the realistic air-brake model.