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Hybrid modeling and predictive control of intelligent vehicle longitudinal velocity considering nonlinear tire dynamics

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Abstract

A hybrid model predictive control (HMPC) strategy is proposed in this paper to autonomously regulate intelligent vehicle longitudinal velocity considering nonlinear tire dynamics. Since the tire longitudinal dynamics, which has significant influence on vehicle longitudinal velocity control performance, exhibits highly nonlinear dynamical behaviors, the piecewise affine (PWA) identification is conducted firstly based on experimental data to accurately model the tire longitudinal dynamics. On this basis, due to that the intelligent vehicle needs to be operated in two distinct modes (drive and brake) for autonomous velocity regulation and because of the affine submodel switching behaviors of the PWA-identified tire model, the intelligent vehicle longitudinal dynamics control process considered in this work can be regarded as a hybrid system with both continuous variables and discrete operating modes. Thus, the mixed logical dynamical framework is further used to model the intelligent vehicle longitudinal dynamics, and a HMPC controller, which allows us to optimize the switching sequences of the operation modes (binary control inputs) and the torques acted on the wheels (continuous control inputs), is tuned based on online mixed-integer quadratic programming. Simulation results finally demonstrate the effectiveness of the proposed HMPC controller for intelligent vehicle longitudinal velocity regulation under typical driving conditions.

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Abbreviations

\(a_{x}\) :

Vehicle acceleration along the forward direction

\(A_{\mathrm{w}}\) :

Windward area

c :

Number of the PWA submodels

\(C_{\mathrm{D}}\) :

Aerodynamic resistance coefficient

\(f_{\mathrm{R} }\) :

Rolling resistance coefficient

\(F_{\mathrm{a}}\) :

Vehicle accelerating resistance

\(F_{\mathrm{G} }\) :

Vehicle climbing resistance

\(F_{\mathrm{R}}\) :

Vehicle rolling resistance

\(F_{\mathrm{w}}\) :

Vehicle aerodynamic resistance

\(F_{\mathrm{z}}\) :

Tire vertical load

\(F_{\mathrm{xl}}\) :

Longitudinal forces generated by the left driving tire

\(F_{\mathrm{xr} }\) :

Longitudinal forces generated by the right driving tire

\(F_{\mathrm{i}}\) :

Coefficient matrices of the polyhedral region

\(g_{\mathrm{i}}\) :

Coefficient matrices of the polyhedral region

g :

Acceleration of gravity

\(i_{\mathrm{r}}\) :

Road slope angle

\(\kappa \) :

Longitudinal slip coefficient

k :

Number of the data points

\(m_{\mathrm{v}}\) :

Vehicle curb weight

\(m_{\mathrm{c}}\) :

Vehicle loading weight

\(M_{\mathrm{rr}}\) :

Rolling resistance torque

\(n_{\mathrm{y}}\) :

PWA model orders

\(n_{\mathrm{u}}\) :

PWA model orders

\(Q_{\mathrm{y}}\) :

Positive penalty weighting parameters

\(Q_{\mathrm{u}}\) :

Positive penalty weighting parameters

N :

Control horizon

\(r_{\mathrm{d}}\) :

Effective wheel rolling radius

\(T_{\mathrm{s}}\) :

Drive torque acted on the wheel

\(T_{\mathrm{b}}\) :

Brake torque acted on the wheel

\(T_{\mathrm{r}}\) :

Rolling resistance torque

u(t):

MLD system inputs

\(v_{\mathrm{w}}\) :

Speed of the tire–road interface

\(v_{\mathrm{wl}}\) :

Speed of the left tire–road interface

\(v_{\mathrm{wr}}\) :

Speed of the right tire–road interface

\(v_{\mathrm{i}}\) :

Initial vehicle velocity

\(v_{\mathrm{v}}\) :

Vehicle actual velocity

y(t):

PWA model output

\({\vartheta }_{i }\) :

Parameter vectors defining each submodel

\({\varphi }(t)\) :

Regression vector of the PWA model

\({\chi }_{i}\) :

Whole polyhedral region of the affine submodels

\({\varTheta }\) :

Moment of inertia of the wheels

\({\rho }_{\mathrm{a}}\) :

Air density

\({\varOmega }_{\mathrm{w}}\) :

Wheel angular velocity

MLD:

Mixed logical dynamical

PWA:

Piecewise affine

HMPC:

Hybrid model predictive control

ITS:

Intelligent transportation systems

MPC:

Model predictive control

MIQP:

Mixed-integer quadratic programming

MPT:

Multi-parametric programming technology

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51705207, U1564201), the China Postdoctoral Science Foundation (Grant No. 2019T120401, 2017M611728), the Postdoctoral Research Foundation of Jiangsu Province (Grant No. 1701112B) and the Six Talent Peaks Project of Jiangsu Province (Grant No. GDZB-163).

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Authors and Affiliations

  1. Automotive Engineering Research Institute, Jiangsu University, Jiangsu, 212013, Zhenjiang, People’s Republic of China

    Xiaoqiang Sun, Houzhong Zhang, Yingfeng Cai & Long Chen

  2. School of Automotive and Traffic Engineering, Jiangsu University, Jiangsu, 212013, Zhenjiang, People’s Republic of China

    Shaohua Wang

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  1. Xiaoqiang Sun
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Sun, X., Zhang, H., Cai, Y. et al. Hybrid modeling and predictive control of intelligent vehicle longitudinal velocity considering nonlinear tire dynamics. Nonlinear Dyn 97, 1051–1066 (2019). https://doi.org/10.1007/s11071-019-05030-5

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