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Page 4 of 15 Chen et al. Complex Eng Syst 2023;3:8 I http://dx.doi.org/10.20517/ces.2022.50

Figure 2. 7-DOF nonlinear vehicle dynamic model.

where denotes the vehicle mass; and denote the longitudinal front and rear tire forces, respectively;
is the total resistance force; and , and , denote the actual and desired longitudinal vehicle
velocities, respectively. Combined with the traditional 2-DOF linear vehicle model, the transfer function of
the 3-DOF reference vehicle model can be expressed as follows:

 , = , /(1 + )


= , /(1 + ) (4)

 = , /(1 + )


where

 ( + )+ 2
 ,
 , =
 2
 ( + ) +( − ) 2
 ,


 ( + ) ,
, = 2
( + ) +( − ) 2
 h , i

 2 2
 + + ( + ) ,
 ,
 = −

2
 ( + ) ( + ) +( − ) 2
 ,
Here, is the steering angle of the front wheel; is the yaw moment of the vehicle inertia; and are the
distances from the mass center to the front and rear axles; and denote the front and rear wheel cornering
stiffnesses; and are the sideslip angle and yaw rate of the vehicle, respectively.
2.2. 7-DOF nonlinear vehicle model
To obtain an accurate model for MPC control in the process of predicting the vehicle state, a 7-DOF nonlinear
vehicle model, illustrated in Figure 2, is established, and it allows for free longitudinal motion, lateral motion,
yawmotion,androtationofthefourwheels. Thedynamicequilibriumequationsofvehiclelongitudinal,lateral,
and yaw motions can be expressed as follows: