*4.1. Vehicle Handling Stability Criterion Model by Neural Network*

The vehicle handling stability criterion model is investigated with test data in this part. In this approach, previous measurements of traffic flow velocity and traffic density are mainly considered. An artificial neural network is represented in Figure 10. As the figure depicts, the inputs of the network include traffic flow speed and traffic density in Equation (1).

$$\delta\_{\text{TFSC}} = f[\rho(1), \rho(2), \rho(3) \dots \rho(n); V(\rho(1)), V(\rho(2)), V(\rho(3)) \dots V(\rho(n))] \dots \tag{1}$$

where *ρ*(1), *ρ*(2), *ρ*(3), ... , *ρ*(*n*) are traffic density,*V*(*ρ*(1)), *V*(*ρ*(2)), *V*(*ρ*(3)), ... , *V*(*ρ*(*n*)) are traffic speed. The *δ*TFSC is the tire force saturation coefficient represented by Equations (2) and (3):

$$
\delta\_{\rm TFSCb} = \left(\frac{F\_{\rm xk}}{\mu F\_{\rm xk}}\right)^2 + \left(\frac{F\_{\rm yk}}{F\_{\rm ymaxk}}\right)^2 . \tag{2}
$$

$$\delta\_{\text{TFSCmax}} = \max(\left(\frac{F\_{\text{xk}}}{\mu F\_{\text{xk}}}\right)^2 + \left(\frac{F\_{\text{yk}}}{F\_{\text{ymaxk}}}\right)^2) . \tag{3}$$

where: *F*xk, *F*yk, *F*zk are the longitudinal, lateral, and vertical tire forces of the vehicle tires, respectively; *μ* is the friction factor between the tire and the road; *k* is the number of the tire (specifically refers to four different tires); *F*ymaxk is the maximum lateral force of the *k*th tire.

**Figure 10.** Artificial neural network structure.

The idea of stability criteria model is that we first build the lateral dynamics model of the vehicle (please refer to our previous work [68]), and then we build the traffic environment shown in Figure 11. A driver-in-the-loop simulation environment for the presented scenario is shown in Figure 12. The traffic environment in the figure mainly shows two main traffic parameters: Distance and speed of SV and HV. Distance represents traffic density; at the same time, the speed of the SV indicates the speed of the traffic. We use this simulation environment to simulate the change in the saturation coefficient of the vehicle's tires when the driver faces different traffic conditions and makes a lane change. For a front-wheel-drive ordinary vehicle, Figure 13 shows the change in the tire's tire saturation coefficient as a function of traffic flow speed and density. As can be seen from Figure 13, the *δ*TFSC increases as the vehicle speed and density increase when the driver performs a lane change.

**Figure 11.** One of the working conditions for collecting driver data.

**Figure 12.** Driver-in-the-loop experiment to collect drivers' reactions to different working conditions.

**Figure 13.** Neural network fitting results of TFSC for traffic speed and density.

#### *4.2. Multi-Objective Optimization Path Planning for Hybrid Vehicles*

In this article, the speed prediction method based on the traffic flow model, speed prediction method based on traffic historical data and real-time data, and speed prediction method based on the vehicle lateral dynamics are reviewed. The relationship between the energy management method and speed prediction of HEVs is briefly summarized. The existing problems of speed prediction methods are presented and a new system structure of a hybrid electric vehicle is constructed. Based on the new system structure of the hybrid electric vehicle and the proposed stability criterion model, a vehicle path planning method and its application case based on the vehicle speed prediction method and vehicle lateral risk assessment are given below. According to the various traffic flow prediction methods reviewed above, this paper assumes that future traffic flow parameters, such as traffic density *ρ* and traffic velocity V, can be accurately predicted. Furthermore, the vehicle tire force saturation factor *δ*TFSC corresponding to each traffic density *ρ* and traffic velocity V was calculated by the vehicle stability criterion model established above. The constructed vehicle stability criterion model based on the use of tire force saturation factors can reflect the result of vehicle safety during driving. Next, the stability criterion model shown in Figure 13 will be used as the basis of the multi-objective optimization path planning to make the vehicle reach its destination safely, quickly, and efficiently. Driving safety, driving time, and energy consumption are trade-offs to achieve the best overall performance. The problem of vehicle path planning and selection is described as an optimization problem. The optimized performance indicators are described below.

#### 4.2.1. Composite Index

The composite index {*J*com} is used to evaluate the overall performance of vehicle driving safety, time, and energy consumption, and the composite index is represented by Equation (4):

$$\min l\_{\text{COM}} = \lambda f\_{\text{\\$}\_i} + \beta f\_{\text{\\$}\_i} + \gamma f\_{\text{\\$}\_i \prime} \tag{4}$$

where *λ, β, γ* represent the weighting factors of vehicle safety, travel time, and energy consumption, respectively.

#### 4.2.2. Driving Safety Index

Using the steering stability criterion of the vehicle, the tire force saturation factor can be used to evaluate this basis, and the driving safety index can be represented by {*J*s*<sup>i</sup>* }. Driving safety is often the most important factor when the driver is driving a vehicle on the road. The larger the driving safety index {*J*s*<sup>i</sup>* }, the greater the influence of path security on the planning result.

$$J\_{\mathbb{K}\_i} = \mathfrak{e}^{\delta\_{\text{TFSC}(i)}},\tag{5}$$
