4.2.3. Travel Time Index

The driver expects that the driving time of the vehicle be as short as possible. However, most of the time, we have an expected period of time to arrive at our destination, and the weight function should reflect penalties that are greater than the expected time and rewards that are less than the expected time. The travel time index of the vehicle path can be represented by {*J*t*<sup>i</sup>* }:

$$J\_{\rm ti} = \begin{cases} 0.8 + \left(t\_i - t^{\rm lb}\right) & t\_i < t^{\rm lb} \\ 0.8 & t^{\rm lb} \le t\_i \le t^{\rm ub} \\ 0.8 + \left(t\_i - t^{\rm ub}\right) & t\_i > t^{\rm ub} \end{cases},\tag{6}$$

where {*ti*} is the travel time of the vehicle on the *i*th path, and *t* lb and *t* ub are the lower and upper bounds of the expected vehicle travel time, respectively.

#### 4.2.4. Energy Expenditure Index

According to the longitudinal vehicle dynamics model, it can be seen that the vehicle is driving on a flat road, which means that there is no up and down gradient during the driving process [65]. At this time, the longitudinal dynamics model is expressed from Equations (7)–(10). The energy consumed is represented by Equation (11):

$$F\_{\omega} = F\_{\text{air}} + F\_{\text{roll}} + F\_{\text{irrertia}} \tag{7}$$

$$F\_{\text{air}} = \frac{C\_D A\_f}{21.15} V^2 \,\text{,}\tag{8}$$

$$F\_{\text{roll}} = mgf\_{\text{\\_}} \tag{9}$$

$$F\_{\text{inertia}} = \sigma m \frac{du}{dt} \,\prime \tag{10}$$

$$J\_{\mathbf{e}\_i} = VtF\_{\omega\prime} \tag{11}$$

where *CD* is the coefficient of air resistance; *Af* is the front area of the vehicle; m is the vehicle quality; g is the acceleration of gravity; *f* is the rolling resistance coefficient; t is the time interval; σ is the rotating mass correction coefficient; *Fω* is the total resistance of the wheel when driving; *F*air is the air resistance; *F*roll is the rolling resistance; *F*inertia is the acceleration resistance; *J*e*<sup>i</sup>* is the energy consumed by the vehicle.

#### 4.2.5. Determination of Weighting Factors

To compare the above three indexes, there is a need to weigh each of them by a coefficient. For driving safety index {*J*s*<sup>i</sup>* }, the weight factor {*λ*} is determined as follows (Equation (12)):

$$
\lambda = \begin{cases} & 1, \text{ normally} \\ & \eta, \text{ other characteristics} \end{cases} \tag{12}
$$

where *η* is adjusted according to the driver's aggressiveness level, road friction coefficient, vehicle stability characteristics, etc. The travel time weighting factor *β* is determined as follows (Equation (13)):

$$
\beta = \begin{cases} & 1, & \text{roundly} \\ & \kappa, & \text{other characteristics} \end{cases} \tag{13}
$$

where *κ* is determined according to the driver anxious degree, the congestion of the road network, rush hour, etc. Note that *κ* is used to avoid excessively congested roads.

Generally, we can find the shortest path from the starting point to the destination. Because the driver expects that the vehicle consumes as little energy as possible, we choose the

energy consumed by the vehicle in the shortest route under a smooth traffic environment as a reference. The energy weight factor {*γ*} is determined as follows (Equation (14)):

$$\gamma = \frac{1}{J\_{\text{normal}}}.\tag{14}$$

where *J*normal is the normally expended energy or the average value of energy consumption from the beginning to the end.

The control framework proposed in this section aims to find a trade-off between driving safety, driving time, and energy consumption during the vehicle driving process under the premise of ensuring the safety of the vehicle, so as to help the vehicle rationally plan and select the path. As shown in Figure 14, consider there are *i* paths available for vehicles to choose, and it is assumed that the parameters of traffic flow can be accurately predicted. Then, the vehicle stability criterion model is used to evaluate the stability of the future parameters of each path, and the saturation factor of the tire force *δ*TFSC is obtained when the vehicle is traveling at a predicted traffic density and speed in the future. To evaluate the tire force saturation factor of each path, if the tire force saturation factor of each path *δ*TFSC*<sup>i</sup>* < 1, vehicles can adopt driving behavior strategies such as lateral overtaking and changing lanes, at this time, calculate the driving safety index of each path *J*s*<sup>i</sup>* . Then we calculate travel time index *Jti* and energy consumption index *J*e*<sup>i</sup>* of each path, respectively, by substituting the driving index of each path and the weighting factor corresponding to each index into the comprehensive index model to obtain the best path. If the tire force saturation factor of each path is *δ*TFSC*<sup>i</sup>* > 1, drivers on such roads should avoid overtaking and changing lanes, and choose conservative driving behaviors, such as following the car in front. Under the premise of ensuring the safety of the vehicle, we then get the travel time index *J*t*<sup>i</sup>* and energy consumption index *J*e*<sup>i</sup>* of each path, and obtain the comprehensive index of each path and the weighting factor corresponding to each index. We then analyze the weight function "composite index" to get the best path. If some sections of a path have a criterion *δ*TFSC*<sup>i</sup>* < 1 and others sections have *δ*TFSC*<sup>i</sup>* > 1, then it needs to be discussed separately. For the sections of *δ*TFSC*<sup>i</sup>* < 1, vehicles are free to make overtaking lane changes. In the sections of *δ*TFSC*<sup>i</sup>* > 1, in order to ensure the stability of the vehicle, the driver needs to follow the traffic flow instead of lane-changing and overtaking. At this time, we recalculate the driving safety index *J*s*<sup>i</sup>* , the travel time index *J*t*<sup>i</sup>* , and energy consumption index *J*e*<sup>i</sup>* of each path, and obtain the weighting factor corresponding to each index, using the composite index model to finally obtain the best choice path.
