Part A. Decision-making and path planning based on skilled driver’s performance for emergency obstacle avoidance

Abstract

Emergency Lane Change (ELC) is a strategic maneuver for collision avoidance (CA) at high speeds where there is an accident risk. In this paper, two algorithms are designed for CA at high speeds based on the vehicle’s initial speed and the distance of the obstacle. The first algorithm selects the more suitable case between Automatic Emergency Braking (AEB) and ELC systems to prevent an accident. Suppose there was no choice except a rapid Lane Change (LC); the second algorithm does path planning for an ELC. The most critical issue in the ELC is time because this maneuver’s duration is less than 2 or 3 s on the dry or wet road. So, designing a fast and safe path planning algorithm is very important. To solve this problem, with a seven-degrees of freedom vehicle dynamic’s equations and the skilled driver behavior manner in the ELC maneuver, scrollable and stable paths for initial speeds of 75–125 km/h are extracted. Then, a neural network (NN) is trained based on this simulated data. The main feature of this network is to design stable paths as fast as possible. Also, this network can plan the paths in the various road friction coefficients between 0.5 and 1. The trajectory is selected based on two geometric constraints including, including (1) not colliding with obstacles and (2) not crossing the road boundary.

Keywords

Autonomous vehicle collision avoidance lane change path planning automatic emergency braking

1. Introduction

Nowadays, many road accidents occur due to driver errors. According to statistics (Wester et al., 2008), in 68% of accidents, the driver’s inattention was the most crucial cause. Efforts to use intelligent technologies in the automotive industry, which reduce traffic accidents, are growing steadily. Research approaches develop driver assistance systems and autonomous vehicles (Huang et al., 2021).

In some cases, there are emergencies on suburban roads that require a quick response from the autonomous vehicle’s decision-making system and, if necessary, a suitable path planning to prevent an accident. These accidents include the sudden appearance of animals on the road (Decker et al., 2021) or the sudden entry of another vehicle from the side streets to the main one (Zhu et al., 2021). In these cases, due to the vehicle’s high speed, the AEB system cannot prevent accidents in terms of time and dynamic constraints (Zhang et al., 2022). On the other hand, by analyzing the skilled driver’s reaction, it is apprehensible that using the lane change maneuver (LCM) (Huang et al., 2021) is a solution in this situation and can prevent accidents. In this condition, the duration of the accident is, on average less than 2 s (Schoettle, 2017). Therefore, the decision-making and control systems must carry out the path planning and steering of the vehicle at a minimum time. In addition to CA, the kinematic and dynamic constraints are satisfied to maintain the vehicle stability at high speeds (more than 70 km/h).

So far, many studies have been done on the autonomous vehicle’s path planning in the LCM. A path planning method is presented in traffic conditions using a time-distance method and two fifth-degree curves (Samiee et al., 2016). One of the problems of this method is the use of four nonlinear equations to avoid collisions. But the weakness of this algorithm is the path curvature discontinuity at the segment’s junction points. The geometry types of the seventh and fifth-degree polynomial functions, the sinusoidal or tangent equations, and the third-degree polynomial combinations are investigated for path planning (Norouzi et al., 2019). This study shows that fifth-degree polynomials curve have better performance than other curves in the same maneuver time. An NN is used for the LCM path planning (Geng et al., 2018). The training data of this network is obtained from the trajectory traveled by several skilled drivers in different environmental conditions. In this method, the network can only path planning based on its training in particular cases. Another limitation of this research is working at speeds below 50 km/h. Two fifth-degree curves are used in the LCM path planning, and the final trajectory is selected by helping a cost function.

The approach of this study is decision-making and path planning of an autonomous vehicle based on a skilled driver’s performance in an ELC maneuver, with the aim of CA, in situations where the AEB system cannot prevent a collision. Also, since this LC is an ELC, in addition to the vehicle’s high speed (above 70 km/h), its average maneuvering time for dry and wet roads is less than 2 and 3 s. Therefore, in this paper, an algorithm is designed to select the most suitable system between AEB and ELC systems based on the conditions for CA, if it’s possible.

In the following, section 2 examines the dynamics equations of the car, wheels, and tire. Section 3 describes the process of path planning and selecting the final trajectory. Section 4 describes the CA strategy in different road conditions and section 5 presents the simulation results.

2. Vehicle dynamic model

In this research, the suspension system dynamics are ignored to avoid increasing the vehicle model complexity. In Figure 1, X–Y represents the inertial coordinates, and x-y is the local coordinates connected to the center of mass (CG).

Applying Newton’s second law, the vehicle motion in terms of the center of mass acceleration can be expressed by the following equations. References (Sazgar et al., 2020; Rajamani, 2012) can be referred for further investigation.

m a_{x} = [(F_{x_{f, l}} + F_{x_{f, r}}) \cos δ - (F_{y_{f, l}} + F_{y_{f, r}}) \sin δ + (F_{x_{r, l}} + F_{x_{r, r}}) - F_{a e r o}]

(1)

m a_{y} = [(F_{x_{f, l}} + F_{x_{f, r}}) \sin δ + (F_{y_{f, l}} + F_{y_{f, r}}) \cos δ + (F_{y_{r, l}} + F_{y_{r, r}})]

(2)

I_{z} \ddot{ψ} = l_{f} [(F_{x_{f, l}} + F_{x_{f, r}}) \sin δ + (F_{y_{f, l}} + F_{y_{f, r}}) \cos δ] - l_{r} (F_{y_{r, l}} + F_{y_{r, r}})

(3)

where $m$ is the vehicle’s mass and $I_{z}$ is the inertia moment around the yaw axis. $δ$ is the wheel steering angle. $l_{f}$ and $l_{r}$ are the distances between the front and the rear axles to the center of mass. The vehicle’s angular acceleration around the yaw axis is also indicated by $\ddot{ψ}$ . $F_{x_{τ, ε}}$ and $F_{y_{τ, ε}}$ are the longitudinal and lateral force of each tire. $F_{a e r o}$ is the aerodynamic drag force. The longitudinal and lateral accelerations of the center of mass in the local coordinate system are also denoted with $a_{x}$ and $a_{y}$ .

2.1. Wheel dynamics

Wheels are one of the most important subsystems in the study of vehicle dynamic behavior. In equation (4), the equations of each wheel are expressed.

I_{w} {\dot{ω}}_{τ, ε} = - F_{x_{τ, ε}} R_{w} + {(T_{b} + T_{d})}_{τ, ε} - T_{r o l l_{τ, ε}} τ \in {f, r}, ε \in {l, r}

(4)

Here, $I_{w}$ is the inertia moment of the wheel, $\dot{ω}$ is the wheel angular acceleration and $R_{w}$ is the effective wheel radius, and $T_{d}$ and $T_{b}$ represent the total traction torque and the total braking torque applied to the wheels, respectively. Rolling resistance torque is also denoted with $T_{r o l l}$ , and is calculated as follows:

T_{r o l l_{τ, ε}} = f_{r} F_{z_{τ, ε}} R_{w} τ \in {f, r}, ε \in {l, r}

where

f_{r}

is the rolling resistance coefficient.

2.2. Tire model

Assuming the linear dependence of the tire’s friction force on each tire’s normal force, the tire’s longitudinal or lateral friction force can be expressed by equations (6)–(8) (Rajamani, 2012).

F_{γ_{τ, ε}} = \frac{S_{γ_{τ, ε}}}{S_{τ, ε}} μ_{τ, ε} F_{z_{τ, ε}} γ \in {x, y}, τ \in {f, r}, ε \in {l, r}

(6)

μ_{τ, ε} = D \sin [C \arctan (B S_{τ, ε})] τ \in {f, r}, ε \in {l, r}

(7)

S_{τ, ε} = \sqrt{{(S_{x_{τ, ε}})}^{2} + {(S_{y_{τ, ε}})}^{2}} τ \in {f, r}, ε \in {l, r}

(8)

where

μ_{τ, ε}

is the friction force,

S_{γ_{τ, ε}}

is the longitudinal/lateral slip, and

S_{τ, ε}

is the total slip of each tire and B, C, and D are tyre constants. The parameters of the vehicle dynamic model are represented in Table 1.

Table 1.

Vehicle parameters.

Symbol	Unit	Value	Symbol	Unit	Value
$m$	kg	1450	$v_{w i n d}$	m/sec	0
$I_{z}$	kg.m²	2740	$I_{w}$	kg.m²	0.9
$l_{f}$	m	1.1	$f_{r}$	—	0.015
$l_{r}$	m	1.6	$B$	—	7
$t_{w}$	m	1.55	$C$	—	1.6
$R_{w}$	m	0.3	$D$	—	0.52

3. Path planning

LC at high speeds, where there are chances of incidents, is a strategic maneuver for CA. The purpose of this is path planning of the LCM based on a skilled driver’s performance at high speed. Also, path planning must cover two goals, CA and scrollable path.

3.1. Simulation of driver’s behavioral pattern

LCM at high speeds is a standard maneuver (ISO 3888-2:2011, 2011). A skilled driver can perform this maneuver in its standard conditions. By studying the behavioral pattern of skilled drivers in the ELC maneuver at high speeds (more than 70 km/h) and analyzing the available videos of these drivers’ performance during the maneuver in the standard LC tests (km77, 2022; Suhyeon and Sukhan, 2020), it can be seen that the driver uses only the steering actuator to perform the maneuver and operates a quasi-sine input to the steer in this scenario. When an emergency occurs, the driver tries to cross the obstacle with a quick steer sinusoidal operation and prevent accidents. In this case, the steps of the LC scenario are divided into two parts: (1) crossing the obstacle and (2) returning to the straight line (Figure 2(c)). The input diagram of the driver’s wheel angle (steering) in these two cases is expressed as to equation (9). In the first step, a sinusoidal input is given to the vehicle wheel (steering wheel) to cross the obstacle; then, a constant angle is applied to the vehicle to return that to a straight line. For the continued maintenance of these two-step diagrams, based on the actual increase rate of the vehicle wheel angle, relation to time is defined so that the endpoint of the wheel angle in the first step reaches a value of $- δ_{f}$ , that is, the starting point of the second case. In this case, the wheel angle change rate is considered to be 30 deg/s. Properly designing the driver’s sinusoidal performance amplitude and period is essential to simulate this behavior. In fact, by choosing these two parameters correctly and accurately, the appropriate paths can be simulated and identified based on the driver’s behavioral pattern.

\begin{array}{c} δ = & \begin{array}{c} {\begin{cases} δ_{f} \sin (\frac{2 π}{t_{a r v}} t) \\ - 30 (t - t_{a r v}) \\ - δ_{f} \\ - δ_{f} + 30 (t - t_{ε}) \\ 0 \end{cases} & \begin{array}{l} t < t_{a r v} \\ t > t_{a r v} & δ > - δ_{f} \\ t > t_{a r v} & θ > ε \\ t > t_{a r v} & θ \leq ε \\ t > t_{a r v} & θ \leq 0 \end{array} \end{array} \end{array}

(9)

where

δ

is the wheel steering angle,

δ_{f}

is the maximum wheel steering angle in the equation (9) sinusoidal cycle or it is the domain of the sinusoidal equation,

ε

is a small value close to zero, and

t_{a r v}

is the time to reach the obstacle and is calculated from equation (10).

t_{a r v} = \frac{X_{a r v}}{V_{x_{0}}}

(10)

where

X_{a r v}

is the distance from the obstacle and

V_{x_{0}}

is the vehicle initial speed.

These stimulation paths are fitted with a fifth-degree polynomials curve (Norouzi et al., 2019). To achieve this, the assumptions of the path curve are:

1. The vehicle’s position at the maneuver beginning is on the origin of the coordinate.

2. At the maneuver beginning, the longitudinal direction of the vehicle trajectory is parallel to the horizontal axis. So, the slope of the curve at $X = 0$ is zero.

Therefore, the boundary conditions are $Y (0) = 0$ and $Y^{'} (0) = 0$ . By applying these boundary conditions to the fifth-degree polynomials curve of equation (11), the curve equation (12) is obtained.

Y (x) = b_{1} X^{5} + b_{2} X^{4} + b_{3} X^{3} + b_{4} X^{2} + b_{5} X + b_{6}

(11)

Y (x) = b_{1} X^{5} + b_{2} X^{4} + b_{3} X^{3} + b_{4} X^{2}

(12)

3.2. Scrollable paths range design

In Figure 2(a), the LCMs trajectory are modeled by a skilled driver’s performance the high speed, extracted as a set of paths that are obtained from Applying the input equation (9) to the vehicle dynamics (Section 2) at different angles range of $δ_{f}$ . For each pair $X_{a r v}$ and $V_{x_{0}}$ , the value of $δ_{f}$ can be increased to a specific limit ( $δ_{f, \max}$ ), and then the obtained paths don’t have stable conditions after this value because the dynamic constraints are out of the defined range during the travel path. These stability constraints are defined as follows and are examined with equations (7) and (8).

1. The friction coefficient of each tire along the path is a maximum of 0.5.

2. The total slip of each tire along the path is a maximum of 0.15.

It is known that the minimum wheel angle ( $δ_{f, \min}$ ) will be for a position where the corresponding lateral displacement of the vehicle $(Y_{a r v, \min})$ at the reaching moment of the obstacle $(t_{a r v})$ is sufficient that this displacement can prevent the collision in three areas shown in Figure 2. If the paths of the LCM are in the red area, there is a collision with the obstacle. Suppose the paths of the LCM enter the yellow area. In that case, the vehicle will lose its stable condition due to non-compliance with the allowable range of the mentioned dynamic constraints. The blue area is the only part where the paths designed LC maneuvers can be implemented; because in this area, a safe LCM can be performed without colliding with an obstacle and maintaining the vehicle’s dynamic stability.

3.3. Trajectory planning

Two geometric constraints are used to avoid collision and exit the road boundary to select the trajectory (final path) in the LC maneuver. These two terms are expressed as follows and based on Figure 2(b):

1. The corner distance of the vehicle when crossing the obstacle is $n_{1}$ . In this situation, the minimum lateral displacement of the vehicle is $Y_{a r v, \min} = Y_{O b s} + t_{w} / 2 + n_{1}$ to prevent a collision. Therefore, the lateral displacement of the vehicle in the trajectory planning should be more than $Y_{a r v} > Y_{a r v, \min}$ at this moment. Also, $Y_{O b s}$ is the obstacle length and $t_{w}$ is the vehicle width.

2. The safe distance of the vehicle from the road boundary is $n_{2}$ . So, Equation $Y_{C r i t} = Y_{r o a d} - (t_{w} / 2 + n_{2}) > Y_{f}$ is required for CA with the boundary road. Also, $Y_{C r i t}$ is the maximum lateral displacement of the vehicle without crossing the road boundary and $Y_{f}$ the vehicle’s final lateral displacement.

Finally, the path that can satisfy the conditions of these two geometric constraints is chosen as the trajectory of the LC maneuver.

4. Collision avoidance strategy

There are two basic solutions to CA: (1). Emergency braking and (2). Emergency lane change (ELC). Today, many advances are made in intelligent braking systems (AEB) to prevent collisions (Sadeghi Namaghi and Moavenian, 2019; Zhang et al., 2022). However, it should be noted that based on the distance from the obstacle, the vehicle’s initial speed, and other environmental conditions such as road friction, can braking prevent collisions or not? In other words, is the obstacle within the car’s braking range? Based on the reference data [14] in Figure 3, the minimum stopping distance by AEB (blue line) for the automatic vehicle (AV) in both ideal conditions (dry road with faster reaction time) and non-ideal (Wet road with slower reaction time) is calculated. The quickest reaction time of detection and decision systems for activating the braking system is considered 0.5 s in ideal conditions and 0.75 s in non-ideal conditions. In reference (Sadeghi Namaghi and Moavenian, 2019), the smart vehicle’s braking distance is simulated by several types of controllers in the Carsim software. The data of this research are also consistent with the data of reference hypotheses (Schoettle, 2017). According to the diagram in Figure 3, for the speed range of 75–125 km/h in dry and wet road conditions, two quadratic equations are extracted according to equation (13). When $X_{a r v} > X_{B r k, \min}$ , that is, the obstacle is above the blue line, the AEB system is recommended for CA. However, when $X_{a r v} < X_{B r k, \min}$ , that is, the obstacle is below the blue line, the ELC system is suggested to CA. But, if the obstacle distance is below the red line, due to the delay of the environment detection sensors and actuators the vehicle cannot avoid the collision in this condition unless these systems and tools are increasingly advanced.

\begin{array}{c} X_{B r k, \min / D r y} = 0.0016 V_{x_{0}}^{2} + 0.76 V_{x_{0}} - 28, D r y R a o d (μ = 0.8) \\ X_{B r k, \min / W e t} = 0.0088 V_{x_{0}}^{2} + 0.575 V_{x_{0}} - 25, W e t R a o d (μ = 0.4) \end{array} 75 < V_{x_{0}} < 125 (k m / h)

(13)

Equation (14) is used to calculate $X_{B r k, \min}$ in the other road friction coefficients.

\frac{X_{B r k, \min / μ} - X_{B r k, \min / D r y}}{X_{B r k, \min / W e t} - X_{B r k, \min / D r y}} = \frac{μ - μ_{D r y}}{μ_{W e t} - μ_{D r y}}

(14)

Figure 4 shows the decision-making algorithm for CA for different road friction conditions at various obstacle distances and initial vehicle speeds. In this algorithm, collisions cannot be avoided in the two following cases:

1. When $Y_{a r v, \max} < Y_{a r v, \min} = Y_{O b s} + t_{w} / 2 + n_{1}$

In this case, the maximum determined lateral displacement by the first NN in the stable conditions and at moment $t_{a r v}$ is less than the obstacle width in addition to its safe distance (Figures 2 and 3). So, it is suggested to activate the AEB system to minimize the possible damage.

2. When $Y_{f, \min} > Y_{C r i t} = Y_{r o a d} - (t_{w} / 2 + n_{2})$

In this case, the minimum final lateral displacement determined by the first NN is more than the road width. Although the vehicle safely crosses the obstacle, it crosses the road boundaries. In the upcoming circumstances, it remains to be analyzed whether whether velocity reduction and accidents will be appropriate or the risks of getting off the road. Now, exciting research and work are being done in this field (Bigman and Gray, 2020; Awad et al., 2018; Tanimotoa et al., 2020). In particular, the philosophical issues also influence decision-making methods and path planning patterns. Also, in the reference (Rahwan, 2016), in one of the lectures of Ted’s seminars, this issue is challenged by designing a smart experiment and examining the opinions of the statistical community of 5 million people.

According to Figure 5, in the first NN, the goal is to find the stable range of the vehicle path for the ELC. In this network, $V_{x_{0}}$ , $X_{a r v}$ , $μ$ , and $(Y_{a r v, \min} = Y_{O b s} + t_{w} / 2 + n_{1})$ are the inputs, and its output is two parameters $Y_{a r v, \max}$ and $Y_{f, \max}$ . For training this network, simulated skilled driver performance data (Section 3.2) and the vehicle dynamics (Section 2) in three coefficients of friction 0.5, 0.7, and 1 have been used. For each friction coefficient, an NN is trained to calculate the output in other friction coefficients; with the help of these three output networks, the parabolic coefficients of equation (15) are calculated and using this relation, two parameters $Y_{a r v, \max}$ and $Y_{f, \max}$ in other road friction coefficients are determined.

Y_{x / μ} = a μ^{2} + b μ + c 0.5 < μ < 1, Y_{x} = {Y_{a r v, \max}, Y_{f, \max}}

(15)

In the second NN, trajectory planning of the LCM is done based on inputs of the amount of $Y_{f}$ (final lateral displacement), $V_{x_{0}}$ and nt), $V_{x_{0}}$ and $X_{a r v}$ .. This network aim determines the fifth-degree equation coefficients (equation (12)). In the training of this network, only the simulated data in the 0.7 friction coefficient is used because the endpoint of the path $(Y_{f})$ is the same in all friction coefficients; As a result, the path curvature in other friction coefficients will be close to the path curvature in the 0.7 friction coefficient and can be used. In the path analysis block, $Y_{f}$ is calculated using equation (16). Based on Figure 2 is $Y_{f, \min} \leq Y_{f, \max} - (Y_{a r v, \max} - Y_{a r v, \min})$ . In equation (16) is assumed $Y_{f, \min} = Y_{f, \max} - (Y_{a r v, \max} - Y_{a r v, \min})$ for the ease of calculation. Also, this value is more than the actual value of $Y_{f, \min}$ , which is a kind of hidden safety factor to maintain the allowable distance of the vehicle from the obstacle.

Y_{f} = {\begin{cases} Y_{f, \max} - 0.5 (Y_{a r v, \max} - Y_{a r v, \min}) Y_{f, \max} < Y_{C r i t} \\ 0.5 (Y_{f, \min} + Y_{C r i t}) Y_{f, \min} < Y_{C r i t} < Y_{f, \max} \\ C o l l i s i o n w i t h r o a d b o u n d e r y Y_{C r i t} < Y_{f, \min} \end{cases}

(16)

The multilayer perceptron (MLP) structure is used in the provided NNs because the MLP is used for interpolation problems (Razzak et al., 2017). In the NNs of Figure 5, the connection between inputs and outputs is done by interpolation; therefore, MLP neural network is used. Also, the lower the number of layers and neurons, the network speed is higher and, as a result, the path planning speed is higher, which is essential and vital in this maneuver.

5. Simulation results and discussion

The training of two NNs stable range of path planning and trajectory planning is done based on the data obtained from the dynamic simulation of the performance of the skilled driver in the ELC maneuver in sections 2 and 3. In these simulations, the range of the initial speed is 70–125 km/h. The outputs data of the vehicle maximum lateral displacement $(Y_{a r v, \max}, Y_{f, \max})$ is 7m in the primary NN. Also, in the secondary NN, the fitted polynomial coefficients range is from 10⁻⁴ to 10⁻⁹. So, by comparing this value with the range of input values, the training data of these networks need normalization. Therefore, prior to the training process, the normalization is done to map all the values on the interval [−1, 1]. In order to increase the stability of NNs, 75% of the data is considered as training data, 15% is related to evaluation data, and the other 10% is related to test data. The training algorithm is the Bayesian regularization back-propagation because it does not have the local minima problem, and its learning ratio is adaptive. The first NN has four hidden layers and in each of those, there are 3, 7, 7, and 3 neurons. Also, the second NN has five hidden layers and in each of those, there are 10, 15, 15, 15, and 10 neurons. The activation function of the hidden layers is bipolar sigmoid and the activation function of the output layer is linear to avoid the saturation of the output. In Figure 6, in the primary NN after 213 iterations, the most optimal value of the mean square error of the validation data is 0.00057 m² (normalized). After returning the data to the original scale, by comparing the original data with the output of the network, the highest percentage of network error is about 3%; so there is an error of ±3 cm in the network for every one meter. In the Secondary NN (Figure 7) after 500 iterations, the most optimal value of the mean square error of the validation data is 0.00000303 m² (normalized). After returning the data to the original scale, by comparing the original data with the output of the network, the highest percentage of network error is about 4.5%; so there is an error of ±4.5 cm in the network for every one meter. Also, in both NNs, the histogram of the data distribution error is Gaussian and with an almost negligible standard deviation, which indicates the proper performance of the networks.

5.1. Decision-making

Three conditions are defined to simulate evaluate the performance of decision-making and path planning in Table 2.

Table 2.

ELC modes simulation.

Parameter	mod1	mod2	mod3
Vehicle’s initial speed (km/h)	82	101	123
Distance from the obstacle (m)	31	39	76
Length of the barrier (m)	1.5	2.1	3.2

Figure 8 shows the minimum distance required for braking at different road friction coefficients using equation (13). The blue line is the minimum distance required for braking at the desired initial speeds. If the distance from the obstacle is more than $(X_{a r v} > X_{B r k . \min})$ in a specific road coefficient of friction, the collision can be prevented with the AEB system. Otherwise, it may be to prevent the collision by ELC and, according to the maximum vehicle’s stable lateral displacement for CA $(Y_{a r v, \max})$ . In the third mode, at the road friction coefficients higher than 0.86, the collision can be prevented using the AEB system. Also, this value is 0.98 and 0.95 in the first and second modes.

Figures 9–11 shows the scrollable path range in the two moments of reaching the obstacle and the end of the maneuver. According to Figure 2, the vehicle will be unstable in the space above the blue line and hit an obstacle below the red line. Therefore, the permissible range of the vehicle lateral displacement is between these two lines. If this area interferes with the road boundaries (third mode), this area will be considered before the road boundaries (Figure 11(b)). Also, there is no way in this mode that the vehicle does not leave road boundaries with a coefficient of friction less than 0.6. In the first two cases (Figures 9 and 10), for the car to cross the obstacle without colliding, the minimum road friction coefficient must be more than 0.5 and 0.6, respectively. The coefficient of friction less than this value cannot be prevented collision due to the blue line below the red line (Figures 9(a) and 10(a)). Also, there is no risk of leaving the road in these two modes because there is a suitable distance from the road boundaries (Figures 9(b) and 10(b)).

Table 3 is explained the proposed strategy for CA at the four road friction coefficients of 0.55, 0.60, 0.85, and 0.95. Also, if necessary, the final lateral displacement of the trajectory is calculated for each of these friction coefficients by Figures 9–11 and equation (15). In the first and third modes, the collision can be prevented with the help of AEB (Figure 8). The AEB system cannot prevent collisions in other friction coefficients, and this weakness is compensated using the ELC system. The collision cannot be avoided in the second mode at

μ = 0.55

, (Figure 10(a)). In the third mode at

μ = 0.55

, although with the help of ELC, it is possible to prevent the collision from the obstacle, it is not possible to prevent the vehicle from leaving the road boundaries (Figure 11(b)). As discussed in section 4, it remains to be analyzed in the upcoming circumstances whether velocity reduction and accidents will be appropriate or the risks of getting off the road (Bigman and Gray, 2020; Awad et al., 2018; Tanimotoa et al., 2020; Rahwan, 2016).

Table 3.

Collision avoidance strategy in different friction conditions.

Meau	mod1		mod2		mod3
Meau	CA^* strategy	Designed Yf	CA strategy	Designed Yf	CA strategy	Designed Yf
0.55	ELC	3.36	Collision	—	RB*Exit	—
0.60	ELC	3.54	ELC	3.79	ELC	5.22
0.85	ELC	3.96	ELC	4.31	ELC	4.75
0.95	AEB	—	ELC	4.07	AEB	—

*Collision Avoidance, *Road Boundary.

5.2. Path planning simulation

In Figures 12–14, designed paths are simulated for CA in each of these three modes. The maximum vehicle wheel angle $(δ_{f, \max})$ in these maneuvers (ELC) to be the vehicle stable is 4.9, 3.3, and 1.6° in the scrollable path section, respectively. In the final path section, the path designed by the NN in two different friction coefficients, based on the $(Y_{f})$ calculated in Table 3, is plotted and compared with the real path (Section 3.2). Comparing the lateral displacement error of these trajectories show that this error is less than 10 cm, which is appropriate according to the safety factor of 50 cm considered in the path planning process. Therefore, the designed Trajectory (final path) in these three modes can prevent the vehicle from colliding with the obstacle in stable conditions with an ELD maneuver. Also, the AEB system cannot prevent collisions in explained road conditions (Figure 8).

6. Conclusion

In this paper, a decision-making and path planning algorithm for the LCM is proposed with the aim of CA in emergencies at high speeds and by modeling a skilled driver’s performance. The most important features of this research are as follows:

• Compared to other research, this research’s computational cost is low since the path planning calculations are done algebraically. This issue is precious due to the possibility of short-time accidents and the need for quick decisions.

• This research’s ELC path planning algorithm has been done so that the path designed is certainly stable in this algorithm in the range of friction coefficient dry and wet $(μ > 0.5)$ . Therefore, if there is a trajectory that can avoid collisions, this trajectory does not need to check the stability conditions, improving the speed of decision-making and path planning.

• In the CA process, the decision-making system adopts the necessary strategy by examining the vehicle speed, distance from the obstacle, and the road friction coefficient. If it concludes that the AEB system cannot prevent the collision, using the ELC system to avoid the collision.

Also, as future activities of this research, the following can be mentioned: The path planning system can operate at a wide range of speeds and distances, and this algorithm can be used in other situations. The driver’s performance model is considered sinusoid-like in this maneuver. The other models can be designed to develop this performance. Assumed in this study that the tire formula coefficients are known. However, for the comprehensiveness of the path planning algorithm, the need for a method to identify these coefficients online is well felt.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Samir Neisy Minaei

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