Research on Autonomous Vehicle Obstacle Avoidance Path Planning with Consideration of Social Ethics

Abstract

Self-driving car research can effectively reduce the occurrence of traffic accidents, but when encountering sudden people or obstacles cutting into the lane, how to reduce the damage hazard to traffic participants and make ethical decisions is the key point that the development of self-driving technology must break through. When faced with sudden traffic participants, self-driving vehicles need to make ethical decisions between ramming into the traffic participants or other obstacles. Therefore, in this paper, we propose a model decision planning method based on multi-objective evaluation function path evaluation of local path planning. This method addresses the ethical model disagreement problem of self-driving vehicles encountering traffic participants and other obstacles. The aim is to ensure the safety of the lives of the traffic participants and achieve the vehicle’s reasonable ethical decision planning. Firstly, when anticipating traffic participants and other obstacles, the vehicle’s planning intention decisions are obtained through fuzzy algorithms. Different sets of curves for various positions are generated based on dynamic programming algorithms. These curves are then fitted using B-spline curves, incorporating obstacle collision costs, and classifying obstacles into different types with varying cost weights. Secondly, factors such as path length and average path curvature are considered for path total cost calculations. Finally, a local path that avoids traffic participants is obtained. This path is then tracked using a pure pursuit algorithm. The proposed algorithm’s effectiveness is verified through simulation experiments and comparative analyses conducted on the MATLAB platform. In conclusion, this research promotes a safer and more sustainable transport system in line with the principles of sustainable development by addressing the challenges associated with safety and ethical decision making in self-driving cars.

1. Introduction

Autonomous vehicles are a new generation of vehicles equipped with advanced on-board sensors, controllers, actuator devices, and integrating modern communication and network technologies to achieve intelligent information interaction and sharing; they have complex environment sensing systems and decision-making and planning systems, collaborative control systems, and execution system functions. The autonomous system architecture of self-driving cars is usually divided into a perception system and a decision-making system. The perception system is usually divided into many subsystems responsible for tasks such as self-driving vehicle localisation, static obstacle mapping, moving obstacle detection and tracking, road mapping, and traffic signal detection and recognition. The decision-making system is also usually divided into many sub-systems responsible for tasks, such as path planning, behaviour selection, motion planning and control, etc., such that the vehicle senses its surroundings and makes decisions to achieve autonomous navigation, obstacle avoidance, and control of the vehicle’s speed and direction, which improves traffic safety and reduces traffic accidents [1,2].

Traffic accidents are a worldwide public health problem, but autonomous vehicles (AVs) have enormous potential to reduce human driving error and significantly reduce the severity and frequency of accidents, promising to save drivers’ lives and reduce traffic accidents, yet what should an AV do when it has no choice but to be involved in a collision? Who should decide which vehicle manoeuvre is the most acceptable? These situations constitute ethical dilemmas that require consideration of the most acceptable and ethical action for the vehicle. Jonathan Robinson et al. [3] explores current research in this area and works to promote ethical solutions. Deema Almaskati et al. [4] developed a series of strategies to address public safety concerns by identifying and categorising factors contributing to accident severity, understanding AV operation on public roads, and recognising the ethical aspects of unavoidable collisions; they identified eleven strategies to address the ethical dilemmas of these accidents and seven strategies to address AV safety issues to improve public perception. Katherine Evans et al. [5] and others have proposed a strategy for AV decision making, ethical value theory, which describes AV decision making as a form of claim mitigation: different road users hold different ethical claims about vehicular behaviour, and vehicles must mitigate these claims in determining their environment. The context of self-driving vehicles is used to derive ethical implementations that are consistent with reality by considering the quantification and consideration of the harm generated by the action and the uncertainty associated with it. David B. Resnik et al. [6] address the significant scientific and moral uncertainties associated with self-driving vehicles, such as the dilemmas of the typical tram problem [7] that may occur when a pedestrian suddenly runs in front of a level 4–5 self-driving vehicle and the system controlling the vehicle must choose between hitting the pedestrian or swerving quickly and crashing the vehicle (which could result in the death of the passenger) problem, proposing an approach to self-driving vehicle ethics and policy based on the precautionary principle.

The above studies provide many corresponding safety strategies for the moral dilemmas faced by AVs, and then when AVs are actually facing moral dilemmas, i.e., whether to rapidly swerve to ram pedestrians or other traffic participants, how AVs make reasonable ethical and moral decisions is an important aspect to be overcome for the development of autonomous driving technology. Therefore, related researchers have started to pay attention to the ethical issues in autonomous driving and use various decision models to plan ethical decisions for autonomous vehicles, and the commonly used decision methods include the Markov decision chain, MPC-based methods, and trajectory planning methods based on cost functions. Nelson de Moura et al. [8] proposed a decision-making algorithm based on the Markov decision process (MDP) to assess the impairment of traffic participants by three different strategies for ethical dilemma situations that arise in the process of automated driving: Rawls’s contractualism, utilitarianism, and egalitarianism. Wang H [9] suggested that when humans addressed the unavoidable collision situation in which humans are under an ethical decision-making problem, a lexicon-optimisation-based model predictive controller (LO-MPC) considering barriers and constraints was designed, and a predictive control framework based on rational ethics for ethical decision making in automated driving was proposed. Maximilian Geisslinger et al. [10] proposed a new framework for trajectory planning that considers uncertainty and risk assessment. In this framework, we translate ethical norms into mathematical equations, thus creating a basis for programming ethical trajectories. We proposed a risk–cost function for trajectory planning that takes into account minimising overall risk, worst-case prioritisation, and equal treatment of people. Wang et al. [11] addressed the issue of moral disagreement by proposing an analytical IFS (avoidance tendency) ethical model that described the relationship between respondents’ ethical intentions and sensitivities, implemented Personal Ethical Setting (PES) with a group model, and performed path planning experiments based on PES. Maximilian Geisslinger et al. [12] proposed an ethical trajectory planning algorithmic framework aiming at fair distribution of risk among road users by combining five basic principles: minimising overall risk, worst-case scenario prioritisation, equal treatment of people, responsibility, and maximum acceptable risk. Jimin et al. [13] addressed the impact of the issue of factors affecting ethical behavioural intentions in self-driving vehicle ethical dilemmas and proposed a “comprehensive theoretical decision-making framework for AV ethical dilemmas”. Maximilian Geisslinger et al. [14] quantified an accepted risk by comparing self-driving vehicles to other types of mobility, taking into account ethical and psychological influences that are important for the acceptance of self-driving vehicles. We show how accepted risk contributes to transparent decision making at the mobility level for self-driving vehicles, proposing a trajectory planning methodology that takes accepted risk into account. Faulhaber et al. [15] designed a scenario in which a human targeted two lanes containing different obstacles (a variety of humanoid avatars of varying ages and group sizes) and asked participants to make a decision about which object they would hit, as well as testing the use of pavements as potential safe harbours and related experiments involving self-sacrificing conditions. Janmes et al. [16] investigated a model-to-decision approach using a model of a collision scenario for the conflict problem of designing collision planning paths that minimise the loss of utility for steering an autopiloted vehicle.

In summary, although scholars have proposed many strategies and methods for moral dilemmas of self-driving vehicles, there are still some unresolved issues: (1) Most of the research only stays at the stage of strategies and methods and does not actually consider the decision making that the vehicles need to make in the face of moral dilemmas. (2) Although Markov decision-making models have a simple form and can handle uncertainty well, they are sensitive to noise and uncertainty and usually require a comprehensive understanding of the environment and the dynamic properties of the system, which may lead to instability in decision making. MPC models are able to flexibly adapt to changes in the environment and make adjustments and decisions based on real-time observations, but the computational complexity is high, and for problems with a continuous state space, the MPC needs to discretise the state space. (3) Although the trajectory-based planning method is able to make ethical decisions, it is still risk-based compared to the decisions of human drivers.

Therefore, it is very important to establish an empirical autonomous driving decision-making model for moral dilemma decision making; accordingly, this paper proposes a model decision planning method for local trajectory planning based on multi-objective evaluation function path evaluation. Through the relative speed and relative distance with traffic participants, the driving experience model is established based on fuzzy logic to obtain trajectory planning willingness, followed by obtaining B-spline curve clusters based on dynamic planning and using path length, road curvature, and obstacle collision cost evaluation curves to obtain collision avoidance paths, which improves the safety of vehicle travel. Finally, the effectiveness of the proposed algorithm is verified by MATLAB simulation experiments.

2. Algorithm Framework

The autonomous driving vehicle moral prevention strategy is only for the moral dilemma aspect of the method research, and no feasible, practical solutions were produced to let the autonomous driving vehicle out of the moral dilemma problem; therefore, it did not make for effective simulation and experimental verification. Although the decision-making scheme of trajectory planning can better plan a trajectory that is more in line with moral requirements, its applicability is still to be studied, and compared with experienced drivers, there is still a certain risk. Therefore, this paper addresses the moral dilemma faced by self-driving vehicles, i.e., self-driving vehicles have no choice but to collide and must calculate how to reduce the degree of damage to traffic participants, and proposes an empirical fuzzy trajectory planning framework based on pre-cutting the obstacles within the range of the main vehicle for the size of the speed and distance to establish a fuzzy rule base, based on the empirical rules used to obtain the trajectory planning willingness, and through the reverse fuzzy to obtain the planning sign position for dynamic planning. Secondly, after a random sampling connection to the state space, the multi-objective evaluation function is used to evaluate the curve clusters to minimise the degree of damage to the traffic participants. Finally, splicing and trajectory are sent down to the control layer for trajectory tracking and driving, i.e., the framework proposed in this paper, as shown in Figure 1.

The steps for implementation are as follows:

(1)

The obstacle information as well as the reference line information and the vehicle’s current position information are sent down to the planning decision layer.

(2)

Based on the relative speed and obstacle distance used to formulate fuzzy rules, obtain the planning willingness to carry out the defuzzification and make dynamic planning decisions.

(3)

Based on the current position of the vehicle as the starting point to the state space horizontal and vertical sampling, the use of dynamic planning algorithms is implemented to obtain a collection of trajectories composed of different horizontal and vertical combinations of coordinate points.

(4)

Based on the trajectory combinations obtained in (3), different path curve clusters are obtained by fitting using B-spline curves.

(5)

Based on the curve clusters, calculate the obstacle cost, path cost, and mean curvature cost for the path points on the curves that meet the distance and then normalise them to obtain the path with the smallest cost as the optimal path output.

(6)

Splice the reference line path with the path obtained based on (5), input it into the downstream controller, and track it using the pure tracking algorithm.

2.1. Fuzzy Algorithm Decision

Autonomous vehicles face challenges in determining whether to initiate path planning solely based on precise driving environment information. For automatic driving vehicles facing a lateral cut into the traffic participants and other obstacles, which suddenly cut into the vehicle driving lanes, automatic driving vehicles at this time are faced with moral decision-making problems, and due to the driving intentions and driving environment there is a great non-linear relationship. In order to ensure that the vehicle can be safe to plan the path and reduce the degree of damage to the traffic participants, this paper adopts fuzzy logic algorithms to mimic the human brain to deal with the problem of uncertainty and to improve the adaptive ability of automatic driving vehicles to deal with different scenarios.

The basic principle of the fuzzy algorithm is to describe the variables and the measures of things with the affiliation function, fuzzify the input variables and output variables, set the fuzzy rule base to obtain the fuzzy output value, and then obtain the output data through the fuzzy inference machine inverse deduction algorithm. The fuzzy logic inference is shown in Figure 2.

When the self-driving vehicle faces traffic participants and other obstacles that suddenly cut into the driving area, the vehicle establishes a fuzzy rule-of-thumb base through the size of the speed difference coefficient and the distance expectation coefficient and outputs the trajectory planning willingness through the fuzzy controller to ensure that the driving process completes the target driving task as well as reduces the damage of the traffic participants.

Defining speed differential coefficient ${\phi }_v$:

$${\phi }_v=\left\{\begin{array}{ll}1& v_e\ge v_f\\ (v_e-v_f)/v_e& v_e\le v_f\end{array}\right.$$

(1)

where $v_e$ is the speed of the main vehicle and $v_f$ is the speed of the traffic participants.

Defining safety distance model:

$$D_{slf}=\frac{{(v_e-v_f)}^2}{2(0.0524v_e-0.1215)}+0.8509v_f+1.6109$$

(2)

The desired distance of the vehicle should be greater than the safety distance model, ensuring the vehicle can promptly adjust its state. This desired distance is defined as:

$$D_f=D_{slf}+10$$

(3)

Definition of desired distance coefficient ${\varphi }_d$:

$${\varphi }_d=\left\{\begin{array}{ll}1& D\ge D_f\\ D/D_f& D\le D_f\end{array}\right.$$

(4)

In the Equation (4), $D$ represents the actual distance.

Fuzzy logic parameters, including speed differential coefficient ${\phi }_v$ and desired distance coefficient ${\phi }_d$, are fuzzified into five levels. For the ${\phi }_v$, the fuzzy subsets {small, moderately small, medium, moderately large, large} are chosen within the domain X, ranging from [0, 1]. Similarly, for the desired ${\phi }_d$, the fuzzy subsets {small, moderately small, medium, moderately large, large} are selected within the domain Y, also ranging from [0, 1]. The planning intention output is fuzzified into five levels, {weak, moderately weak, medium, moderately strong, strong}, with the domain W and values within [0, 1]. ${\phi }_v$ and its membership function are shown in Figure 3. ${\phi }_d$ and its membership function are depicted in Figure 4.

Fuzzy rule for planning intention ${\phi }_h$ as shown in

Table 1. Fuzzy rules for planning intentions.

φh		φv
φd		small	moderately small	medium	moderately strong	strong
	small	moderately weak	moderately strong	moderately strong	strong	strong
	moderately small	moderately weak	moderately strong	moderately strong	strong	strong
	medium	weak	moderately weak	moderately strong	moderately strong	moderately strong
	moderately strong	weak	weak	moderately weak	moderately strong	moderately strong
	strong	weak	weak	weak	moderately weak	moderately strong

.

2.2. Dynamic Programming Algorithm

Dynamic programming (DP) is a branch of operations research that solves for the optimality of a decision-making process [17]. The dynamic programming process is that each decision depends on the current state, which in turn causes a shift in the state. A sequence of decisions is generated in changing states, so this multi-stage process of optimal decision making to solve a problem is called dynamic planning, as shown in Figure 5. When conducting decision planning for moral dilemma problems, dynamic programming can open up a better convex space for solving the optimisation problem and can achieve the goal of reducing traffic participant injuries by sampling the spatial state of the environment in which the self-driving vehicle is located. In this paper, the steps of using dynamic programming are as follows:

(1)

Take the current point of the vehicle as the starting point and set the number of layers and columns in terms of horizontal and vertical distances, i.e., determine the width and length of the state space sampling.

(2)

Search and solve the cost function of the first layer through the dynamic programming algorithm, and the surrogate value of each layer is stored in the current node, and the node of the previous layer serves as the parent node of the next layer when incrementing step by step, accumulating the cost values until the end of the cycle, and then finally obtaining the minimum value of the cost of the last layer and backtracking to the previous parent node in turn to obtain the longitudinal position of the discrete points of the trajectory of the obstacle avoidance, and finally obtaining each point by transverse displacement scattering. Carry out horizontal displacement scattering points, and finally obtain the coordinate information of each point.

(3)

Finally, the B-spline curve is fitted to ensure the smoothness of the trajectory, and a planned trajectory is finally output.

2.3. B-Spline Curves

To maintain smoothness in the position, velocity, and acceleration of the path points, this study employs third-order B-spline curves for fitting the points derived from dynamic programming. The specific calculations are provided in Equations (5) and (6).

$$\left\{\begin{array}{l}{B}_{0,3}(u)=\frac{1}{6}(-u^3+3u^2-3u+1)\\ B_{1,3}(u)=\frac{1}{6}(3u^3-6u^2+4)\\ B_{2,3}(u)=\frac{1}{6}(-3u^3+3u^2+3u+1)\\ B_{3,3}(u)=\frac{1}{6}{u}^3\end{array}\right.$$

(5)

$$P_0(u)=\frac{1}{6}\left[\begin{array}{cccc}1& t& t^2& t^3\end{array}\right]\left[\begin{array}{cccc}1& 4& 1& 0\\ -3& 0& 3& 0\\ 3& -6& 3& 0\\ -1& 3& -3& 1\end{array}\right]\left[\begin{array}{c}{P}_0\\ P_1\\ P_2\\ P_3\end{array}\right]$$

(6)

2.4. Cost Function

To maintain dimensional consistency and select the optimal path, all components of the cost function are uniformly normalized, as shown in Equation (7).

$$f_{i\_norm}=\frac{f_i}{f_{\max }}$$

(7)

In Equation (7), $f_i$ signifies the value of individual points, while $f_{\max }$ represents the maximum value among all the path points.

1.

Path length cost

The total path length is calculated by accumulating the Euclidean distance for each discrete point, as shown in Equations (8) and (9).

$${\mathrm{Distance}\_\mathrm{total}}_i={\displaystyle \sum _{i=0}^{n-1}{(x_{(i+1)}-x_i)}^2+{(y_{(i+1)}-y_i)}^2}$$

(8)

In Equation (8), ${\mathrm{Distance}\_\mathrm{total}}_i$ represents the length of the planned curve and (x_i, y_i) denotes the coordinate points.

$${\mathrm{Cos}\mathrm{t}\_\mathrm{distance}}_{\mathrm{i}}{=\mathrm{f}}_{{\mathrm{distance}\_\mathrm{total}}_{\mathrm{i}}}{/\mathrm{f}}_{\mathrm{distance}\_\max }$$

(9)

${\mathrm{Cos}\mathrm{t}\_\mathrm{diatance}}_{\mathrm{i}}$ represents the normalized cost of each path as shown in Equation (9).

2.

Average curvature of the path cost

To enhance the overall smoothness of the path, the average curvature of the path is computed using the parametric equations passing through three adjacent discrete points A, B, and C. The coordinate parameter expression for the points is represented as shown in Equation (10).

$$\left\{\begin{array}{l}x(t)=a_0+a_{1}t+a_2{t}^2\\ y(t)=b_0+b_{1}t+b_2{t}^2\end{array}\right.$$

(10)

The curvature calculation formula is shown as Equation (11).

$$\kappa =\frac{x^{″}{y}^{\prime }-x^{\prime }{y}^{″}}{{({x^{\prime }}^2+{y^{\prime }}^2)}^{3/2}}$$

(11)

Here, $x^{\prime }$ represents the first derivative with respect to $t$, $x^{″}$ represents the second derivative, $y^{\prime }$ corresponds to the first derivative with respect to $t$, and y represents the second derivative. The average curvature of the road is calculated using Equations (12) and (13).

$$\kappa \_av{g}_i={\displaystyle \sum _{i=0}^{n-1}{\kappa }_i}/n$$

(12)

Within Equation (12), $\kappa$ stands for curvature, while $\kappa \_av{g}_i$ denotes the average curvature of all discrete points along the curve.

$$\cos t\_{\kappa }_i=\kappa \_av{g}_i/\kappa \_av{g}_{\max }$$

(13)

In Equation (13) $\kappa \_av{g}_{\max }$ introduces the maximum average curvature across all paths and $\cos t\_{\kappa }_i$ represents the normalized average curvature for each path.

3.

Obstacle type cost

Autonomous vehicles establish larger desired following distances and speed preferences through fuzzy rules. During high-speed travel, the system activates the emergency evasion mode when other obstacles and traffic participants abruptly enter the current lane. The planning intent is switched to a strong mode, employing higher obstacle costs and path curvature costs to navigate around the obstacles, ensuring both vehicle stability and travel safety. In low-speed and urban traffic scenarios, when external traffic participants and other vehicles suddenly enter the vehicle’s lane, the planning intent is determined based on the current distance and vehicle speed. A path to avoid these participants is charted by assigning higher costs to external traffic participants.

a. 

Calculate the matching points of obstacles on the path

The path reference point index is determined using obstacle position information. Then, distances for each planned path point are computed based on the coordinates of matching points. A collection of path points, denoted as S, which are influenced by obstacles, is selected by filtering points that meet the specified distance criteria.

$$Distanc{e}_i={({(x_{pat{h}_i}-x_{match\_index})}^2+{(y_{pat{h}_i}-y_{match\_index})}^2)}^{1/2}(i=0,\dots ,n-1)$$

(14)

Here, $(x_{pat{h}_i},y_{pat{h}_i})$ represents the planned path points and $(x_{match\_index},y_{match\_index})$ represents the matching points of obstacles on the reference line.

b. 

Lateral displacement of S from the obstacle

To ensure the vehicle can safely avoid obstacles, the lateral offset between obstacles and planned path points is calculated using the projection method, as shown in Figure 6.

The lateral displacement is calculated as shown in Equations (15) and (16).

$$\begin{array}{l}\overrightarrow{BA}=((X_1-X_0),(Y_1-Y_0))\\ \overrightarrow{BC}=((X-X_0),(Y-Y_0))\\ Delta\_s=\overrightarrow{BA}•\overrightarrow{BC}/\left|\overrightarrow{BA}\right|\\ BD=Delta\_s\ast \overrightarrow{BC}/\left|\overrightarrow{BC}\right|\\ D=B+BD\end{array}$$

(15)

$$l=\sqrt{{(X-D_x)}^2+{(Y-D_y)}^2}$$

(16)

where A, B, and C are waypoints, and D is the projection point of C onto line AB.

Computing cost functions for traffic participants within set S.

$${obs\_ped}_i=\left\{\begin{array}{ll}\inf & l\Leftarrow {flag}_1\\ w_{small}sig\mathrm{mod}(l)& {flag}_1<l\Leftarrow {flag}_2\\ w_{big}sig\mathrm{mod}(l)& fla{g}_2<l\Leftarrow {flag}_3\\ 0& else\end{array}\right.$$

(17)

where $sigmoid$ is an S-type function, which is a nonlinear function that can map any value between [0, 1], ${flag}_1$, ${flag}_2$, and ${flag}_3$ are the lateral distance threshold, and when the different lateral distances between the main vehicle and the traffic participant are within the threshold, different weight coefficients are set by triggering a calculation of the cost of the traffic participant.

$$ob{s}_{i\_p\_total}={\displaystyle \sum _{i=0}^{n-1}obs\_pe{d}_i}$$

(18)

$$\cos t\_ob{s}_{i-p}=ob{s}_{i\_p\_total}/ob{s}_{i\_p\_total\_\max }$$

(19)

Here, $\cos t\_ob{s}_{i-p}$ signifies the cost incurred by traffic participants, including external participants and vehicles operated by other drivers.

Cost of other obstacles:

$$obs\_other=\left\{\begin{array}{ll}{w}_{np}sig\mathrm{mod}(l_1)& fla{g}_1<l_1\Leftarrow fla{g}_3\\ 0& else\end{array}\right.$$

(20)

Here, $l$ represents the lateral distance between vehicles and obstacles and $fla{g}_1, fla{g}_2, fla{g}_3$ denotes the lateral distance threshold.

$$ob{s}_{i\_other\_total}={\displaystyle \sum _{i=0}^{n-1}obs\_othe{r}_i}$$

(21)

$$\cos t\_ob{s}_{i\_other}=ob{s}_{i\_other\_total}/ob{s}_{i\_other\_total\_\max }$$

(22)

Here, $obs\_other$ represents the cost associated with non-human obstacles, excluding human entities.

When the vehicle is relatively far away from the traffic participant or other obstacles, the weight coefficient is set to $w_{small}$, and when the distance between the traffic participant and the vehicle is very close, the weight coefficient is set to $w_{big}$. If faced with a sudden cut-in traffic participant, in order to ensure that the vehicle travels on a path that deviates from the traffic participant, i.e., when making ethical and moral decisions about the traffic participant and the other obstacles, the proposed algorithm should avoid colliding with the traffic participant as much as possible to reduce the casualties and thus set the cost of the traffic participant to infinity and the cost of the other obstacles to $w_{small}$. The overall multi-objective evaluation function can be expressed as follows:

$$J=w_d\cos t\_diatanc{e}_i+w_k\cos t\_{\kappa }_i+w_{pobs}\cos t\_ob{s}_{i-p}+w_{other}\cos t\_ob{s}_{i-other}$$

(23)

Here, $w_d$ indicates the weight allocated to path length, $w_k$ denotes the weight attributed to average curvature, $w_{pobs}\mathrm{c}$ represents the cost incurred by traffic participants, and $w_{other}$ stands for the cost related to other obstacles. Importantly, $w_d+w_k+w_{pobs}+w_{other}=1$.

2.5. Pure Pursuit

The pure pursuit algorithm, as a classic lateral control method, exhibits strong robustness and can achieve excellent lateral control performance. Based on the Ackermann model, the relationship between the lookahead point and the vehicle’s position is calculated through geometric considerations. Subsequently, the steering angle for the front wheels is determined by calculating the turning radius. The principle of the pure tracking algorithm is shown in Figure 7.

Point C is the pre-sighting point on the reference route, L is the wheelbase, $\alpha$ is the angle between the pre-sighting point and the vehicle’s forward direction, R is the turning radius, δ is the vehicle’s turning angle, and $l_d$ is the pre-sighting distance.

Derivable from geometric relationships:

$$\frac{L}{\sin (2\alpha )}=\frac{R}{\sin (\pi /2-\alpha )}\Rightarrow R=\frac{L}{2\sin (\alpha )}$$

(24)

$$\tan \delta =\frac{L}{R}\Rightarrow \delta =\arctan (\frac{L}{R})$$

(25)

By simultaneously solving Equations (24) and (25), we can obtain the following:

$$\delta =\arctan (\frac{2L\sin \alpha }{l})$$

(26)

3. Simulation

Based on the MATLAB platform, the proposed mathematical model is simulated, and the effectiveness of the proposed algorithm is verified by establishing the curved road condition and straight-line condition. The simulation is divided into curve condition and straight-line condition analyses. Based on the upper layer of sensors to distinguish the type of obstacles, the use of fuzzy inference logic to determine the relative distance and relative speed of the main vehicle and traffic participants and other obstacles, and the output of the planning of obstacle avoidance willingness, the self-driving vehicle adopts the dynamic planning algorithm to carry out the local obstacle avoidance planning, through the setting of the cost function, to make ethical decision making for the participants in the traffic and obstacles. In this way, the vehicle can plan a more reliable path by avoiding colliding with traffic participants, minimising the degree of harm to them, and approaching in the direction of other obstacles.

(1)

Curve condition

The black solid line in Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 indicates the boundary, the working condition is unidirectional two-lane, the dotted line sub-table indicates the virtual centerline of the left and right lanes, the yellow border is other obstacles, the black border indicates the traffic participant, i.e., two different types of obstacles that suddenly cut into the current lane, the red point indicates the actual path, the orange is the reference path line, and the blue curves are the clusters of curves for planning. Figure 8, Figure 9 and Figure 10 show the current vehicle and obstacle safety distance of 10 m planning path curve clusters, when the distance between the vehicle and the obstacle reaches the desired distance threshold, through the fuzzy controller for inference decision making, to obtain the output of the willingness to change lanes, after the dynamic planning algorithm and B spline curve fitting to obtain the corresponding planning path curve clusters. As can be seen from the figure, when changing different cost penalty weights, the vehicle is able to plan a planning curve to avoid traffic participants and is able to safely avoid different types of obstacles to achieve vehicle safety. As shown in Figure 8, when the cost coefficient of traffic participants is set higher, the geometry of the curve clusters obtained are deviated from the traffic participants, and the optimal paths obtained are better able to achieve safe avoidance of obstacles, thus reducing the damage of the traffic participants and realizing the stable driving of the vehicle. As can be seen from Figure 10, when the weight coefficient of the traffic participant is set to 0.5, and the weight coefficient of other obstacles is set to 0.2, when the self-driving vehicle makes the decision to avoid obstacles, it prioritises the reasonable avoidance of the traffic participant and turns the steering wheel to other obstacles, which is in line with the ethical constraints of the human society, i.e., it makes the decision in accordance with the social morality, thus reducing the occurrence of traffic accidents. Figure 11 and Figure 12 show the clusters of planning path curves for a safe distance of 15 m between the vehicle and the obstacle, from which it can be seen that the vehicle acquires a smoother path when planning the path at a larger safe distance, all of which can safely avoid the obstacle.

(2)

Straight-line condition

Figure 13, Figure 14, Figure 15 and Figure 16 show the optimal lane changing obstacle avoidance planning paths generated when different cost functions are set. As can be seen from Figure 13, when a traffic participant suddenly appears in the lane where the vehicle is traveling, a large weighting factor is taken to set the traffic participant cost function so that the optimal path is obtained to travel away from the traffic participant so that when the vehicle is close to the traffic participant, the vehicle is as far away from the traffic participant as possible. The planned obstacle avoidance path is traveled towards other obstacles to keep the vehicle as far as possible from the traffic participant. Thus, the proposed ethical decision-making planning framework can respond and plan the path away from the traffic participant in time. It is obvious from the straight-line case in Figure 14 that the planned route is smoother when the cost function only considers the road curvature. Figure 15 shows a comprehensive consideration of the impact of various factors, when the front vehicle is 10 m away from the obstacle, by setting a larger cost of other obstacles, and the planning willingness obtained by fuzzy logic reasoning decision making can respond in time and plan to avoid the path of the traffic participants. At the same time, it can consider the length of the road, the road curvature, and other factors to avoid the vehicle, because of the encounter with the traffic participants and the sudden cut into the lane, to make a sharp turn of the steering wheel to avoid the obstacle and ensure the safety of vehicle driving. Meanwhile, it can be seen from the figure that the optimal planning path obtained by the vehicle is smoother, and in the face of the collision of traffic participants and other obstacles, the proposed algorithm model gives priority to the planning of paths toward other obstacles, thus reducing the collision of traffic participants, which is in line with the requirements of social ethics and morality. Figure 16 shows the paths considering only the effect of the considered road length, the length of the planned paths is significantly smaller than the other curves and also bypasses the obstacles in a reasonable way.

4. Discussion

We propose a local path planning model decision-making method using a multi-objective evaluation function. By applying a fuzzy algorithm that accurately predicts traffic participants and obstacles, taking into account the collision cost and type classification of obstacles, local paths that can effectively avoid traffic participants are generated, and path tracking is achieved by a pure tracking algorithm. This paper acknowledges the progress made in implementing ethical action planning in real vehicles, while recognising the need for further research into the equitable distribution of risk in future road traffic and the complex ethical dilemmas involved. Exploring these ethical issues will be a key breakthrough in the development of self-driving cars, and we eagerly look forward to working with more partners to advance this research.

5. Conclusions

In this paper, we propose a decision for self-driving vehicles facing the problem of moral dilemmas when set to collide with a traffic participant or other obstacle that bursts into a cut-through lane. The decision is made using a trajectory planning approach with a multi-optimisation problem that aims to reduce the level of damage to the traffic participant. From the simulation experiments, it can be seen that the adopted fuzzy decision-making method is very good at triggering the timely and effective trajectory planning when traffic participants cut into the main vehicle range. And after the dynamic planning algorithm opens up the convex space to solve the decision making, the use of multi-optimisation to evaluate the cost function can achieve a timely response to the traffic participants, reducing the risk of collision with the traffic participants, and finally, achieve the accurate control of the planned trajectory. Although the adopted trajectory planning model minimises the risk of colliding with a traffic participant for obstacles cutting into the main vehicle lane, the situation may not be the same in a real-world environment. Complex urban traffic environments still require better strategies and decision making to accommodate self-driving vehicles to obtain better assessment and optimisation when faced with different moral dilemma scenarios to reduce the damage to traffic participants.