Intelligent automobile probability constraint type path planning method in dynamic overtaking scene

Abstract

The invention relates to an intelligent vehicle probability constraint type path planning method in a dynamic overtaking scene, and the method comprises the following steps: collecting the historical track of a barrier vehicle through a vehicle-mounted sensor, and building a barrier vehicle track prediction model through a conditional linear Gaussian method; establishing a control-oriented automobile kinematic model, considering transverse path planning in an overtaking scene, and establishing safety constraints of the main vehicle and the obstacle vehicle according to the predicted obstacle vehicle trajectory; the method comprises the steps of opportunity constraint MPC optimization control, objective function and constraint setting, and optimal problem solving based on a quadratic programming method. The obstacle trajectory randomness is considered, the probability distribution of the distance relation between the main vehicle and the obstacle vehicle in the overtaking process is obtained, the corresponding probability constraint is designed, it is guaranteed that a feasible solution exists when an optimal problem is solved, and therefore a safe overtaking path is obtained and serves as a reference value of a follow-up trajectory tracking control module.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent vehicle technology, and specifically relates to a probability-constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario. Background Art

[0002] Due to the heavy workload of drivers and the increasing number of cars, as well as the increasing proficiency of non-professional drivers, traffic accidents are becoming more frequent. Improving active vehicle safety and traffic safety has become a pressing social issue. As a hot area of ​​intelligent technology, the emergence and development of smart cars will effectively reduce the probability of traffic accidents.

[0003] As one of the core modules of autonomous driving, path planning plays a crucial role in vehicle navigation. Its output guides the vehicle from its current position to its target location and provides control for the path tracking module. Due to the high complexity and uncertainty of real-world roads, it is difficult for intelligent vehicles to effectively plan their entire overtaking maneuvers in complex and dynamic road environments. Therefore, considering the uncertainty of dynamic obstacles during driving is crucial for mitigating safety risks and ensuring that path planning methods can adapt to various dynamically changing road environments.

[0004] MPC, as a rolling optimization method, plans a reasonable overtaking path by explicitly processing control system constraints and combining them with the vehicle's lateral dynamics model. It has many applications in path planning problems. However, in existing MPC-based path planning systems, the description of the obstacle vehicle's future trajectory is usually set as single-lane straight-line driving or turning according to a fixed trajectory. This does not take into account the randomness of the obstacle vehicle's driving process, which affects the safety of the main vehicle during the overtaking process. The present invention predicts the future trajectory of the obstacle vehicle in the path planning algorithm and quantifies the uncertainty. This uncertainty information is integrated into the path planning system, and probabilistic constraints are used to ensure a safe distance between the main vehicle and the obstacle vehicle, thereby ensuring the safety of the planned overtaking path. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that actual roads are highly complex and uncertain, and the accuracy of future trajectories of deterministic prediction methods cannot be guaranteed. Therefore, the present invention proposes a probabilistically constrained path planning method for intelligent vehicles in dynamic overtaking scenarios.

[0006] To achieve the above object, the present invention provides the following technical solutions: A probabilistically constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario comprises the following steps: 1) The historical trajectory of the obstacle vehicle is collected through the on-board sensors, and the obstacle vehicle trajectory prediction model is established using the conditional linear Gaussian method; 2) Build a control-oriented vehicle kinematic model, consider lateral path planning in overtaking scenarios, and establish safety constraints between the host vehicle and the obstacle vehicle based on the predicted trajectory of the obstacle vehicle; 3) Optimal control of chance-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods.

[0007] As a further technical solution of the present invention, in step 1), the step of establishing an obstacle vehicle trajectory prediction model using a conditional linear Gaussian method includes: Vehicle trajectory prediction is essentially a probability estimation problem based on historical information. Bayesian networks (BNs), with their superior mathematical representation and uncertainty management, are well-suited for modeling and inferring complex nonlinear dynamic systems. Assuming that the obstacle vehicle's trajectory follows a Gaussian distribution, and that the probability distributions of the obstacle vehicle's X and Y coordinate positions in the geodetic coordinate system are mutually independent, this paper utilizes a special variant of the Bayesian network, the Conditional Linear Gaussian (CLG) model. This model can handle both discrete and continuous variables and make predictions based on their joint probability distribution.

[0008] The Conditional Linear Gaussian (CLG) model is the same as the Bayesian network and is defined by its directed acyclic graph, which consists of a set of nodes and links between nodes. Nodes represent random variables, and links between two nodes represent linear dependencies in the case of CLG distribution. The output node X has a continuous parent node Z and a discrete parent node I. The distribution L of node X is a conditional linear Gaussian distribution, which is expressed as: ; Where N represents a Gaussian distribution, μ is the mean vector, B represents the matrix containing the continuous paternal regression parameters, Σ is the covariance matrix, and the parameter matrix B is solved using maximum likelihood estimation. The Bayesian toolbox is used for data training and prediction. To better define the trajectory prediction problem and quantify its uncertainty, we introduce a set of random variables and design a directed acyclic graph (DAG) for trajectory prediction. The DAG consists of boxes and circles. The variables within the boxes are discrete quantities, while the variables within the circles are continuous quantities. Observations from real-world test drives indicate that in urban traffic environments, a vehicle's future position primarily depends on the following variables, which can be categorized into two types: 1) traffic environment information; and 2) vehicle status, as shown below: T: Traffic conditions. During normal driving, traffic conditions are divided into two categories: T∈{Cr,Cl}, where Cr indicates congested roads and Cl indicates unobstructed roads. This is distinguished by sampling the number of vehicles within 100m before and after the prediction object. Vx: longitudinal vehicle speed, this variable mainly affects the longitudinal position of the obstacle vehicle; δ: front wheel angle, this variable mainly affects the lateral position of the obstacle vehicle; Vp: The speed of the vehicle in front of the obstacle vehicle, because the reaction of the preceding vehicle usually also affects the judgment of the driver of the following vehicle and a certain time delay; P: observation node of vehicle trajectory in the geodetic coordinate system, P∈{X,Y}; As a further technical solution of the present invention, in step 2), a control-oriented vehicle kinematic model is established, lateral path planning in an overtaking scenario is considered, and safety constraints between the host vehicle and the obstacle vehicle are established based on the predicted trajectory of the obstacle vehicle, including the following steps: v x and v y are the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, X and Y are the lateral displacement and longitudinal displacement in the rectangular coordinate system, φ is the vehicle yaw angle, a y is the vehicle's lateral acceleration. Since the vehicle's lateral control and lateral path planning are the main considerations in overtaking scenarios, the lateral speed is set constant. The vehicle kinematic model is established based on the vehicle single-track model as shown below: Formula 1: ; Among them, the state quantity of the system is , control quantity ; The discrete nonlinear system is expressed as: Formula 2: .

[0009] As a further technical solution of the present invention, the main vehicle system is a deterministic system, and the obstacle vehicle system includes a probabilistic component. Therefore, before setting the constraints to ensure the obstacle avoidance function, it is necessary to obtain a predicted sequence of obstacle vehicle distances with a probabilistic distribution, thereby obtaining the subsequent chance constraints. In step 3), the steps of the chance-constrained MPC optimization control include: 3.1) Linearization of state equation and state prediction sequence: According to Formula 2, at any point The system status is represented as: Formula 3: ; Discrete nonlinear system at point Perform Taylor expansion: Formula 4: ; make , , then Equation 4 becomes: Formula 5: ; After expansion: Formula 6: ; in, ; According to Equation 6, the predicted sequence of the state is as follows: p is the prediction range, N c For control range: Formula 7: ; Sorting out formula 7 gives: Formula 8: ; Taking (X, Y) as the system state output, we get Equation 9: Formula 9: ; in, ; 3.2) Opportunity Constraints: Based on Equation 9, the probability distribution is introduced and the future trajectory of the obstacle vehicle is obtained through conditional linear Gaussian. P , P Obeying Gaussian distribution, the distance between the vehicle and the dynamic obstacle is l X 、 l Y as follows: Formula 10: ; in, , , , , ; Combining Equation 8, we can derive the recursive relationship between the expectation and variance of the distance between the ego vehicle and the dynamic obstacle, as shown in Equation 11: Formula 11: ; Considering the most important safety requirement during the overtaking process of autonomous driving, the host vehicle performs lateral control in the overtaking scenario. Therefore, the longitudinal speed of the host vehicle is set to be constant, and lateral path planning is performed to constrain the distance between the ego vehicle and the obstacle vehicle, as shown in Equation 12: Formula 12: ; in, L X 、 L Y The safe distance between the vehicle and the obstacle vehicle is stipulated by relevant laws. β is the confidence of the chance constraint, which has an impact on the optimal solution; The probability density function of the Gaussian distribution is , σ is the standard deviation of the Gaussian distribution, μ is the expectation, and the cumulative distribution function of the Gaussian distribution is derived, as shown in Equation 13: Formula 13: ; Substituting Equation 12 into the above equation, the transformed deterministic constraint is shown in Equation 14: Equation 14: ; As a further technical solution of the present invention, in step 3), the steps of setting the objective function and constraints include: Given a known global planned path, the objective function is designed to minimize deviations from the globally planned lane centerline. Comfort during the overtaking process is also considered, minimizing changes in the control variable. Local path planning is performed by designing the objective function and constraints to ensure the safety of the vehicle following the planned path. Combining Equation 14, the objective function and constraints are as follows: Equation 15: ; Equation 16: ; in, η ref is the global reference path, μ 地 is the ground friction coefficient, is the acceleration due to gravity, y max and y min is the geodetic axis position of the lane boundary, taking into account the ground friction constraint and lane boundary constraint.

[0010] Terminology explanation: The following English abbreviations are used in the embodiments of the present invention: MPC, Model Predictive Control.

[0011] BN, Bayesian Network.

[0012] CLG, Conditional linear Gaussian.

[0013] QP, Quadratic Programming.

[0014] Compared with the prior art, the present invention has the following beneficial effects: 1. Prediction of future trajectory of dynamic obstacles Considering the high complexity and uncertainty of actual roads, the accuracy of future trajectories of deterministic prediction methods cannot be guaranteed. Therefore, the CLG method is used to predict the probability distribution of future trajectories of dynamic obstacles and obtain the Gaussian distribution of future trajectories. Taking into account the randomness of dynamic obstacles, a safe path is obtained through the MPC path planning method.

[0015] 2. Design an MPC path planning method considering randomness in dynamic traffic overtaking scenarios Compared to path planning under deterministic driving conditions, this strategy considers the uncertainty of the traffic environment and develops a lateral control overtaking path planning strategy for dynamic traffic environments based on the probability distribution of the preceding vehicle's trajectory. By accounting for the randomness of obstacle trajectories, the probability distribution of the distance between the leading vehicle and the obstacle during the overtaking process is derived. Appropriate probabilistic constraints are designed to ensure a feasible solution to the optimal solution, thereby obtaining a safe overtaking path that serves as a reference for the subsequent trajectory tracking control module. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flowchart of a probabilistically constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario provided by an embodiment of the present invention.

[0017] Figure 2 A directed acyclic graph for trajectory prediction provided by an embodiment of the present invention.

[0018] Figure 3 A diagram of a vehicle monorail model provided in an embodiment of the present invention.

[0019] Figure 4 A schematic diagram of a safety distance provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0020] The technical solution of this patent is further described in detail below in conjunction with specific implementation methods.

[0021] See also Figures 1 to 4 , a probabilistically constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario, the method comprising the following steps: 1) The historical trajectory of the obstacle vehicle is collected through the on-board sensors, and the obstacle vehicle trajectory prediction model is established using the conditional linear Gaussian method; 2) Build a control-oriented vehicle kinematic model, consider lateral path planning in overtaking scenarios, and establish safety constraints between the host vehicle and the obstacle vehicle based on the predicted trajectory of the obstacle vehicle; 3) Optimal control of chance-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods.

[0022] In step 1) of this embodiment, the step of establishing the obstacle vehicle trajectory prediction model using the conditional linear Gaussian method includes: Vehicle trajectory prediction is essentially a probability estimation problem based on historical information. Bayesian networks (BNs), with their superior mathematical representation and uncertainty management, are well-suited for modeling and inferring complex nonlinear dynamic systems. Assuming that the obstacle vehicle's trajectory follows a Gaussian distribution, and that the probability distributions of the obstacle vehicle's X and Y coordinate positions in the geodetic coordinate system are mutually independent, this paper utilizes a special variant of the Bayesian network, the Conditional Linear Gaussian (CLG) model. This model can handle both discrete and continuous variables and make predictions based on their joint probability distribution.

[0023] The Conditional Linear Gaussian (CLG) model is the same as the Bayesian network and is defined by its directed acyclic graph, which consists of a set of nodes and links between nodes. Nodes represent random variables, and links between two nodes represent linear dependencies in the case of CLG distribution. The output node X has a continuous parent node Z and a discrete parent node I. The distribution L of node X is a conditional linear Gaussian distribution, which is expressed as: ; Where N represents a Gaussian distribution, μ is the mean vector, B represents the matrix containing the continuous paternal regression parameters, Σ is the covariance matrix, and the parameter matrix B is solved using maximum likelihood estimation. The Bayesian toolbox is used for data training and prediction. In order to better define the trajectory prediction problem and quantify the uncertainty of trajectory prediction, a set of random variables are introduced and a directed acyclic graph of trajectory prediction is designed, such as Figure 2 As shown in the figure, the directed acyclic graph consists of boxes and circles. The variables in the boxes are discrete quantities, and the variables in the circles are continuous quantities. According to observations during test drives on real roads, in an urban traffic environment, the future position of a vehicle mainly depends on the following variables, which are divided into two categories: 1) traffic environment information; 2) vehicle status, as shown below: T: Traffic conditions. During normal driving, traffic conditions are divided into two categories: T∈{Cr,Cl}, where Cr indicates congested roads and Cl indicates unobstructed roads. This is distinguished by sampling the number of vehicles within 100m before and after the prediction object. Vx: longitudinal vehicle speed, this variable mainly affects the longitudinal position of the obstacle vehicle; δ: front wheel angle, this variable mainly affects the lateral position of the obstacle vehicle; Vp: The speed of the vehicle in front of the obstacle vehicle, because the reaction of the preceding vehicle usually also affects the judgment of the driver of the following vehicle and a certain time delay; P: observation node of vehicle trajectory in the geodetic coordinate system, P∈{X,Y}; In step 2) of this embodiment, the steps of establishing a control-oriented vehicle kinematic model, considering lateral path planning in an overtaking scenario, and establishing safety constraints between the host vehicle and the obstacle vehicle based on the predicted obstacle vehicle trajectory include: Vehicle single track model Figure 3 As shown, ，v x and v y are the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, X and Y are the lateral displacement and longitudinal displacement in the rectangular coordinate system, φ is the vehicle yaw angle, a y is the vehicle's lateral acceleration. Since the vehicle's lateral control and lateral path planning are the main considerations in overtaking scenarios, the lateral speed is set constant. The vehicle kinematic model is established based on the vehicle single-track model as shown below: Formula 1: ; Among them, the state quantity of the system is , control quantity ; The discrete nonlinear system is expressed as: Formula 2: .

[0024] In this embodiment, the main vehicle system is a deterministic system, while the obstacle vehicle system includes a probabilistic component. Therefore, before setting constraints to ensure obstacle avoidance, it is necessary to obtain a predicted sequence of obstacle vehicle distances with a probabilistic distribution, thereby obtaining subsequent chance constraints. In step 3), the steps of the chance-constrained MPC optimization control include: 3.1) Linearization of state equation and state prediction sequence: According to Formula 2, at any point The system status is represented as: Formula 3: ; Discrete nonlinear system at point Perform Taylor expansion: Formula 4: ; make , , then Equation 4 becomes: Formula 5: ; After expansion: Formula 6: ; in, ; According to Equation 6, the predicted sequence of the state is as follows: p is the prediction range, N c For control range: Formula 7: ; Sorting out formula 7 gives: Formula 8: ; Taking (X, Y) as the system state output, we get Equation 9: Formula 9: ; in, ; 3.2) Opportunity Constraints: Based on Equation 9, the probability distribution is introduced and the future trajectory of the obstacle vehicle is obtained through conditional linear Gaussian. P , P Obeying Gaussian distribution, the distance between the vehicle and the dynamic obstacle is l X 、 l Y as follows: Formula 10: ; in, , , , , ; Combining Equation 8, we can derive the recursive relationship between the expectation and variance of the distance between the ego vehicle and the dynamic obstacle, as shown in Equation 11: Formula 11: ; Considering the most important safety requirement during the overtaking process of autonomous driving, the main vehicle performs lateral control in the overtaking scenario. Therefore, the longitudinal speed of the main vehicle is set to be constant and the lateral path planning is performed. Figure 4 The safe distance diagram of the obstacle vehicle is shown in Figure 12, where the shaded area is the infeasible area for the ego vehicle. The distance between the ego vehicle and the obstacle vehicle is constrained as shown in Equation 12: Formula 12: ; in, L X 、 L Y The safe distance between the vehicle and the obstacle vehicle is stipulated by relevant laws. β is the confidence of the chance constraint, which has an impact on the optimal solution; The probability density function of the Gaussian distribution is , σ is the standard deviation of the Gaussian distribution, μ is the expectation, and the cumulative distribution function of the Gaussian distribution is derived, as shown in Equation 13: Formula 13: ; Substituting Equation 12 into the above equation, the transformed deterministic constraint is shown in Equation 14: Equation 14: ; In step 3) of this embodiment, the steps of setting the objective function and constraints include: Given a known global planned path, the objective function is designed to minimize deviations from the globally planned lane centerline. Comfort during the overtaking process is also considered, minimizing changes in the control variable. Local path planning is performed by designing the objective function and constraints to ensure the safety of the vehicle following the planned path. Combining Equation 14, the objective function and constraints are as follows: Equation 15: ; Equation 16: ; in, η ref is the global reference path, μ 地 is the ground friction coefficient, is the acceleration due to gravity, y max and y min is the geodetic axis position of the lane boundary, taking into account the ground friction constraint and lane boundary constraint.

[0025] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0026] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A probabilistically constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario, characterized in that: The method comprises the following steps: 1) The historical trajectory of the obstacle vehicle is collected through the on-board sensor, and the obstacle vehicle trajectory prediction model is established using the conditional linear Gaussian method; 2) Establish a control-oriented vehicle kinematic model, consider lateral path planning in overtaking scenarios, and establish safety constraints between the host vehicle and the obstacle vehicle based on the predicted trajectory of the obstacle vehicle; 3) Optimal control of chance-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods.

2. The method for probabilistically constrained path planning of an intelligent vehicle in a dynamic overtaking scenario according to claim 1 is characterized in that: In step 1), the steps of establishing the obstacle vehicle trajectory prediction model using the conditional linear Gaussian method include: The conditional linear Gaussian model is the same as the Bayesian network and is defined by its directed acyclic graph, which consists of a set of nodes and links between nodes. The nodes represent random variables, and the links between two nodes represent linear dependencies in the case of CLG distribution. The output node X has a continuous parent node Z and a discrete parent node I. The distribution L of node X is a conditional linear Gaussian distribution, which is expressed as: ； Among them, N represents Gaussian distribution, μ is the mean vector, B represents the matrix containing the continuous paternal regression parameters, Σ is the covariance matrix, and the parameter matrix B is solved by maximum likelihood estimation. The Bayesian toolbox is used for data training and prediction; A set of random variables is introduced to design a directed acyclic graph for trajectory prediction. The directed acyclic graph includes boxes and circles. The variables in the boxes are discrete quantities, and the variables in the circles are continuous quantities. According to observations during test driving on real roads, in an urban traffic environment, the future position of a vehicle mainly depends on the following variables, which are divided into two categories: 1) traffic environment information; 2) vehicle status, as shown below: T: Traffic conditions; in the normal driving process, the traffic conditions are divided into two categories: T∈{Cr, Cl}, where Cr indicates congested roads and Cl indicates unobstructed roads, which are distinguished by sampling the number of vehicles within 100m before and after the prediction object; Vx: longitudinal vehicle speed; δ: front wheel turning angle; Vp: speed of the vehicle in front of the obstacle vehicle; P: Observation node of vehicle trajectory in the geodetic coordinate system, P∈{X,Y}.

3. The method for probabilistically constrained path planning of an intelligent vehicle in a dynamic overtaking scenario according to claim 2 is characterized in that: In step 2), a control-oriented vehicle kinematic model is established, and the lateral path planning in the overtaking scenario is considered. The steps of establishing the safety constraints between the main vehicle and the obstacle vehicle according to the predicted trajectory of the obstacle vehicle include: v x and v y is the longitudinal velocity and lateral velocity of the center of mass in the vehicle coordinate system, X and Y are the lateral displacement and longitudinal displacement in the rectangular coordinate system, φ is the vehicle yaw angle, a y is the lateral acceleration of the vehicle. Since the lateral control and lateral path planning of the vehicle are mainly considered in the overtaking scenario, the lateral speed is set constant, and the vehicle kinematic model is established according to the vehicle single track model, as shown below: Formula 1: ; Among them, the state quantity of the system is , control amount ; The discrete nonlinear system is expressed as: Formula 2: .

4. The method for probabilistically constrained path planning of an intelligent vehicle in a dynamic overtaking scenario according to claim 3 is characterized in that: In step 3), the steps of optimizing control of the opportunity-constrained MPC include: 3.1) Linearization of state equation and state prediction sequence: According to Formula 2, at any point The system status is represented by: Formula 3: ; Discrete nonlinear system at point Perform Taylor expansion: Formula 4: ; make , , then formula 4 becomes: Formula 5: ; After expansion: Formula 6: ; in, ; According to Formula 6, the predicted sequence of states is as follows: p is the prediction range, N c For control range: Formula 7: ; Arrange formula 7 to get: Formula 8: ; Taking (X, Y) as the system state output, we get Equation 9: Formula 9: ; in, ; 3.2) Opportunity Constraints: Based on Equation 9, the probability distribution is introduced and the future trajectory of the obstacle vehicle is obtained through conditional linear Gaussian. P , P Obeying Gaussian distribution, the distance between the vehicle and the dynamic obstacle is l X , l Y as follows: Formula 10: ; in, , , , , ; Combining Formula 8, the recursive relationship between the expectation and variance of the distance between the vehicle and the dynamic obstacle is derived, as shown in Formula 11: Formula 11: ; In the overtaking scenario, the main vehicle performs lateral control, so the longitudinal speed of the main vehicle is set constant, and the lateral path planning is performed to constrain the distance between the ego vehicle and the obstacle vehicle, as shown in Equation 12: Formula 12: ; in, L X , L Y is the safe distance between the vehicle and the obstacle vehicle, β is the confidence level for the chance constraint; The probability density function of the Gaussian distribution is , σ is the standard deviation of the Gaussian distribution, μ is the expectation, and the cumulative distribution function of the Gaussian distribution is derived, as shown in Equation 13: Formula 13: ; Substituting Equation 12 into the above equation, the transformed deterministic constraint is shown in Equation 14: Formula 14: .

5. The method for probabilistically constrained path planning of an intelligent vehicle in a dynamic overtaking scenario according to claim 4 is characterized in that: In step 3), the steps of setting the objective function and constraints include: By designing the objective function and constraints for local path planning, the safety of the main vehicle driving along the planned path is ensured. Combining equation 14, the objective function and constraints are as follows: Formula 15: ; Formula 16: ; in, η ref is the global reference path, μ 地 is the ground friction coefficient, is the acceleration due to gravity, y max and min is the geodetic axis position of the lane boundary.

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