Probabilistically constrained path planning method for intelligent vehicles in dynamic overtaking scenarios
Through the probability-constrained path planning method, the conditional linear Gaussian method and Bayesian network are used to predict obstacle vehicle trajectory, and opportunity constraints are introduced in MPC, which solves the safety hazards of path planning in the dynamic overtaking scenarios of smart cars in complex road environments, and achieves safer and more adaptable path planning.
Patent Information
- Application Number
- CN202411755311.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-03
- Publication Date
- 2025-03-14
- Estimated Expiration
- 2044-12-03
AI Technical Summary
In complex and uncertain road environments, it is difficult for smart cars to achieve effective path planning throughout the whole process in dynamic overtaking scenarios, resulting in safety hazards.
The probability-constrained path planning method is adopted to collect the historical trajectory of the obstacle vehicle through vehicle-mounted sensors, and a conditional linear Gaussian method is used to establish an obstacle vehicle trajectory prediction model, combine it with Bayesian network to make predictions, and opportunity constraints are introduced in the model prediction control (MPC) to ensure the safe distance between the main vehicle and the obstacle vehicle.
It effectively reduces the safety risks of the main car during overtaking, improves the adaptability and safety of path planning, and is suitable for dynamically changing complex road environments.
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Figure CN119225187B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of intelligent vehicles, 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 increase in the number of cars, the proficiency of non-professional drivers has increased, resulting in frequent traffic accidents. How to improve the active safety and traffic safety of cars has become a social problem that needs to be solved urgently. As a hot area of intelligence, 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, the output of the path planning module plays a key navigation role in the vehicle's driving. It guides the vehicle from its current position to the target position and provides a control basis for the path tracking module. Due to the high complexity and uncertainty of actual roads, it is difficult for intelligent vehicles to achieve effective planning throughout the entire process when performing overtaking operations in complex and dynamic road environments. Therefore, before planning the overtaking path, it is necessary to consider the uncertainty of dynamic obstacles during driving, which has positive practical significance for reducing safety hazards and enabling the path planning method to adapt to various dynamically changing road environments.
[0004] As a rolling optimization method, MPC plans a reasonable overtaking path by explicitly processing the constraints of the control system and combining the lateral dynamics model of the vehicle. It has many applications in path planning problems. However, in the existing MPC-based path planning system, the description of the future trajectory of the obstacle vehicle is usually set as a single lane straight driving or turning according to a fixed trajectory, and the randomness of the obstacle vehicle during driving is not considered, 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, integrates the uncertainty information into the path planning system, and guarantees the safe distance between the main vehicle and the obstacle vehicle with probability constraints, 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 probabilistic 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:
[0007] A probabilistically constrained path planning method for an intelligent vehicle in a dynamic overtaking scenario, the method comprising the following steps:
[0008] 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;
[0009] 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;
[0010] 3) Optimal control of chance-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods.
[0011] 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:
[0012] Vehicle trajectory prediction is essentially a probability estimation problem based on historical information. The excellent performance of Bayesian network (BN) in mathematical representation and uncertainty makes it suitable for modeling and inference from complex nonlinear dynamic systems. The obstacle vehicle trajectory is assumed to obey Gaussian distribution, and the probability distributions of the obstacle vehicle coordinate positions X and Y in the geodetic coordinate system are independent of each other. Therefore, the present invention uses a special variant of Bayesian network, namely conditional linear Gaussian (CLG) model, which can process discrete variables and continuous variables at the same time and make predictions based on their joint probability distribution.
[0013] 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, expressed as:
[0014] ;
[0015] 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;
[0016] In order to better define the trajectory prediction problem and quantify the uncertainty of trajectory prediction, a set of random variables is introduced and a directed acyclic graph of trajectory prediction is designed. 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:
[0017] 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;
[0018] Vx: longitudinal vehicle speed, this variable mainly affects the longitudinal position of the obstacle vehicle;
[0019] δ: front wheel steering angle, this variable mainly affects the lateral position of the obstacle vehicle;
[0020] Vp: The speed of the vehicle in front of the obstacle vehicle, because the reaction of the vehicle in front will usually also affect the judgment and specific time delay of the driver of the following vehicle;
[0021] P: observation node of vehicle trajectory in the geodetic coordinate system, P∈{X,Y};
[0022] As a further technical solution of the present invention, in step 2), a control-oriented vehicle kinematics model is established, lateral path planning in an overtaking scenario is considered, and the steps of establishing safety constraints between the host vehicle and the obstacle vehicle according to the predicted trajectory of the obstacle vehicle include:
[0023] 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:
[0024] Formula 1: ;
[0025] Among them, the state quantity of the system is , control amount ;
[0026] The discrete nonlinear system is expressed as:
[0027] Formula 2: .
[0028] 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 part. Therefore, before setting the constraints to ensure the obstacle avoidance function, it is necessary to obtain a prediction sequence of the obstacle vehicle distance with a probabilistic distribution, so as to obtain the subsequent chance constraints. In step 3), the steps of the optimization control of the chance-constrained MPC include:
[0029] 3.1) Linearization of state equation and state prediction sequence:
[0030] According to Formula 2, at any point The system status is represented by:
[0031] Formula 3: ;
[0032] Discrete nonlinear system at point Perform Taylor expansion:
[0033] Formula 4: ;
[0034] make , , then formula 4 becomes:
[0035] Formula 5: ;
[0036] After expansion:
[0037] Formula 6: ;
[0038] in, ;
[0039] According to Formula 6, the predicted sequence of states is as follows: p is the prediction range, N c For control range:
[0040] Formula 7: ;
[0041] Arrange formula 7 to get:
[0042] Formula 8: ;
[0043] Taking (X, Y) as the system state output, we get Equation 9:
[0044] Formula 9: ;
[0045] in, ;
[0046] 3.2) Opportunity Constraints:
[0047] 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:
[0048] Formula 10: ;
[0049] in, , , , , ;
[0050] Combined with 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:
[0051] Formula 11: ;
[0052] Considering the most important safety requirement in the process of overtaking by autonomous driving, the main vehicle performs lateral control in the overtaking scenario. Therefore, 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 Formula 12:
[0053] Formula 12: ;
[0054] 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;
[0055] 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:
[0056] Formula 13: ;
[0057] Substituting equation 12 into the above equation, the transformed deterministic constraint is shown in equation 14:
[0058] Formula 14: ;
[0059] As a further technical solution of the present invention, in step 3), the steps of setting the objective function and constraints include:
[0060] Assume that a global planning path is known, and design the objective function so that the planned overtaking path does not deviate from the center line of the global planning lane as much as possible, and consider the comfort during the overtaking process to minimize the change in the control amount. By designing the objective function and constraints for local path planning, the safety of the main vehicle driving along the planned path is guaranteed. Combined with formula 14, the objective function and constraints are as follows:
[0061] Formula 15: ;
[0062] Formula 16: ;
[0063] 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, taking into account the ground friction constraint and lane boundary constraint.
[0064] Terminology explanation: Some English abbreviations involved in the embodiments of the present invention are explained as follows:
[0065] MPC, Model Predictive Control.
[0066] BN, Bayesian Network.
[0067] CLG, Conditional linear Gaussian.
[0068] QP, Quadratic Programming.
[0069] Compared with the prior art, the present invention has the following beneficial effects:
[0070] 1. Prediction of future trajectory of dynamic obstacles
[0071] Considering the high complexity and uncertainty of actual roads, the accuracy of the future trajectory of the deterministic prediction method cannot be guaranteed. Therefore, the CLG method is used to predict the probability distribution of the future trajectory of dynamic obstacles, and the Gaussian distribution of the future trajectory is obtained. Considering the randomness of dynamic obstacles, a safe path is obtained through the MPC path planning method.
[0072] 2. Design an MPC path planning method considering randomness in dynamic traffic overtaking scenarios
[0073] Compared with the path planning under deterministic driving conditions, the uncertainty of the traffic environment is taken into account, and the overtaking path planning strategy for the lateral control of the main vehicle in a dynamic traffic environment is made based on the probability distribution of the trajectory of the preceding vehicle. The randomness of the obstacle trajectory is taken into account, and the probability distribution of the distance relationship between the main vehicle and the obstacle vehicle during the overtaking process is obtained, and the corresponding probability constraints are designed to ensure that there is a feasible solution when solving the optimal problem, thereby obtaining a safe overtaking path as a reference value for the subsequent trajectory tracking control module. BRIEF DESCRIPTION OF THE DRAWINGS
[0074] Figure 1 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.
[0075] Figure 2 A directed acyclic graph for trajectory prediction provided by an embodiment of the present invention.
[0076] Figure 3 A diagram of a vehicle single track model provided in an embodiment of the present invention.
[0077] Figure 4 A schematic diagram of a safety distance provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0078] The technical solution of this patent is further described in detail below in conjunction with specific implementation methods.
[0079] See also Figures 1 to 4 , a probabilistic constraint path planning method for an intelligent vehicle in a dynamic overtaking scenario, the method comprising the following steps:
[0080] 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;
[0081] 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;
[0082] 3) Optimal control of chance-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods.
[0083] In step 1) of this embodiment, the step of establishing an obstacle vehicle trajectory prediction model using the conditional linear Gaussian method includes:
[0084] Vehicle trajectory prediction is essentially a probability estimation problem based on historical information. The excellent performance of Bayesian network (BN) in mathematical representation and uncertainty makes it suitable for modeling and inference from complex nonlinear dynamic systems. The obstacle vehicle trajectory is assumed to obey Gaussian distribution, and the probability distributions of the obstacle vehicle coordinate positions X and Y in the geodetic coordinate system are independent of each other. Therefore, the present invention uses a special variant of Bayesian network, namely conditional linear Gaussian (CLG) model, which can process discrete variables and continuous variables at the same time and make predictions based on their joint probability distribution.
[0085] 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, expressed as:
[0086] ;
[0087] 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;
[0088] 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 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:
[0089] 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;
[0090] Vx: longitudinal vehicle speed, this variable mainly affects the longitudinal position of the obstacle vehicle;
[0091] δ: front wheel steering angle, this variable mainly affects the lateral position of the obstacle vehicle;
[0092] Vp: The speed of the vehicle in front of the obstacle vehicle, because the reaction of the vehicle in front will usually also affect the judgment and specific time delay of the driver of the following vehicle;
[0093] P: observation node of vehicle trajectory in the geodetic coordinate system, P∈{X,Y};
[0094] In step 2) of this embodiment, a control-oriented vehicle kinematic model is established, lateral path planning in an overtaking scenario is considered, and the steps of establishing safety constraints between the host vehicle and the obstacle vehicle according to the predicted trajectory of the obstacle vehicle include:
[0095] Vehicle single track model Figure 3 As shown, ,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:
[0096] Formula 1: ;
[0097] Among them, the state quantity of the system is , control amount ;
[0098] The discrete nonlinear system is expressed as:
[0099] Formula 2: .
[0100] The main vehicle system of this embodiment is a deterministic system, and the obstacle vehicle system includes a probabilistic part. Therefore, before setting the constraints to ensure the obstacle avoidance function, it is necessary to obtain a prediction sequence of the obstacle vehicle distance with a probabilistic distribution, so as to obtain the subsequent chance constraints. In step 3), the steps of the optimization control of the chance-constrained MPC include:
[0101] 3.1) Linearization of state equation and state prediction sequence:
[0102] According to Formula 2, at any point The system status is represented by:
[0103] Formula 3: ;
[0104] Discrete nonlinear system at point Perform Taylor expansion:
[0105] Formula 4: ;
[0106] make , , then formula 4 becomes:
[0107] Formula 5: ;
[0108] After expansion:
[0109] Formula 6: ;
[0110] in, ;
[0111] According to Formula 6, the predicted sequence of states is as follows: p is the prediction range, N c For the control range:
[0112] Formula 7: ;
[0113] Arrange formula 7 to get:
[0114] Formula 8: ;
[0115] Taking (X, Y) as the system state output, we get Equation 9:
[0116] Formula 9: ;
[0117] in, ;
[0118] 3.2) Opportunity Constraints:
[0119] 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:
[0120] Formula 10: ;
[0121] in, , , , , ;
[0122] Combined with 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:
[0123] Formula 11: ;
[0124] 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 is a schematic diagram of the safe distance of the obstacle vehicle, 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 formula 12:
[0125] Formula 12: ;
[0126] 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;
[0127] 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:
[0128] Formula 13: ;
[0129] Substituting equation 12 into the above equation, the transformed deterministic constraint is shown in equation 14:
[0130] Formula 14: ;
[0131] In step 3) of this embodiment, the steps of setting the objective function and constraints include:
[0132] Assume that a global planning path is known, and design the objective function so that the planned overtaking path does not deviate from the center line of the global planning lane as much as possible, and consider the comfort during the overtaking process to minimize the change in the control amount. By designing the objective function and constraints for local path planning, the safety of the main vehicle driving along the planned path is guaranteed. Combined with formula 14, the objective function and constraints are as follows:
[0133] Formula 15: ;
[0134] Formula 16: ;
[0135] in, η ref is the global reference path, μ 地 is the ground friction coefficient, is the acceleration due to gravity, y max and minis the geodetic axis position of the lane boundary, taking into account the ground friction constraint and lane boundary constraint.
[0136] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the existence of other identical elements in the process, method, article or device including the element.
[0137] 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 specification 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 opportunity-constrained MPC, setting of objective functions and constraints, and solving optimal problems based on quadratic programming methods; In step 2), a control-oriented vehicle kinematics model is established, and lateral path planning in an overtaking scenario is considered. The steps of establishing 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, 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 quantity u=a y ; The discrete nonlinear system is expressed as: Formula 2: ξ(k+1)=f(ξ(k),u(k)); 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 equation 4 becomes: Formula 5: After expansion: Formula 6: ξ(k+1)=Aξ(k)+Bu(k)+d; in, According to Formula 6, the predicted sequence of states is as follows: p is the prediction range, N c For the 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: y(k+1)=CAξ(k)+CBu(k)+Cd(k); in, 3.2) Opportunity Constraints: Based on Equation 9, we introduce probability distribution and obtain the future trajectory P of the obstacle vehicle through conditional linear Gaussian. P obeys Gaussian distribution, so the distance l between the vehicle and the dynamic obstacle is X , l Y as follows: Formula 10: l(k+1)=CAξ(k)+CBu(k)+Cd(k)+DP(k); in, Combined with 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: Among them, L X , L Y is the safe distance between the ego vehicle and the obstacle vehicle, β is the confidence of 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: 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: Among them, η ref is the global reference path, μ 地 is the ground friction coefficient, g 重 is the acceleration due to gravity, y max and min is the geodetic axis position of the lane boundary.
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 an obstacle vehicle trajectory prediction model using a 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: L(X|Z=z,I=i)=N{μ(i)+B(i)z,Σ(i)}; 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 means the road is congested and Cl means the road is unobstructed, and the distinction is made 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}.
Citation Information
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