Automatic driving vehicle trajectory planning method under influence of intersection accidents

Abstract

The invention discloses an automatic driving vehicle trajectory planning method under the influence of an intersection accident, and belongs to the field of automatic driving vehicle trajectory planning control. The problem that the traffic efficiency of the intersection is low after an accident is solved. According to the method, the intersection environment after an accident is accurately sensed and analyzed, the driving risk field is constructed through the expected trajectory field, the accident rejection field and the vehicle motion field, the influence of various factors on the vehicle is quantified, and real-time path adjustment guidance can be provided for the automatic driving vehicle by calculating transverse and longitudinal driving force and acceleration; long-time detention and traffic jam of the vehicles caused by accidents are avoided, the vehicle passing efficiency under the intersection accident scene can be effectively improved, traffic delay is reduced, meanwhile, the driving safety is enhanced, it is ensured that the vehicles safely pass through in the complex intersection environment, and the risk of secondary occurrence of the accidents is reduced. The method can be applied to automatic driving vehicle trajectory planning under the influence of intersection accidents.

Description

Technical Field

[0001] The present invention belongs to the field of trajectory planning and control of autonomous driving vehicles, and in particular relates to a trajectory planning method for autonomous driving vehicles under the influence of intersection accidents. Background Art

[0002] At present, various types of traffic flow cross each other at urban road intersections. Due to the large number of conflict areas, various types of traffic accidents are easily caused, leading to traffic congestion. With the increasing development of cities, there are more and more vehicles, and the traffic pressure is increasing accordingly. There are more and more traffic accidents at urban road intersections. Once the internal space of the intersection is occupied by traffic accidents, the passage space of vehicles is compressed, which will affect multiple traffic flows in different directions. The process of vehicles bypassing obstacles to pass through the intersection may cause chaos and reduce traffic efficiency. However, the current research on the post-accident scene of the intersection is very limited, especially the lack of effective methods to optimize the traffic behavior of autonomous driving vehicles to reduce the negative impact of accidents on vehicle traffic efficiency. Therefore, in order to solve the problem of low traffic efficiency at the intersection after the accident, a trajectory planning method for autonomous driving vehicles passing through the intersection under the influence of accidents is needed. Summary of the invention

[0003] The purpose of the present invention is to solve the problem of low traffic efficiency at an intersection after an accident, and to propose a trajectory planning method for an autonomous driving vehicle under the influence of an intersection accident.

[0004] The technical solution adopted by the present invention to solve the above technical problems is: a method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident, the method specifically comprising the following steps:

[0005] Step 1: The autonomous driving vehicle uses an environmental perception device to perceive the environmental information of the intersection after the accident. The perceived environmental information of the intersection after the accident includes intersection geometric layout information, accident obstacle information, and vehicle motion status information;

[0006] Step 2: Determine whether the accident range overlaps with the expected trajectory based on the accident obstacle information;

[0007] If the accident range does not overlap with the expected trajectory, then the vehicle motion field model is constructed according to the vehicle motion state information and then step three is executed;

[0008] If the accident range overlaps with the expected trajectory, then the vehicle motion field model is constructed based on the vehicle motion state information and then step 4 is executed;

[0009] Step 3: After constructing the expected trajectory field model according to the intersection geometric layout information, construct the intersection post-accident driving risk field model according to the expected trajectory field model and the vehicle motion field model, and then execute step 5;

[0010] Step 4: After constructing the accident exclusion field model, construct the intersection post-accident driving risk field model based on the accident exclusion field model and the vehicle movement field model, and then execute step 5;

[0011] Step 5: Plan the trajectory of the autonomous driving vehicle based on the driving risk field model after the intersection accident.

[0012] The post-accident driving risk field model is:

[0013]

[0014] in, It is the driving risk field model after the accident. S = 0 indicates that the accident range has no overlap with the expected trajectory, and S = 1 indicates that the accident range has overlap with the expected trajectory.

[0015] Furthermore, the environmental perception device includes a camera sensor, a radar sensor and a lidar sensor.

[0016] Furthermore, the intersection geometric layout information includes the intersection's entrance lane width, the number of exit lanes, the exit lane width, the entrance and exit lane positions, and the intersection shape and size.

[0017] Furthermore, the accident obstacle information includes the accident location and the area occupied by the accident.

[0018] Furthermore, the vehicle motion state information includes the position of the autonomous driving vehicle in the intersection, the driving direction of the autonomous driving vehicle, the speed of the autonomous driving vehicle, the mass of the autonomous driving vehicle, the position of the front adjacent vehicle in the intersection, the driving direction of the front adjacent vehicle, the speed of the front adjacent vehicle, and the distance between the autonomous driving vehicle and the front adjacent vehicle.

[0019] Furthermore, the expected trajectory field model is constructed according to the geometric layout information of the intersection where the traffic accident occurs:

[0020]

[0021] in, is the expected trajectory field model; lat is the normal gravitational coefficient; d exp is the vertical distance between the spatial point (x, y) and the desired trajectory; W is the track width; λ des is the terminal coefficient, which attracts vehicles to move toward the terminal; l exit It is the trajectory length from the vertical point of the spatial point (x, y) on the desired trajectory to the end point of the desired trajectory; represents the desired direction of the autonomous vehicle at time t.

[0022] Furthermore, the desired direction of the autonomous driving vehicle at time t is:

[0023]

[0024] Among them, x0(t) represents the current position of the autonomous driving vehicle, x d (t) represents the desired position of the autonomous vehicle.

[0025] Furthermore, the vehicle motion field model is constructed according to the vehicle motion state information, specifically:

[0026]

[0027] Among them, λ con is the repulsion coefficient of the motion repulsion effect; λ ita is the obstacle rejection coefficient; is the velocity vector of the autonomous vehicle at time t; Δv (t) is the difference between the speed of the autonomous driving vehicle and the speed of the neighboring vehicle in front at time t; d k is the distance between the autonomous driving vehicle and the neighboring vehicle in front; gui is the attraction coefficient of the motion attraction; L is the safety distance in the intersection; is the angle between the driving direction vector of the autonomous driving vehicle and the vehicle in front;

[0028]

[0029] Among them, v (t) is the speed of the autonomous driving vehicle at time t; s0 is the static safety distance; T is the expected headway; α0 is the maximum acceleration of the autonomous driving vehicle; d is the comfortable deceleration of the autonomous driving vehicle.

[0030] Furthermore, the accident rejection field model is:

[0031]

[0032] Among them, λ ita is the obstacle rejection coefficient; d ita Indicates the shortest distance between the spatial point (x, y) and the obstacle edge; d exit Indicates the straight-line distance from the spatial point (x, y) to the end point; λ itades is the endpoint coefficient of the accident repulsion field.

[0033] Furthermore, the specific process of step five is as follows:

[0034] The start time of the nth time step is recorded as t. After calculating the driving risk field of the autonomous driving vehicle at the intersection (x, y) at time t according to the post-accident driving risk field model, the lateral field driving force and longitudinal field driving force obtained by the autonomous driving vehicle are calculated:

[0035]

[0036] Among them, F X(n) is the lateral driving force of the autonomous driving vehicle in the nth time step, F Y(n) is the longitudinal driving force of the autonomous driving vehicle in the nth time step;

[0037] According to the mass, lateral field driving force and longitudinal field driving force of the autonomous driving vehicle, the lateral acceleration and longitudinal acceleration in the nth time step are calculated:

[0038]

[0039] Among them, a X(n) is the lateral acceleration of the autonomous vehicle, a Y(n) is the longitudinal acceleration of the autonomous vehicle, and M is the mass of the autonomous vehicle;

[0040] By default, the autonomous vehicle moves along the X and Y axes with uniform acceleration in a shorter time step. The autonomous vehicle will avoid obstacles and reach the end of the trajectory in time without deviating as much as possible, completing the process of passing through the intersection with obstacles.

[0041] The trajectory planning result for the autonomous driving vehicle is:

[0042]

[0043] Among them, (X (n) ,Y (n) ) is the position coordinate of the autonomous driving vehicle at the beginning of the nth time step; t′ is the length of a time step, (X (n+1) ,Y (n+1) ) is the position coordinate of the autonomous driving vehicle at the beginning of the n+1th time step; and are the X-axis and Y-axis speeds of the autonomous driving vehicle at the n+1th time step, respectively; and are the X-axis and Y-axis velocities of the autonomous driving vehicle at the nth time step, respectively.

[0044] The beneficial effects of the present invention are:

[0045] The present invention accurately perceives and analyzes the intersection environment after the accident, constructs a driving risk field through the expected trajectory field, the accident rejection field and the vehicle motion field, quantifies the impact of various factors on the vehicle, and provides real-time path adjustment guidance for the autonomous driving vehicle by calculating the lateral and longitudinal driving forces and accelerations, thereby avoiding long-term vehicle detention and traffic congestion caused by accidents, and can effectively improve the vehicle traffic efficiency in intersection accident scenarios, reduce traffic delays, and at the same time enhance driving safety, ensure the safe passage of vehicles in complex intersection environments, and reduce the risk of secondary accidents.

[0046] The method proposed in the present invention can dynamically respond to different types of accidents and the environmental changes caused by them, and has strong adaptability. For intersections with different geometric layouts and different types of traffic accidents, the method of the present invention can perform effective trajectory planning, showing good robustness and versatility. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident of the present invention. DETAILED DESCRIPTION

[0048] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident, and the method specifically includes the following steps:

[0049] Step 1: The autonomous driving vehicle uses environmental perception equipment to perceive environmental information of the intersection after the accident, and the environmental perception equipment used includes but is not limited to camera sensors, radar sensors and lidar sensors, and the environmental perception technology used includes but is not limited to VTX technology;

[0050] The perceived post-accident intersection environment information includes intersection geometry layout information, accident obstacle information, and vehicle motion status information;

[0051] The intersection geometry layout information specifically includes the intersection entrance lane width, exit lane number, exit lane width, entrance and exit lane position, intersection shape and size. The number of entrance and exit lanes determines the number of track strips, and the shape of the track strip (curvature, radius, etc.) is related to the entrance and exit lane position and the intersection shape and size.

[0052] The accident obstacle information specifically includes the accident location and the area occupied by the accident.

[0053] The vehicle motion state information specifically includes the position of the autonomous driving vehicle in the intersection, the driving direction of the autonomous driving vehicle, the speed of the autonomous driving vehicle, the mass of the autonomous driving vehicle, the position of the front adjacent vehicle in the intersection, the driving direction of the front adjacent vehicle, the speed of the front adjacent vehicle, and the distance between the autonomous driving vehicle and the front adjacent vehicle.

[0054] Step 2: If there is no traffic accident at the intersection, based on the intersection size layout and vehicle traffic habits, a short driving trajectory that complies with driving rules can be used to constrain the vehicle's traffic behavior. This driving trajectory is called the expected trajectory. When vehicles travel on the expected trajectory, due to individual differences, a trajectory range will be formed, namely the trajectory belt. Vehicles will travel to the end of the trajectory under the constraints of the traffic range formed by the expected trajectory belt. Therefore, when a traffic accident occurs at an intersection, the first thing to be clear is whether the vehicle can travel to the end point according to the expected trajectory, namely

[0055] Determine whether the accident range overlaps with the expected trajectory based on the accident obstacle information;

[0056] If the accident range does not overlap with the expected trajectory, execute step 3;

[0057] If the accident range overlaps with the expected trajectory, execute step 4;

[0058] Step 3: If the accident range does not overlap with the expected trajectory of each entrance and exit lane, that is, the accident range does not affect the vehicles on each entrance lane from traveling along the expected trajectory to the target exit lane, the expected trajectory field model is constructed based on the geometric layout information of the intersection where the traffic accident occurred:

[0059]

[0060] Among them, λ lat is the normal gravitational coefficient; d exp is the vertical distance between the spatial point (x, y) and the desired trajectory; W is the track width, which is generally 3.5, and can also be set according to the width of the entrance and exit lanes; λ des is the terminal coefficient, which attracts vehicles to move toward the terminal; l exit It is the trajectory length from the vertical point of the spatial point (x, y) on the desired trajectory to the end point of the desired trajectory; represents the desired direction of the autonomous vehicle at time t;

[0061]

[0062] Among them, x0(t) represents the current position of the autonomous driving vehicle, x d (t) represents the desired position of the autonomous vehicle and ||·|| represents the 2-norm.

[0063] When an autonomous vehicle is driving in an intersection, it is not only repelled by accident obstacles and attracted by the end of the trajectory, but also needs to adopt certain strategies to maintain its own safety margin in order to avoid the risk of collision from surrounding moving vehicles. Therefore, the motion state of the neighboring vehicle in front also affects the motion state of the vehicle in real time. The driving direction, speed, speed difference and distance between the two will become factors affecting the forward movement of the vehicle. The vehicle is affected by the neighboring vehicle in front, and there is a critical distance when the force direction changes. This distance is defined as the safety distance of the vehicle. Due to the complex movement direction of vehicles in the intersection, there is a safety distance in all directions for moving vehicles. The closed area surrounded by these safety distance points is the safety range. The neighboring vehicles within the safety range repel the vehicle, and the neighboring vehicles outside the safety range attract the vehicle. When the distance between the vehicle and the neighboring vehicle is the safety distance, the vehicle is neither affected by gravity nor repulsion. The safety distance is not a fixed value, but an instant state parameter. Therefore, the motion state of the neighboring vehicle also affects the motion state of the vehicle in real time. The safety distance between the two is related to parameters such as their driving direction, speed, speed difference and distance.

[0064] Specifically, the vehicle motion field model constructed based on the safe distance formed by the motion state of the autonomous driving vehicle and the neighboring vehicle in front and the mutual attraction and repulsion within and outside the safe distance is:

[0065]

[0066] Among them, λ con is the repulsion coefficient of the motion repulsion effect; λ ita is the obstacle rejection coefficient; is the velocity vector of the autonomous vehicle at time t; Δv (t) is the difference between the speed of the autonomous driving vehicle and the speed of the neighboring vehicle in front at time t; d k is the distance between the autonomous driving vehicle and the neighboring vehicle in front; gui is the attraction coefficient of the motion attraction; L is the safety distance in the intersection; It is the angle between the driving direction vector of the autonomous driving vehicle and the vehicle in front.

[0067]

[0068] Among them, v (t) is the speed of the autonomous driving vehicle at time t; s0 is the static safety distance, which is generally 2m; T is the expected headway, which is generally 1.1s; α0 is the maximum acceleration of the vehicle, which is 1m / s 2 ; d is the comfortable deceleration of the vehicle, which is 1.5m / s 2 .

[0069] Then, a post-accident driving risk field model for the intersection is constructed based on the expected trajectory field model and the vehicle motion field model, and then step five is executed;

[0070] Step 4: construct an accident exclusion field model, and then construct a post-accident driving risk field model for the intersection based on the accident exclusion field model and the vehicle motion field model, and then execute step 5;

[0071] In the case where the accident range overlaps with the expected trajectory of each entrance and exit lane, that is, the accident range affects the vehicles on the entrance lane to travel to the target exit lane, an accident exclusion field model is constructed according to the degree to which the traffic behavior of the autonomous driving vehicle is affected by the accident in the intersection:

[0072]

[0073] Among them, λ ita is the obstacle rejection coefficient; d ita Indicates the shortest distance between the spatial point (x, y) and the obstacle edge; d exit Indicates the straight-line distance from the spatial point (x, y) to the end point; λ itades is the end point coefficient of the accident repulsion field;

[0074] Combining steps 3 and 4, the post-accident driving risk field model can be obtained as follows:

[0075]

[0076] in, is the driving risk field model after the accident, S = 0 means that the accident range does not overlap with the expected trajectory, and S = 1 means that the accident range overlaps with the expected trajectory;

[0077] Step 5: Plan the trajectory of the autonomous vehicle based on the post-intersection accident driving risk field model;

[0078] Specifically, the starting time of the nth time step is recorded as t, and the driving risk field of the autonomous driving vehicle at the intersection (x, y) at time t is calculated according to the post-accident driving risk field model, and then the lateral field driving force and longitudinal field driving force obtained by the autonomous driving vehicle are calculated:

[0079]

[0080] Among them, F X(n) is the lateral driving force of the autonomous driving vehicle in the nth time step, F Y(n) is the longitudinal driving force of the autonomous driving vehicle in the nth time step;

[0081] According to the mass, lateral field driving force and longitudinal field driving force of the autonomous driving vehicle, the lateral acceleration and longitudinal acceleration in the nth time step are calculated:

[0082]

[0083] Among them, a X(n) is the lateral acceleration of the autonomous vehicle, a Y(n) is the longitudinal acceleration of the autonomous vehicle, and M is the mass of the autonomous vehicle;

[0084] By default, the autonomous vehicle moves along the X and Y axes with uniform acceleration in a short time step. The autonomous vehicle will avoid obstacles and reach the end of the trajectory in time without deviating as much as possible, completing the process of passing through the intersection with obstacles.

[0085] The trajectory planning result for the autonomous vehicle is:

[0086]

[0087] Among them, (X (n) ,Y (n) ) is the coordinate of the autonomous driving vehicle at the beginning of the nth time step; t′ is the length of a time step, (X (n+1) ,Y (n+1) ) is the coordinate of the autonomous driving vehicle at the start time of the n+1th time step; and are the X-axis and Y-axis speeds of the autonomous driving vehicle at the n+1th time step, respectively; and are the X-axis and Y-axis velocities of the autonomous driving vehicle at the nth time step, respectively.

[0088] Experimental Section

[0089] The specific intersection parameters are shown in Table 1:

[0090] Table 1 Intersection parameters

[0091]

[0092] Using the simulation parameters shown in Table 2, based on the model, the obstacle avoidance path planning effect of the vehicle in the intersection after a traffic accident can be obtained.

[0093] Table 2 Simulation parameter design

[0094]

[0095] The present invention constructs the expected trajectory field, accident exclusion field and moving vehicle field based on the acquired post-accident intersection environment information, and performs trajectory planning in combination with the post-accident driving risk field of the intersection to obtain a safe obstacle avoidance path for the vehicle in the intersection where the accident occurred. The method of the present invention accurately and finely expresses the various elements of the post-accident intersection driving environment, models the impact of each element on vehicle behavior, and realizes the dynamic adjustment of the driving state and path of the autonomous driving vehicle when passing through the intersection where the accident occurred.

[0096] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident, characterized in that: The method specifically comprises the following steps: Step 1: The autonomous driving vehicle uses an environmental perception device to perceive the environmental information of the intersection after the accident. The perceived environmental information of the intersection after the accident includes intersection geometric layout information, accident obstacle information, and vehicle motion status information; Step 2: Determine whether the accident range overlaps with the expected trajectory based on the accident obstacle information; If the accident range does not overlap with the expected trajectory, then the vehicle motion field model is constructed according to the vehicle motion state information and then step three is executed; If the accident range overlaps with the expected trajectory, then the vehicle motion field model is constructed based on the vehicle motion state information and then step 4 is executed; Step 3: After constructing the expected trajectory field model according to the intersection geometric layout information, construct the intersection post-accident driving risk field model according to the expected trajectory field model and the vehicle motion field model, and then execute step 5; Step 4: After constructing the accident exclusion field model, construct the intersection post-accident driving risk field model based on the accident exclusion field model and the vehicle movement field model, and then execute step 5; Step 5: Plan the trajectory of the autonomous driving vehicle based on the driving risk field model after the intersection accident.

2. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 1, characterized in that: The intersection geometric layout information includes the intersection's entrance lane width, exit lane number, exit lane width, entrance and exit lane positions, intersection shape and size.

3. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 2, characterized in that: The accident obstacle information includes the accident location and the area occupied by the accident.

4. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 3, characterized in that: The vehicle motion state information includes the position of the autonomous driving vehicle in the intersection, the driving direction of the autonomous driving vehicle, the speed of the autonomous driving vehicle, the mass of the autonomous driving vehicle, the position of the front adjacent vehicle in the intersection, the driving direction of the front adjacent vehicle, the speed of the front adjacent vehicle, and the distance between the autonomous driving vehicle and the front adjacent vehicle.

5. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 4, characterized in that: The expected trajectory field model is constructed according to the geometric layout information of the intersection where the traffic accident occurs: in, is the expected trajectory field model; lat is the normal gravitational coefficient; d exp is the vertical distance between the spatial point (x, y) and the desired trajectory; W is the track width; λ des is the end point coefficient; l exit It is the trajectory length from the vertical point of the spatial point (x, y) on the desired trajectory to the end point of the desired trajectory; represents the desired direction of the autonomous vehicle at time t.

6. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 5, characterized in that: The desired direction of the autonomous vehicle at time t is: Among them, x0(t) represents the current position of the autonomous driving vehicle, x d (t) represents the desired position of the autonomous vehicle and ||·|| represents the 2-norm.

7. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 6, characterized in that: The vehicle motion field model is constructed according to the vehicle motion state information, specifically: Among them, λ con is the repulsion coefficient of the motion repulsion effect; ita is the obstacle rejection coefficient; is the velocity vector of the autonomous vehicle at time t; Δv (t) is the difference between the speed of the autonomous driving vehicle and the speed of the neighboring vehicle in front at time t; d k is the distance between the autonomous driving vehicle and the neighboring vehicle in front; gui is the attraction coefficient of the motion attraction; L is the safety distance in the intersection; is the angle between the driving direction vector of the autonomous driving vehicle and the vehicle in front; Among them, v (t) is the speed of the autonomous driving vehicle at time t; s0 is the static safety distance; T is the expected headway; α0 is the maximum acceleration of the autonomous driving vehicle; d is the comfortable deceleration of the autonomous driving vehicle.

8. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 7, characterized in that: The accident rejection field model is: in, is the accident exclusion field model, λ ita is the obstacle rejection coefficient; d ita Indicates the shortest distance between the spatial point (x, y) and the obstacle edge; d exit Indicates the straight-line distance from the spatial point (x, y) to the end point; λ itades is the endpoint coefficient of the accident repulsion field.

9. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 8, characterized in that: The post-accident driving risk field model is: in, It is the driving risk field model after the accident. S = 0 indicates that the accident range has no overlap with the expected trajectory, and S = 1 indicates that the accident range has overlap with the expected trajectory.

10. The method for trajectory planning of an autonomous driving vehicle under the influence of an intersection accident according to claim 9, characterized in that: The specific process of step five is as follows: The start time of the nth time step is recorded as t. After calculating the driving risk field of the autonomous driving vehicle at the intersection (x, y) at time t according to the post-accident driving risk field model, the lateral field driving force and longitudinal field driving force obtained by the autonomous driving vehicle are calculated: Among them, F X(n) is the lateral driving force of the autonomous driving vehicle in the nth time step, F Y(n) is the longitudinal driving force of the autonomous driving vehicle in the nth time step; According to the mass, lateral field driving force and longitudinal field driving force of the autonomous driving vehicle, the lateral acceleration and longitudinal acceleration in the nth time step are calculated: Among them, a X(n) is the lateral acceleration of the autonomous vehicle, a Y(n) is the longitudinal acceleration of the autonomous vehicle, and M is the mass of the autonomous vehicle; The trajectory planning result for the autonomous driving vehicle is: Among them, (X (n) ,Y (n) ) is the position coordinate of the autonomous driving vehicle at the beginning of the nth time step; t′ is the length of a time step, (X (n+1) ,Y (n+1) ) is the position coordinate of the autonomous driving vehicle at the beginning of the n+1th time step; and are the X-axis and Y-axis speeds of the autonomous driving vehicle at the n+1th time step, respectively; and are the X-axis and Y-axis velocities of the autonomous driving vehicle at the nth time step, respectively.

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