Intelligent vehicle obstacle avoidance path planning method based on improved RRT and back-end optimization strategy

Abstract

The intelligent vehicle obstacle avoidance path planning method based on improved RRT and back-end optimization strategy comprises the following steps: 1, optimizing the RRT algorithm sampling space, adding a heuristic strategy to expand the RRT tree node; 2, detecting the vehicle nonholonomic constraint of the expanded node, and screening the node meeting the drivability; 3, assigning the attribute cost and expansion cost to the node in the RRT tree, and reallocating the parent node for the newly expanded node until the target point; 4, generating an initial path by reverse search, and constructing a "driving corridor" and an approximate convex space based on the initial path; 5, considering the path smoothness, curvature continuity and other costs, and solving the optimal path in the convex space range combined with multiple constraint conditions. The method is suitable for the intelligent vehicle autonomous obstacle avoidance path planning problem of the Ackerman steering mechanism intelligent vehicle driving at low speed in the Frenet coordinate system, and can quickly generate a smooth and safe local obstacle avoidance path.

Description

Technical Field

[0001] This invention relates to the field of intelligent vehicle local obstacle avoidance path planning technology, specifically to an intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategies. Background Technology

[0002] In recent years, significant advancements in artificial intelligence and computer technology have propelled autonomous vehicles to the forefront of attention across multiple fields, including military, agriculture, and daily life, placing higher demands on the autonomy and safety of vehicle driving.

[0003] Local obstacle avoidance path planning is a key challenge in the field of autonomous driving. It requires providing a feasible and collision-free local path for the intelligent vehicle based on the global path to meet the obstacle avoidance requirements of potential dynamic and static obstacles. The safety of the intelligent vehicle and some performance indicators during driving are directly affected by the quality of the planned path. Therefore, how to plan a high-quality path for the intelligent vehicle under the multiple constraints of the local obstacle avoidance problem is an urgent problem to be solved.

[0004] Based on the continuity of the configuration space, intelligent vehicle local obstacle avoidance path planning methods can be divided into two main categories: optimization-based methods and sampling-based methods.

[0005] Optimization-based methods comprehensively consider constraints related to the vehicle and its surrounding environment, aiming to minimize or maximize the designed cost function to obtain the optimal smooth path. Their greatest advantage is the ability to obtain the optimal obstacle avoidance solution within each planning cycle. However, optimization problems are typically convex, requiring solutions to be found within a convex space, which is inherently challenging. Furthermore, optimization-based algorithms often exhibit poor real-time performance. The solution speed is heavily dependent on the nonlinearity of the objective function, the tightness of the constraints, and the solver's operating principle, all of which place a significant computational burden on the hardware. Therefore, how to reasonably simplify the convex space approximation and improve the algorithm's real-time performance is a current challenge for optimization-based local path planning algorithms.

[0006] Sampling-based methods do not require specific environmental modeling; they generate collision-free paths connecting the start and end points by randomly sampling the state or control space. Existing algorithms such as RRT, RRT*, and PRM are widely used in complex obstacle avoidance problems for intelligent vehicles due to their probabilistic completeness, low computational cost, and strong environmental adaptability. However, sampling-based algorithms typically only generate a path without considering convergence speed or path optimality. Often, the generated paths do not meet basic requirements such as curvature continuity and smoothness, making them unusable by path tracking systems. Furthermore, many existing algorithms lack heuristic search capabilities, potentially leading to low execution efficiency and the generation of many useless intermediate values. Therefore, improving the goal-oriented nature and execution speed of the algorithms while ensuring that the generated paths meet requirements such as smoothness and curvature continuity are urgent problems that sampling-based local path planning algorithms need to solve.

[0007] The differences compared to existing technologies are as follows:

[0008] Technical Comparison with Patent CN 114193457 A "A Method for Generating Autonomous Obstacle Avoidance Path for a Robotic Arm Based on a Local Search Algorithm"

[0009] In patent CN 114193457 A, the autonomous obstacle avoidance path generation method based on local search algorithm controls a robotic arm, while the intelligent obstacle avoidance path planning method we propose, which improves the search and optimizes the backend, controls an intelligent vehicle with a four-wheel Ackerman steering mechanism.

[0010] In patent CN 114193457 A, the local search algorithm expands feasible path points by starting from the angle and judging whether the angle constraint is met; while the method we use is vehicle non-integrity constraint detection, which filters expandable nodes based on the minimum turning radius of the intelligent vehicle. The judgment mechanism is significantly different.

[0011] In patent CN 114193457 A, the cost function designed for selecting the optimal path point only considers the distance between the robotic arm and the obstacle; while the cost function we designed for reallocating parent nodes to new extended nodes comprehensively considers obstacle avoidance requirements, reference path similarity requirements, etc., and solves the problem of possible decision fluctuations.

[0012] In patent CN 114193457 A, the final path is generated by connecting discrete path points using a fifth-order polynomial. Our approach, however, employs a back-end optimization strategy. Based on the initial path, we construct a driving corridor and an approximate convex space. Within the convex space, we comprehensively consider path smoothness, curvature continuity, Jerk, and the cost of initial path similarity. We then use the QP algorithm to solve the problem, combining multiple constraints. The final output is a smooth and highly safe optimal obstacle avoidance path.

[0013] Patent CN 114193457 A does not emphasize the real-time performance of the autonomous obstacle avoidance path generation method based on local search algorithm or its advantages compared with other algorithms. However, in our specification, we provide simulation experiments comparing our improved RRT and backend optimization strategy with advanced algorithms IBi-RRT*, Dp-Opt, and AC on straight and curved road sections, highlighting the advantages and good real-time performance of our method.

[0014] Technical Comparison with Patent CN 114740869 A "Robot Obstacle Avoidance Method and System Based on Multi-sensor Fusion Estimation and Iterative Pre-search"

[0015] Patent CN 114740869 A primarily focuses on pose estimation for mobile robots, employing UWB, fusion of LiDAR and odometry data, and IMU information to obtain robot pose estimation via a Kalman filter algorithm. Our work, however, focuses more on the local obstacle avoidance path planning problem for intelligent vehicles with a four-wheel Ackerman steering mechanism. We investigate how to provide a smooth, collision-free local obstacle avoidance path connecting the starting point and the target point based on the global path. In our work, we assume that vehicle pose, obstacle pose, global path, and high-precision map are all obtained through upstream perception, localization, and global path planning modules, and are considered prior information.

[0016] In patent CN 114740869 A, the robot obstacle avoidance uses an iterative pre-search A* algorithm. It adjusts the intermediate target point based on whether there are obstacles on the straight path between the robot and the target point, and then directly calls the A* algorithm. Essentially, it belongs to the search algorithm category. Our proposed method combines the advantages of sampling-based algorithms and optimization-based algorithms. First, we improve the RRT algorithm to increase its execution efficiency and reduce the number of redundant sampling points. Then, we execute a back-end optimization strategy based on the initial path to output the optimal obstacle avoidance path. This is essentially a two-layer obstacle avoidance path planning framework that can ensure the real-time performance of the algorithm and improve the quality of the planned path.

[0017] Patent CN 114740869 A does not consider the feasibility of the planned path. As can be seen from the principle of the A* algorithm, the planned path will have many redundant inflection points and will not meet the basic requirements such as curvature continuity and smoothness. However, the authors did not emphasize the smoothing of the path. Our method considers the requirements of smoothness, curvature continuity, Jerk, and initial path similarity in the objective function of the back-end optimization part, and adds model constraints, curvature constraints, and feasible region constraints to improve the quality of the final path. The simulation results show that our method can obtain a smooth, safe, and curvature continuous local obstacle avoidance path. Summary of the Invention

[0018] To address the problems existing in current intelligent vehicle obstacle avoidance path planning technologies, this invention proposes an intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategies. This method integrates the advantages of optimization-based and sampling-based algorithms to quickly provide intelligent vehicles with a smooth and safe local obstacle avoidance path.

[0019] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0020] The intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategy includes the following steps:

[0021] Step 1: Sampling area optimization:

[0022] Adding boundary constraints and heuristic sector constraints guides the RRT tree to expand toward the target point, improving the algorithm's execution efficiency;

[0023] Step 2: Vehicle non-integrity constraint detection:

[0024] Based on the minimum turning radius of the vehicle, construct the circumcircle of adjacent path points and retain the new extended nodes that are fully drivable;

[0025] Step 3: Cost Allocation and Parent Node Re-election:

[0026] Considering obstacle avoidance and reference path similarity requirements, a cost function is assigned to the nodes in the RRT tree, and the point with the minimum cost is reselected as the parent node of the new extended node.

[0027] Step 4: Approximate dimensions of the driver's aisle and convex space:

[0028] Starting from the target point, search backwards to the parent node and back to the starting point to generate an initial path. Based on the initial path points, construct a "driving corridor" that meets safety requirements and approximate the obstacle avoidance convex space accordingly.

[0029] Step 5: Finding the optimal path:

[0030] Within a convex space, considering the costs of path curvature continuity, smoothness, and comfort, the optimal obstacle avoidance path is solved using the QP algorithm, which combines model constraints, curvature constraints, and drivable area constraints.

[0031] As a further improvement of the present invention, step 1, sampling area optimization, includes the following steps:

[0032] (1-1) Boundary constraints are defined as follows:

[0033]

[0034] Where (s0, l0) represents the vehicle position at the initial time (s... goal ,lgoal ) is the target location. Defined as the boundary between the sampling points s and l in the Frenet coordinate system, this constraint adds a new node (s) to the tree. i ,l i ) after (s i ,l i ) and (s goal , l goal Re-determine;

[0035] (1-2) The heuristic sector constraint is defined as follows;

[0036] Connection (s) i , l i ) and the sampling boundary obtained from (1-1) Forming a triangle, with the angle between two sides and the reference path being θ. With (s i , l i (s) is the center of the circle. i , l i ) and (s goal , l goal The Euclidean distance R between them i A sector can be obtained within the triangle with radius , such that (s i , l i ) and (s goal , l goal Based on the direction of the connection, set variables. Used to expand random points, adding heuristic costs to make The angle should be as small as possible so that the expansion direction of nodes in the RRT tree will tend towards the target point;

[0037] (1-3) Vehicles and obstacles are represented by rectangles and circumcircles. The extended node coordinate calculation method is as follows:

[0038] Calculate the distance from the current node to the circumcircle of the nearest rectangle representing the obstacle. If it is greater than the threshold Then, both boundary constraints and heuristic sector constraints are used to optimize the sampling space; if it is less than the threshold Then only boundary constraints are used to ensure that the random sampling process has a sufficiently large region in space without getting stuck in a dead zone. The coordinates of the extended nodes are represented as follows:

[0039]

[0040] in These are the Frenet coordinates of the extended node. Defined as (s) i , l i ) and (sgoal , l goal The angle between the direction of the connecting line and the direction of the reference line. This indicates the generation of uniformly random numbers between 0 and 1. This indicates that the generated mean is 0 and the standard deviation is . Normally distributed random numbers.

[0041] As a further improvement to the present invention, step 2, vehicle non-integrity constraint detection, is defined as follows:

[0042] With (s i , l i ), (s i-1 , l i-1 The direction of the connecting line is tangent, and the minimum turning radius of the vehicle is R. min Draw the circumcircle O for the radius, and draw it in the same way. and (s) i , l i The circumcircle O′ of ). i , l i ), (s i-1 , l i-1 ) direction of the line and (s i , l i The angle between the directions of the lines connecting O and O' is... The calculation method is as follows:

[0043]

[0044] in From (s) i , l i A vector pointing to O′. From (s) i-1 , l i-1 ) points to (s i , l i A vector of type ), where ||||2 is the L2 norm. If The new extended node is considered to satisfy the vehicle non-integrity constraint and is added to the tree; if If the non-integrity constraint of the vehicle is not met, return to step (2-1) to resample random points.

[0045] As a further improvement of the present invention, step 3, cost allocation and parent node reselection, is as follows:

[0046] First, design the node attribute cost function:

[0047] (3-1) Obstacle distance cost:

[0048] Considering the actual volume of the vehicle, let d be the sum of the distances d between the centers of the circumcircle of the vehicle rectangle and the circumcircle of the obstacle rectangle. 1∶4 As a standard, construct the obstacle distance cost function:

[0049]

[0050] Where d thr For the threshold;

[0051] (3-2) Cost of reference line distance:

[0052] With the current node (s) i , l i ) and the point on the reference line that is closest to this point. The Euclidean distance between them is used as the basis for defining the reference line distance cost:

[0053]

[0054] (3-3) Cost of ipsilaterality:

[0055] If adjacent nodes (s) i-1 , l i-1 ), (s i , l i If the cost is smaller on the same side as the reference line, a larger cost is assigned otherwise to avoid fluctuations in the planning results. Unit vectors perpendicular to the reference line are defined as follows: and The cost of ipsilaterality is expressed as:

[0056]

[0057] The total cost of node attributes is written as:

[0058] cost att =w obs cost obs +w ref cost ref +w ips cost ips

[0059] Where w obs w ref w ips These are the weighting coefficients;

[0060] Furthermore, the cost introduced when expanding nodes is also considered:

[0061] (3-4) Cost of similarity in heading angle:

[0062] Assumption (s i , li ) and (s i-1 , l i-1 The initial parent nodes of ) are (s i , l i ), (s i-1 , l i-1 ) and (s i-2 , l i-2 To avoid abrupt changes in the path heading angle, the heading angle similarity cost is defined as follows:

[0063]

[0064] in Defined as the heading angle error between adjacent path points;

[0065] (3-5) Cost of extending distance:

[0066] Using the cumulative step size of the expansion and the Euclidean distance between the current node and the newly expanded node as the evaluation criteria, the expansion distance cost expression is as follows:

[0067]

[0068] in To extend the step size of the RRT tree step by step.

[0069] The total expansion cost is written as:

[0070] cost exp =w hs cost hs +w exp_dist cost exp_dist

[0071] Where w hs w exp_dist These are the weighting coefficients;

[0072] The total cost from an existing node in the tree to the newly expanded node is:

[0073] cost total =cost att +cost exp

[0074] The RRT tree has the minimum total cost. total The node was re-elected as the new expansion node. The parent node.

[0075] As a further improvement to the present invention, the driving corridor and convex space in step 4 are approximated as follows;

[0076] (4-1) When the RRT tree is expanded to the target point, the parent node is searched in reverse to the starting point to obtain the planned initial path;

[0077] (4-2) Draw a circular sequence C centered on each initial path point. i ∈C O ,i=0,...n is as follows,

[0078] radius of a circle Defined as:

[0079]

[0080] Where d i It is the distance from the i-th path point to the circumcircle of the nearest rectangle representing the obstacle, and its radius is R. r ;

[0081] (4-3) In the circular sequence C i ∈C O ,i=0,...n draws an inscribed rectangle sequence inside Forming the "driving corridor" C 0：n :

[0082] Its definition is as follows:

[0083]

[0084] When there is no overlapping between rectangles, local padding is used.

[0085] (4-4) Combining the obstacle location and the coordinates of the corner point of the driver's corridor, the obstacle avoidance convex space A is... vx Approximately shaded area:

[0086] The convex space is defined as the drivable area:

[0087]

[0088] Where I(s, l) is the cost raster map with a default value of all zeros, if and only if (s i , l i When within a convex space, f assigns I(s) i , l i The value is 1.

[0089] As a further improvement to the present invention, the optimal path solution in step 5 is specifically as follows;

[0090] With a step size of Δs, find a smooth path point sequence l = D(s) with continuous curvature and close to the reference line in the generated convex space;

[0091] (5-1) Consider optimizing the objective function:

[0092]

[0093]

[0094] in Used to measure the degree of deviation between the generated path and the reference path; Defined as the cost of curvature continuity; Jerk-related costs are used to improve path comfort; This indicates the degree of similarity between the optimized path and the initial path. The l-coordinate of the initial path point;

[0095] (5-2) Consider the following multiple constraints:

[0096] iv. Kinematic Model Constraints: Considering the kinematic model, the vehicle's movement must satisfy the model constraints:

[0097]

[0098] Where x i y i These are the vehicle's coordinates in the Cartesian coordinate system at time i, and θ is the coordinate of the vehicle at time i. i That is the corresponding heading angle;

[0099] v. Curvature Constraint: To ensure the drivability of the path, the curvature of the optimized path is constrained.

[0100]

[0101] in It is the maximum permissible curvature, and its value is equal to 1 / R. min ;

[0102] vi. Feasible Area Constraints: To ensure safety, the vehicle needs to be confined within the obstacle avoidance convex space:

[0103] f(~,l i -d sinθ i / 4+R v ) = 1

[0104] f(~,l i +d sinθ i / 4+R v ) = 1

[0105] f(~,l i +d sinθ i / 4-R v ) = 1

[0106] f(~,l i-d sinθ i / 4-R v ) = 1

[0107] Where R v d represents the radius of the circumcircle of the vehicle's rectangle, and d is the vehicle's wheelbase.

[0108] (5-3) Optimal Solution: By combining the cost function from (5-1) with the multiple constraints from (5-2) into a standard quadratic form, and then substituting it into the QP solver, the final optimal local obstacle avoidance path can be obtained. Beneficial Effects:

[0109] Compared with advanced algorithms IBi-RRT*, Dp-Opt, and AC in planning results involving both straight and curved road segments, the improved RRT and back-end optimization strategy produce smoother, safer, and more continuous curvature paths compared to the three algorithms. Within a planning cycle, the number of random sampling points can be reduced by 50.49%, 59.17%, and 68.2%, respectively, and the average planning time can be reduced by 11.21%, 49.53%, and 65.8%, respectively. This method is applicable to obstacle avoidance path planning for low-speed Ackerman structure vehicles in the Frenet coordinate system, fulfilling the obstacle avoidance path planning requirements and improving the quality of the planned path and the algorithm's execution speed. Attached Figure Description

[0110] Figure 1 This is a flowchart of the method disclosed in this invention;

[0111] Figure 2 This is a schematic diagram of heuristic sector constraint sampling;

[0112] Figure 3 This is a schematic diagram showing the rectangular representation of vehicles and obstacles, along with their corresponding circumcircles.

[0113] Figure 4 This is a schematic diagram of vehicle non-integrity constraint detection;

[0114] Figure 5 This is a schematic diagram of the similarity cost of heading angle;

[0115] Figure 6 This is a schematic diagram of the driver's corridor and an approximately convex space;

[0116] Figure 7 This is a comparison chart of the improved RRT and back-end optimization strategies for straight and curved road segments with other algorithm path planning results and average planning time;

[0117] Figure 8 This is a statistical chart showing the number of sampling points of the improved RRT and backend optimization strategies compared to other algorithms. Detailed Implementation

[0118] The present invention will be further described below with reference to specific embodiments.

[0119] like Figure 1 As shown, this invention discloses an intelligent vehicle obstacle avoidance path planning algorithm based on an improved RRT and backend optimization strategy, comprising the following steps:

[0120] An obstacle avoidance path planning algorithm for intelligent vehicles based on improved RRT and backend optimization strategies includes the following steps:

[0121] Step 1: Sampling region optimization: Add boundary constraints and heuristic sector constraints to guide the RRT tree to expand toward the target point and improve the algorithm's execution efficiency;

[0122] Sampling region optimization includes the following steps:

[0123] (1-1) Boundary constraints are defined as follows:

[0124]

[0125] Where (s0, l0) represents the vehicle position at the initial time (s... goal , l goal ) is the target location. Defined as the boundary between the sampling points s and l in the Frenet coordinate system. This constraint adds a new node (s) to the tree. i , l i ) after (s i , l i ) and (s goal , l goal Re-determine.

[0126] (1-2) Heuristic sector constraint definition as follows: Figure 2 Connection (s) i , l i ) and the sampling boundary obtained from (1-1) This can form a triangle, with the angle between two sides and the reference path being θ. With (s i , l i (s) is the center of the circle. i , l i ) and (s goal , l goal The Euclidean distance R between them i Using a radius of , an inscribed sector can be obtained within the triangle. (s) i , l i ) and (s goal , l goal Based on the direction of the connection, set variables. Used to expand random points. Adding a heuristic cost makes... The angle should be as small as possible so that the expansion direction of nodes in the RRT tree tends towards the target point. The colored areas in the diagram represent the probability of random points being generated within a sector; the closer to (s...)... i , l i ) and (s goal , l goal The darker the color of the connecting line, the greater the probability of generating a random point.

[0127] (1-3) Vehicles and obstacles are represented using rectangles and circumcircles, such as... Figure 3 Calculate the distance from the current node to the circumcircle of the nearest rectangle representing the obstacle. If it is greater than the threshold Then, both boundary constraints and heuristic sector constraints are used to optimize the sampling space; if it is less than the threshold Then only boundary constraints are used to ensure that the random sampling process has a sufficiently large region in space without getting stuck in a dead zone. The coordinates of the extended nodes are represented as follows:

[0128]

[0129] in These are the Frenet coordinates of the extended node. Defined as (s) i , l i ) and (s goal , l goal The angle between the direction of the connecting line and the direction of the reference line. This indicates the generation of uniformly random numbers between 0 and 1. This indicates that the generated mean is 0 and the standard deviation is . Normally distributed random numbers.

[0130] Step 2: Vehicle non-integrity constraint detection: Based on the vehicle's minimum turning radius, construct the circumcircle of adjacent path points and retain the new extended nodes that fully satisfy drivability;

[0131] Vehicle non-integrity constraint detection is defined as follows:

[0132] like Figure 4 As shown, with (s i , l i ), (s i-1 , l i-1 The direction of the connecting line is tangent, and the minimum turning radius of the vehicle is R. min Draw the circumcircle O for the radius, and draw it in the same way. and (s) i , l i The circumcircle O′ of ). i , l i ), (s i-1 , li-1 ) direction of the line and (s i , l i The angle between the directions of the lines connecting O and O' is... The calculation method is as follows:

[0133]

[0134] in From (s) i , l i A vector pointing to O′. From (s) i-1 , l i-1 ) points to (s i , l i A vector of type ), where ||||2 is the L2 norm. If like Figure 4 (a) then the new extended node is considered to satisfy the vehicle non-integrity constraint and can be added to the tree; if like Figure 4 (b) If the vehicle non-integrity constraint is not met, return to step (2-1) to resample random points.

[0135] Step 3: Cost Allocation and Parent Node Reselection: Considering obstacle avoidance and reference path similarity requirements, a cost function is assigned to the nodes in the RRT tree, and the point with the minimum cost is reselected as the parent node of the new extended node;

[0136] Cost allocation and parent node reselection. To avoid fluctuations in vehicle decision-making results caused by the randomness of the RRT algorithm, and considering both obstacle avoidance requirements and reference line similarity requirements, a node attribute cost function is first designed:

[0137] (3-1) Obstacle Distance Cost: Considering the actual volume of the vehicle, the cost is the sum of the distance d between the centers of the circumcircle representing the vehicle rectangle and the circumcircle representing the obstacle rectangle. 1∶4 As a standard, construct the obstacle distance cost function:

[0138]

[0139] Where d thr The threshold value is used.

[0140] (3-2) Reference line distance cost: based on the current node (s i , l i ) and the point on the reference line that is closest to this point. The Euclidean distance between them is used as the basis for defining the reference line distance cost:

[0141]

[0142] (3-3) Cost of same-sideness: If adjacent nodes (si-1 , l i-1 ), (s i , l i A smaller cost is assigned if the reference line is on the same side; otherwise, a larger cost is assigned to avoid fluctuations in the planning results. The unit vectors perpendicular to the reference line are defined as follows: and The cost of ipsilaterality can be expressed as:

[0143]

[0144] The total cost of node attributes can be written as:

[0145] cost att =w obs cost obs +w ref cost ref +w ips cost ips

[0146] Where w obs w ref w ips These are the weighting coefficients.

[0147] Furthermore, the cost introduced when expanding nodes is also considered:

[0148] (3-4) Heading angle similarity cost: Assuming (s i , l i ) and (s i-1 , l i-1 The initial parent nodes of ) are (s i , l i ), (s i-1 , l i-1 ) and (s i-2 , l i-2 To avoid abrupt changes in path heading angle, a heading angle similarity cost is defined as follows: Figure 5 :

[0149]

[0150] in Defined as the heading angle error between adjacent path points.

[0151] (3-5) Expansion Distance Cost: Using the cumulative expansion step size and the Euclidean distance between the current node and the newly expanded node as the evaluation criteria, the expansion distance cost is expressed as:

[0152]

[0153] in To extend the step size of the RRT tree step by step.

[0154] The total expansion cost can be written as:

[0155] cost exp =w hs cost hs +w exp_dist cost exp_dist

[0156] Where w hs w exp_dist These are the weighting coefficients.

[0157] The total cost from an existing node in the tree to the newly expanded node is:

[0158] cost total =cost att +cost exp

[0159] The RRT tree has the minimum total cost. total The node was re-elected as the new expansion node. The parent node.

[0160] Step 4: Driving Corridor and Convex Space Approximation: Starting from the target point, search backwards to the parent node until the starting point to generate an initial path. Based on the initial path points, construct a "driving corridor" that meets safety requirements, and approximate the obstacle avoidance convex space accordingly.

[0161] The driving corridor and convex space are similar, as detailed below.

[0162] (4-1) When the RRT tree is expanded to the target point, the parent node is searched in reverse to the starting point to obtain the planned initial path.

[0163] (4-2) Draw a circular sequence C centered on each initial path point. i ∈C O , i=0,...n such as Figure 6 (a) The radius of the circle Defined as:

[0164]

[0165] Where d i It is the distance from the i-th path point to the circumcircle of the nearest rectangle representing the obstacle, and its radius is R. r .

[0166] (4-3) In the circular sequence C i ∈C O , i=0,...n draws an inscribed rectangular sequence inside Forming the "driving corridor" C0：n like Figure 6 (b), its definition is as follows:

[0167]

[0168] When there is no overlap between rectangles, local padding is used, such as... Figure 6 (b) The area within the middle circle.

[0169] (4-4) Combining the obstacle location and the coordinates of the corner points of the driver's corridor, the obstacle avoidance convex space A is... vx Approximately Figure 6 The shaded area in (c) is defined as the drivable region within the convex space:

[0170]

[0171] Where I(s, l) is the cost raster map with a default value of all zeros. The cost raster map is defined if and only if (s... i , l i When within a convex space, f assigns I(s) i , l i The value is 1.

[0172] Step 5: Optimal Path Solution: Within the convex space, considering the costs of path curvature continuity, smoothness, and comfort, the optimal obstacle avoidance path is solved using the QP algorithm, combining model constraints, curvature constraints, and drivable area constraints.

[0173] The optimization problem can be described as:

[0174] Using Δs as the step size, find a smooth sequence of path points l = D(s) with continuous curvature and close to the reference line in the generated convex space.

[0175] (5-1) Consider optimizing the objective function:

[0176]

[0177]

[0178] in Used to measure the degree of deviation between the generated path and the reference path; Defined as the cost of curvature continuity; Jerk-related costs are used to improve path comfort; This indicates the degree of similarity between the optimized path and the initial path. It is the l-coordinate of the initial path point.

[0179] (5-2) Consider the following multiple constraints:

[0180] vii Kinematic Model Constraints: Considering the kinematic model, the vehicle's movement must satisfy the model constraints:

[0181]

[0182] Where x i y i These are the vehicle's coordinates in the Cartesian coordinate system at time i, and θ is the coordinate of the vehicle at time i. i That is the corresponding heading angle.

[0183] viii. Curvature Constraint: To ensure the drivability of the path, the curvature of the optimized path is constrained.

[0184]

[0185] in It is the maximum permissible curvature, and its value is equal to 1 / R. min .

[0186] ix. Feasible Area Constraints: To ensure safety, the vehicle needs to be confined within the obstacle avoidance convex space:

[0187] f(~,l i -d sinθ i / 4+R v ) = 1

[0188] f(~,l i +d sinθ i / 4+R v ) = 1

[0189] f(~,l i +d sinθ i / 4-R v ) = 1

[0190] f(~,l i -d sinθ i / 4-R v ) = 1

[0191] Where R v d represents the radius of the circumcircle of the vehicle's rectangle, and d is the vehicle's wheelbase.

[0192] (5-3) Optimal solution: Combine the cost function (5-1) with the multiple constraints (5-2) to form a standard quadratic form, and substitute it into the QP solver to obtain the final optimal local obstacle avoidance path.

[0193] Figure 7 The presentation showcases the path planning results and average planning time comparisons in a simulation environment for the improved RRT and backend optimization strategies, as well as the advanced algorithms IBi-RRT*, Dp-Opt, and AC. Figure 7 (a) is a straight road segment. Figure 7 (b) represents a curved road segment. From the planning results, due to the inclusion of node attributes and the extended cost function, the path generated by this scheme effectively balances the obstacle avoidance requirements of the intelligent vehicle with the reference line similarity requirements in both straight and curved road segment simulation scenarios, compared to the other three algorithms. The backend optimization strategy ensures that the path exhibits smooth, continuous curvature characteristics and conforms to the vehicle's non-holonomic constraints. The optimality of the obstacle avoidance path generated by the algorithm is guaranteed.

[0194] Figure 8 This demonstrates the improved RRT and backend optimization strategies, as well as the advanced algorithms IBi-RRT*, Dp-Opt, and AC, generating the average number of path points in 10 repeated experiments. Combined with... Figure 2 According to the box plot of average planning time, the proposed method reduces the average number of sampling nodes by 11.21%, 49.53%, and 65.8% respectively compared to IBi-RRT*, Dp-Opt, and AC, thus improving the algorithm's execution efficiency; the average time consumption is reduced by 50.49%, 59.17%, and 68.2% respectively, improving the algorithm's real-time performance. This is attributed to the sampling region optimization and node heuristic expansion strategy adopted in this scheme. The real-time performance and efficiency of the obstacle avoidance path generation algorithm are guaranteed.

[0195] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any modifications or equivalent changes made based on the technical essence of the present invention shall still fall within the scope of protection claimed by the present invention.

Claims

1. A method for intelligent vehicle obstacle avoidance path planning based on improved RRT and backend optimization strategies, characterized in that, Includes the following steps: Step 1: Sampling area optimization: Adding boundary constraints and heuristic sector constraints guides the RRT tree to expand toward the target point, improving the algorithm's execution efficiency; Step 2: Vehicle non-integrity constraint detection: Based on the minimum turning radius of the vehicle, construct the circumcircle of adjacent path points and retain the new extended nodes that are fully drivable; Step 3: Cost Allocation and Parent Node Re-election: Considering obstacle avoidance and reference path similarity requirements, a cost function is assigned to the nodes in the RRT tree, and the node with the minimum cost is reselected as the parent node of the newly expanded node. Step 4: Approximate dimensions of the driver's aisle and convex space: Starting from the target point, search backwards to the parent node and back to the starting point to generate an initial path. Based on the initial path points, construct a "driving corridor" that meets safety requirements and approximate the obstacle avoidance convex space accordingly. The approximate approximation of the driving corridor and convex space in step 4 is as follows; (4-1) When the RRT tree is expanded to the target point, the parent node is searched in reverse to the starting point to obtain the planned initial path; (4-2) Draw a sequence of circles centered on each initial path point. as follows, radius of a circle Defined as: ； in It is the first The distance from each path point to the circumcircle of the nearest rectangle representing the obstacle, with radius [missing information]. , and The sampling point in the Frenet coordinate system at time i is the time of planning. The coordinate boundaries; (4-3) In the circular sequence Draw a sequence of inscribed rectangles internally Constitutes a "driving corridor" : Its definition is as follows: ； When there is no overlapping between rectangles, local padding is used. (4-4) Combining the obstacle location and the coordinates of the corner points of the driver's corridor, the obstacle avoidance convex space is analyzed. Approximately shaded area: The convex space is defined as the drivable area: ； in It is a cost raster map with all default values ​​of 0 if and only if Within the convex space Give The value is 1; Step 5: Finding the optimal path: Within a convex space, considering the costs of path curvature continuity, smoothness, and comfort, the optimal obstacle avoidance path is solved using the QP algorithm, which combines model constraints, curvature constraints, and drivable area constraints.

2. The intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategy according to claim 1, characterized in that, Step 1, sampling region optimization, includes the following steps: (1-1) Boundary constraints are defined as follows: ； in The vehicle's position at the start time. For the target location, , , , Defined as sampling points in the Frenet coordinate system and Coordinate boundary, this constraint adds a new node to the tree. Later by and Re-determine; (1-2) The heuristic sector constraint is defined as follows; connect and the sampling boundary obtained from (1-1) , Forming a triangle, with the angle between two sides and the reference path being θ. , ,by With the center of the circle, and Euclidean distance between A sector can be obtained within the triangle with a radius of 1, so that and Based on the direction of the connection, set variables. Used to expand random points, adding heuristic costs to make The angle should be as small as possible so that the expansion direction of nodes in the RRT tree will tend towards the target point; (1-3) Vehicles and obstacles are represented by rectangles and circumcircles. The calculation method for extended node coordinates is as follows: Calculate the distance from the current node to the circumcircle of the nearest rectangle representing the obstacle. If it is greater than the threshold Then, both boundary constraints and heuristic sector constraints are used to optimize the sampling space; if it is less than the threshold Then only boundary constraints are used to ensure that the random sampling process has a sufficiently large region in space without getting stuck in the dead zone. The coordinates of the extended nodes are represented as follows: ； in These are the Frenet coordinates of the extended node. Defined as and The angle between the direction of the connecting line and the direction of the reference line. This indicates the generation of uniformly random numbers between 0 and 1. This indicates that the generated mean is 0 and the standard deviation is . Normally distributed random numbers.

3. The intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategy according to claim 2, characterized in that, Step 2, vehicle non-integrity constraint detection, is defined as follows: by , The direction of the line is tangent, and the minimum turning radius of the vehicle. Draw the circumcircle for the radius. Draw in the same way and circumcircle , , Direction of connection and , The angle between the directions of the connecting lines is The calculation method is as follows: ； in From point to The vector, From point to The vector, It is a norm 2, if The new extended node is considered to satisfy the vehicle non-integrity constraint and is added to the tree; if If the vehicle non-integrity constraint is not met, return to steps (1-1) to (1-3) to resample random points.

4. The intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategy according to claim 1, characterized in that, Step 3, cost allocation and parent node reselection, consists of the following steps; First, design the node attribute cost function: (3-1) Obstacle distance cost: Considering the actual volume of the vehicle, let the sum of the distances between the centers of the circumcircle of the vehicle rectangle and the circumcircle of the obstacle rectangle be represented. As a standard, construct the obstacle distance cost function: ； in For the threshold; (3-2) Cost of distance from reference line: With the current node And the point on the reference line that is closest to this point The Euclidean distance between them is used as the basis for defining the reference line distance cost: ； (3-3) Ipsilateral Cost: If adjacent nodes , A smaller cost is assigned to the side of the reference line; otherwise, a larger cost is assigned to avoid fluctuations in the planning results. The unit vectors perpendicular to the reference line are defined as follows: and The cost of ipsilaterality is expressed as: ； The total cost of node attributes is written as: ； in , , These are the weighting coefficients; Furthermore, the cost introduced when expanding nodes is also considered: (3-4) Cost of similarity in heading angle: Assumption , and The initial parent nodes are respectively , and To avoid abrupt changes in the path heading angle, the heading angle similarity cost is defined as follows: ； in Defined as the heading angle error between adjacent path points; (3-5) Cost of extending distance: Using the cumulative step size of the expansion and the Euclidean distance between the current node and the newly expanded node as the evaluation criteria, the expansion distance cost expression is as follows: ； in To extend the step size of the RRT tree step by step; The total expansion cost is written as: ； in , These are the weighting coefficients; The total cost from an existing node in the tree to the newly expanded node is: ； The minimum total cost is found in the RRT tree. The node was re-elected as the new expansion node. The parent node.

5. The intelligent vehicle obstacle avoidance path planning method based on improved RRT and backend optimization strategy according to claim 1, characterized in that, The specific steps for finding the optimal path in step 5 are as follows; by Using a step size, find a smooth sequence of path points with continuous curvature close to the reference line within the generated convex space. ; (5-1) Consider optimizing the objective function: ； ； in Used to measure the degree of deviation between the generated path and the reference path; Defined as the cost of curvature continuity; Jerk-related costs are used to improve path comfort; This indicates the degree of similarity between the optimized path and the initial path. It is the initial path point coordinate; (5-2) Consider the following multiple constraints: i. Kinematic model constraints: Considering the kinematic model, the vehicle's movement must satisfy the model constraints: ； in , They are The coordinates of the vehicle in the Cartesian coordinate system at any given time. That is the corresponding heading angle; ii. Curvature Constraint: To ensure the drivability of the path, the curvature of the optimized path is constrained. ； in It is the maximum permissible curvature, and its value is equal to , It is the vehicle's minimum turning radius; iii. Feasible Area Constraints: To ensure safety, the vehicle needs to be confined within the obstacle avoidance convex space: ； ； in It represents the radius of the circumcircle of the vehicle's rectangle. It is the vehicle's wheelbase; (5-3) Optimal solution: Combine the cost function (5-1) with the multiple constraints (5-2) to form a standard quadratic form, and substitute it into the QP solver to obtain the final optimal local obstacle avoidance path.

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