A path smoothing optimization method and system based on multi-target gaussian mixture regression

Abstract

A path smoothing optimization method and system based on multi-target Gaussian mixture regression, the path smoothing optimization method comprising: collecting motion environment information to generate a collision-free initial path; assigning a label to each path point, training a multi-target Gaussian mixture model using the parameterized collision-free initial path and the label; inputting the parameterized collision-free initial path into the trained multi-target Gaussian mixture model, and generating a smooth path using a multi-target Gaussian mixture regression method; introducing an obstacle repulsion force field to update the position of each path point; introducing a path adhesion control mechanism to weight and fuse the original path and the updated smooth path; and introducing a global consistency optimization mechanism to adjust the main direction vector of the smooth path to obtain a final optimized smooth path. The present application improves the smoothness of the RRT path through the multi-target Gaussian mixture regression method, while having effective obstacle avoidance capability and structure feature retention capability.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot path optimization, in particular to a path smoothing optimization method and system based on multi-objective Gaussian mixture regression. BACKGROUND

[0002] With the continuous development of artificial intelligence and robot technology, robots are increasingly widely used in industrial production, medical health, service industry and other fields. In robot autonomous navigation and motion control, path planning technology is a key link to ensure that robots can safely and efficiently complete tasks.

[0003] Currently, the Rapidly-exploring Random Tree (RRT) method is a classic sampling-based path planning method, which is widely used because it can efficiently handle path planning problems in high-dimensional space. However, the traditional RRT method has obvious shortcomings: the path generated by it is usually zigzag-shaped and lacks smoothness, resulting in discontinuous motion of the robot in actual execution, high energy consumption, and because the path points are not smooth, the traditional RRT method generates a discrete point directly connected planning, which produces a polyline effect. The path formed by this polyline can bring a lot of vibration to the robot's travel, and if the vibration is too much and the zigzag is too large, the robot is likely to cause more wear and tear and additional wear and tear to the mechanical system.

[0004] In the prior art, the following methods are mainly used for RRT path smoothing: 1) post-processing methods such as B-spline fitting and polynomial interpolation, which can improve the smoothness of the path but are prone to cause the smoothed path to collide with obstacles; 2) online optimization methods such as introducing a path optimization mechanism in , but the computational complexity is high and the real-time performance is poor; 3) simple filtering methods such as moving average filtering, but the smoothing effect is limited and cannot adapt to complex environments.

[0005] Therefore, there is an urgent need for a method that can simultaneously optimize path smoothness, obstacle avoidance ability, and structure preservation to meet the demand for high-quality motion trajectories of modern robots. SUMMARY

[0006] The present application provides a path smoothing optimization method and system based on multi-objective Gaussian mixture regression to solve the technical problems mentioned in the background art.

[0007] To achieve the above purpose, the technical solution of the present application is as follows:

[0008] The present application provides a path smoothing optimization method based on multi-objective Gaussian mixture regression, comprising the following steps:

[0009] S1, collect robot motion environment information, establish an environment model containing obstacles and environmental constraints, and use the rapid exploration random tree method RRT to generate a collision-free initial path in the environment model;

[0010] S2, parameterize the collision-free initial path and assign a label to each path point in the collision-free initial path, train the constructed multi-target Gaussian mixture model using the parameterized collision-free initial path and the corresponding label pair, and obtain the trained multi-target Gaussian mixture model;

[0011] S3, input the parameterized collision-free initial path into the trained multi-target Gaussian mixture model, and generate a smooth path based on the multi-target Gaussian mixture regression method;

[0012] S4, introduce an obstacle repulsion force field in the smooth path, calculate the obstacle repulsion force received by each path point in the smooth path, and update the position of each path point combined with the obstacle repulsion force to obtain multiple predicted points of the smooth path;

[0013] S5, introduce a path adhesion control mechanism, and weight and fuse the original path and the updated smooth path in S4 according to the path adhesion control mechanism to keep the structure of the updated smooth path in S4 consistent with that of the original path;

[0014] S6, introduce a global consistency optimization mechanism, adjust the main direction vector of the optimized smooth path in S5 according to the global consistency optimization mechanism, so that the main direction vector of the original path is consistent with that of the smooth path obtained in S5, and obtain the final optimized smooth path.

[0015] Further, the S1 specifically comprises the following steps:

[0016] S11, construct an obstacle model of the robot workspace, represent the obstacles as geometric bodies in three-dimensional space, each obstacle contains position coordinates and shape parameters, define the starting point and target point of the robot;

[0017] S12, set the boundary constraints of the workspace, determine the activity range and motion limit of the robot, integrate the obstacle information and the boundary constraints to form a complete environment model;

[0018] S13, in the environment model, search for a path by the rapid exploration random tree algorithm, construct a search tree from the starting point, expand new nodes in a random direction, verify whether the path collides with obstacles, and when the tree is connected to the target point, backtrack to obtain a collision-free initial path from the starting point to the end point.

[0019] Further, the S2 specifically comprises the following steps:

[0020] S21, define parameters , making Corresponding path starting point, For the corresponding path endpoint, then for each path point in the initial collision-free path. Calculate the corresponding parameter values. This is done to complete the parameterization of the initial collision-free path; then, for each path point... Perform tag assignment;

[0021] S22. Construct a multi-objective Gaussian mixture model and introduce a joint loss function into the multi-objective Gaussian mixture model;

[0022] S23. Using the parameterized collision-free initial path and corresponding label from S21 as training data, the multi-objective Gaussian mixture model is trained using the training data and the expectation-maximization algorithm (EM) to maximize the joint loss. During the iteration process, the weights of the multi-objective Gaussian mixture model are adjusted according to the joint loss to obtain the trained multi-objective Gaussian mixture model.

[0023] Furthermore, the joint loss function is as follows:

[0024] ;

[0025] in, This is the log-likelihood function of a standard Gaussian Mixture Model (GMM), used to represent how well the GMM fits the data. These are the parameters of a standard Gaussian mixture model (GMM). For classifying losses, For the number of samples, For the first One sample, For the first The label of each sample, For the first The predicted values ​​for each sample are used to help maintain structural consistency between the smooth path and the original path; the last item For regularization terms, The number of Gaussian components. For the first A Gaussian distribution, For the first The square of the second norm of a vector with a Gaussian distribution mean. For the first The trace of the covariance matrix of a Gaussian distribution; , and Indicates the weight.

[0026] Furthermore, step S3 specifically includes the following steps:

[0027] S31. Input the parameterized collision-free initial path into the trained multi-objective Gaussian mixture model, and calculate the parameters of the trained multi-objective Gaussian mixture model. The conditional distribution of each Gaussian component is determined, and then the parameters are calculated based on the conditional distribution of each Gaussian component. The probability-weighted combination result of each Gaussian component within the component;

[0028] S32, then calculate the parameters. The expected value of the probability-weighted combination of each Gaussian component is used to obtain the predicted position of the smooth path point, thus completing the generation of the smooth path point.

[0029] Furthermore, the parameters The formula for calculating the probability-weighted combination of each Gaussian component is:

[0030] ;

[0031] in, Indicates parameters The probability-weighted combination result of each Gaussian component within the component; For the first Conditional distribution under Gaussian components For input parameters Belongs to the The posterior probability of each Gaussian component;

[0032] The formula for calculating the predicted position of the smooth path point is:

[0033] ;

[0034] in, Indicates parameters The corresponding predicted point location; E represents the expected value; For the first The expected value of the conditional distribution under each Gaussian component.

[0035] Furthermore, the formula for calculating the repulsive force from the obstacle experienced by each path point is:

[0036] ;

[0037] in, Indicates the prediction point The repulsive force from the obstacle, The number of obstacles, For point To the obstacle Euclidean distance, The repulsive force coefficient, For safe distance threshold, to repel from obstacles pointing to the point unit vector of the direction;

[0038] The position update of each path point in S4 is expressed by the formula as follows:

[0039] ;

[0040] wherein, represents the predicted point after adjustment of the repulsion force of obstacles, represents the influence coefficient of the repulsion force field of obstacles.

[0041] Further, the path attachment control mechanism is expressed by the formula as follows:

[0042] ;

[0043] wherein, represents the position of the path point after optimization, is an attachment weight function, and the calculation formula of the attachment weight function is as follows:

[0044] ;

[0045] wherein, is a parameter of the curvature of the original path at the point, is a curvature threshold value, when , is close to 0, indicating that the current path is a normal area, allowing greater adjustment; when , is close to 1, indicating that the current path is a key feature area, and more original features need to be preserved; is an adjustment coefficient.

[0046] Further, S6 specifically comprises the following steps:

[0047] S61, first calculate the principal direction vectors of the original path and the smoothed path obtained in S5, the principal direction vectors are obtained by principal component analysis (PCA), and the calculation formulas of the principal direction vectors of the two paths are as follows:

[0048] ;

[0049] wherein, is the principal direction vector of the original path, is the principal direction vector of the smoothed path obtained in S5;

[0050] S62, then according to the main direction vector of the two paths, the direction deviation angle of the original path and the smooth path obtained in S5 is calculated, and the calculation formula is as follows:

[0051] ;

[0052] Wherein, represents the direction deviation angle of the original path and the smooth path obtained in S5;

[0053] S63, according to the direction deviation angle of the original path and the smooth path obtained in S5, a rotation matrix is constructed , and the main direction vector of the smooth path obtained in S5 is adjusted according to the rotation matrix , so that the main direction vector of the original path is consistent with the main direction vector of the smooth path obtained in S5, and a twice-optimized smooth path is obtained, which is expressed by the formula as follows:

[0054] ;

[0055] Wherein, represents the twice-optimized smooth path;

[0056] S64, the curvature distribution of the original path is analyzed, the key turning points are identified, and the curvature of the twice-optimized smooth path is adjusted to ensure that the smooth path changes within the set curvature range in these areas, so that the curvature of the turning point area is not more than the preset curvature tolerance error , to obtain a final optimized smooth path.

[0057] Another aspect of the present application also provides a path smoothing optimization system based on multi-target Gaussian mixture regression, comprising a device end, and the device end is configured or the execution path smoothing optimization method.

[0058] The beneficial effects of the present application are:

[0059] The present application discloses a path smoothing optimization method based on multi-target Gaussian mixture regression, compared with the traditional path smoothing method, the multi-target Gaussian mixture regression method (MOGMR) in the present application combines path smoothing and structure reservation in a unified framework, which overcomes the problem that the traditional smoothing method is difficult to consider these aspects at the same time. Secondly, the smoothing strategy based on Gaussian mixture regression can automatically capture the key features of the path, improve the smoothness of the path, and ensure that the smoothed path can effectively avoid obstacles through repulsive force field mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 The flowchart of the path smoothing optimization method in the present application;

[0061] Figure 2 Path comparison chart generated for various different methods in embodiments of the present application;

[0062] Figure 3 Comparison chart of distance length of paths for various different methods in embodiments of the present application;

[0063] Figure 4 Comparison chart of smoothness for various different methods in embodiments of the present application;

[0064] Figure 5 Comparison chart of calculation time for various different methods in embodiments of the present application. DETAILED DESCRIPTION

[0065] In order to facilitate the understanding of the present application, the present application will be described more fully below with reference to the accompanying drawings. The preferred embodiments of the present application are given in the accompanying drawings. However, the present application can be implemented in many other different forms, and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the disclosure of the present application more thorough and comprehensive.

[0066] Reference Figure 1 The embodiment of the present application provides a path smoothing optimization method based on multi-target Gaussian mixture regression, comprising the following steps:

[0067] S1, collecting robot motion environment information, establishing an environment model containing obstacles and environmental constraints, using a rapid exploration random tree method RRT to generate a collision-free initial path in the environment model, the collision-free initial path satisfying the start and end point constraints and avoiding obstacles;

[0068] S2, parameterizing the collision-free initial path, and assigning a label to each path point in the collision-free initial path, training the multi-target Gaussian mixture model constructed by using the parameterized collision-free initial path and the corresponding label pair, to obtain a trained multi-target Gaussian mixture model;

[0069] S3, inputting the parameterized collision-free initial path into the trained multi-target Gaussian mixture model, and generating a smooth path with obstacle avoidance capability based on a multi-target Gaussian mixture regression method;

[0070] S4, to ensure that the smooth path generated by the multi-target Gaussian mixture regression method MOGMR does not collide with obstacles, an obstacle repulsion force field is introduced into the smooth path, and the obstacle repulsion force received by each path point in the smooth path is calculated, and the position of each path point is updated in combination with the obstacle repulsion force, to obtain a plurality of predicted points of the smooth path;

[0071] S5, introducing a path attachment control mechanism in the multi-target Gaussian mixture regression method MOGMR, and fusing the original path and the updated smooth path in S4 according to the path attachment control mechanism to keep the structure of the updated smooth path in S4 consistent with the original path;

[0072] S6, introducing a global consistency optimization mechanism in the multi-target Gaussian mixture regression method MOGMR, adjusting the main direction vector of the optimized smooth path in S5 according to the global consistency optimization mechanism, so that the main direction vector of the original path is consistent with the smooth path obtained in S5, and finally obtaining the optimized smooth path.

[0073] The multi-target Gaussian mixture regression method improves the smoothness of the RRT path, has effective obstacle avoidance ability and structure feature reservation ability, can be applied to various different application scenarios including mechanical arm path planning, helps to improve the safety of the system, and ensures smooth operation of the system.

[0074] In some embodiments, S1 specifically comprises the following steps:

[0075] S11, constructing an obstacle model of the robot workspace, representing the obstacles as geometric bodies in three-dimensional space, each obstacle containing position coordinates and shape parameters, defining the starting point and target point of the robot;

[0076] Specifically, in the workspace of the robot, the motion range of the robot is defined as a bounded region, represented by a vector as , wherein , , min and max respectively represent the minimum value of the x, y and z axes, , , max respectively represent the maximum value of the x, y and z axes. In this space, the obstacles are represented as a set of geometric bodies, the first obstacle can be represented by three-dimensional coordinates and radius, that is , wherein represents the obstacle center position, represents the obstacle radius. The starting position of the robot is defined as , and the target position is defined as ;

[0077] S12, setting the boundary constraint of the workspace, determining the activity range and motion limit of the robot, integrating the obstacle information and the boundary constraint to form a complete environment model;

[0078] S13, in the environment model, path searching is performed by a rapid exploration random tree algorithm, a search tree is constructed from the starting point, a new node is expanded in a random direction, it is verified whether the path collides with an obstacle, when the tree is connected to the target point, an initial collision-free path from the starting point to the terminal point is obtained by backtracking.

[0079] Specifically, the basic steps of the rapid exploration random tree algorithm are as follows: first, a root node is created in the starting point , then in each iteration, a point is randomly sampled in the configuration space with a certain probability , or the target point is directly selected as the sampling point; then the node closest to the sampling point is found in the current random tree , and a step is expanded in the direction from the point to the point to obtain a new node ; if the line connecting the point to the point does not intersect with any obstacle, the point is added to the random tree; the above process is repeated until the random tree can be connected to the target point or the maximum number of iterations is reached. Finally, the path sequence from the point to the point is obtained by backtracking , wherein .

[0080] In some embodiments, the S2 specifically comprises the following steps:

[0081] S21, defining a parameter , so that corresponds to the starting point of the path, corresponds to the terminal point of the path, and then for each path point in the initial collision-free path, the corresponding parameter value of the path point is calculated to complete the parameterization of the initial collision-free path; the calculation formula of the parameter value is as follows:

[0082] ;

[0083] wherein, is the i-th point, is the total number of path points, represents the Euclidean distance between two adjacent points on the path; and , .

[0084] After that, for each path point ​Assigning labels; path labels are assigned according to the location characteristics of the path points in the overall path, which can be divided into the following categories: starting point area, ending point area, turning point area and intermediate connection area. For each path point , a label is assigned according to its location characteristics . The label can be represented by one-hot encoding, for example, if the path point is labeled as category , then , and the other positions are 0. This label assignment method helps the model to capture the key feature points of the path and provides a basis for the multi-target Gaussian mixture regression method MOGMR to retain the structural characteristics of the path;

[0085] S22, constructing a multi-target Gaussian mixture model, and introducing a joint loss function in the multi-target Gaussian mixture model;

[0086] S23, using the parameterized collision-free initial path and the corresponding label in S21 as training data, training the multi-target Gaussian mixture model using the training data and adopting the expectation maximization algorithm EM, maximizing the joint loss, and adjusting the weights of the multi-target Gaussian mixture model according to the joint loss in the iteration process to obtain the trained multi-target Gaussian mixture model.

[0087] Among them, the E step in the expectation maximization algorithm EM is used to calculate the posterior probability of each data path point belonging to each Gaussian component, and the M step is used to update the parameters of the multi-target Gaussian mixture model to maximize the joint loss function.

[0088] In some embodiments, the joint loss function is specifically as follows:

[0089] ;

[0090] Among them, is the log-likelihood function of the standard Gaussian mixture model GMM, which is used to represent the fitting degree of the standard Gaussian mixture model GMM to the data, is the parameter of the standard Gaussian mixture model GMM; is the classification loss, is the number of samples, is the th sample, is the label of the th sample, is the predicted value of the th sample, which is used to help maintain the structural consistency of the smooth path with the original path; the last term is the regularization term, is the number of Gaussian components, is the th Gaussian distribution, the square of the second norm of the mean vector of the first the trace of the covariance matrix of the first , and represent weights. This joint loss function enables the multi-objective Gaussian mixture model MOGMM to simultaneously learn the path data distribution and the structure feature, providing a basis for subsequent path smoothing and structure reservation.

[0091] In some embodiments, the S3 specifically comprises the following steps:

[0092] S31, inputting the parameterized processed collision-free initial path into the trained multi-objective Gaussian mixture model, the trained multi-objective Gaussian mixture model calculating the conditional distribution of each Gaussian component in the parameter , and then calculating the probability weighted combination result of each Gaussian component in the parameter according to the conditional distribution of each Gaussian component;

[0093] S32, then calculating the expectation of the probability weighted combination result of each Gaussian component in the parameter , obtaining the predicted position of the smoothed path point, thereby completing the generation of the smoothed path point.

[0094] In some embodiments, the calculation formula of the probability weighted combination result of each Gaussian component in the parameter is as follows:

[0095] ;

[0096] wherein, represents the probability weighted combination result of each Gaussian component in the parameter ; represents the conditional distribution under the first is the posterior probability that the input parameter belongs to the first Gaussian component;

[0097] The calculation formula of the predicted position of the smoothed path point is as follows:

[0098] ;

[0099] wherein, represents the corresponding predicted point position of the parameter , and this predicted value is calculated through the conditional expectation; E represents expectation; is the first​​​​ The expectation value of the conditional distribution under the Gaussian component. The multi-objective Gaussian mixture regression method MOGMR not only realizes the smoothing of the path, but also forms a complete path optimization framework by fusing the obstacle avoidance and structure reservation mechanisms described later.

[0100] In some embodiments, the calculation formula of the obstacle repulsion force borne by each path point is:

[0101] ;

[0102] wherein, represents the predicted point bears the obstacle repulsion force, is the number of obstacles, is the Euclidean distance from the point to the obstacle , is the repulsion force coefficient, is the safety distance threshold, is the unit vector from the obstacle to the point ;

[0103] The position update of each path point in the S4 is represented by the formula, which is as follows:

[0104] ;

[0105] wherein, represents the predicted point after adjustment of the obstacle repulsion force, represents the influence coefficient of the obstacle repulsion force field.

[0106] In some embodiments, the path adhesion control mechanism is represented by the formula, which is as follows: ;

[0107] wherein, represents the position of the path point after optimization, is the adhesion weight function, and the calculation formula of the adhesion weight function is as follows:

[0108] ;

[0109] wherein, is the curvature of the original path at the parameter , is the curvature threshold, and when , , , , Close to 0, indicating that the current path is a normal area, allowing greater adjustment, the normal area usually corresponds to the path is relatively straight or slowly curved part, its characteristics have less impact on the overall path structure; when , , , , Close to 1, indicating that the current path is a key feature area, which needs to retain more original features, and the key feature area is the part of the path with greater curvature, such as sharp turns or turning points, which has a greater impact on the path structure and execution accuracy; is the adjustment coefficient. The path adhesion control mechanism further enhances the ability of the multi-objective Gaussian mixture regression method MOGMR to retain the path structure.

[0110] In some embodiments, S6 specifically comprises the following steps:

[0111] S61, first calculate the principal direction vectors of the original path and the smoothed path obtained in S5, the principal direction vectors are obtained by principal component analysis PCA, and the calculation formulas of the principal direction vectors of the two paths are as follows:

[0112] ;

[0113] Wherein, is the principal direction vector of the original path, is the principal direction vector of the smoothed path obtained in S5;

[0114] S62, then calculate the direction deviation angle of the original path and the smoothed path obtained in S5 according to the principal direction vectors of the two paths, and the calculation formula is specifically as follows:

[0115] ;

[0116] Wherein, represents the direction deviation angle of the original path and the smoothed path obtained in S5;

[0117] S63, construct a rotation matrix according to the direction deviation angle of the original path and the smoothed path obtained in S5, and adjust the principal direction vector of the smoothed path obtained in S5 according to the rotation matrix , so that the principal direction vector of the original path is consistent with the principal direction vector of the smoothed path obtained in S5, and a twice optimized smoothed path is obtained, which is expressed by the formula as follows:

[0118] ;

[0119] Wherein, represents the twice optimized smoothed path;

[0120] S64, analyze the curvature distribution of the original path, identify key turning points, and adjust the curvature of the smoothed path after quadratic optimization to ensure that the smoothed path remains within the set curvature range in these areas, so that the curvature in the turning point area differs from the curvature of the original path by no more than a preset curvature tolerance error , to obtain the final optimized smoothed path, and the set curvature range is preferably .

[0121] In order to verify the effectiveness of the present application, the following comparative experiments are carried out, as follows:

[0122] Experimental object: rapid exploration random tree method RRT, algorithm, moving average filtering method, B-spline curve method and MOGMR in the present application;

[0123] Comparative experiment process: first, in a 20x20x20 three-dimensional space environment (vacuum space), since the abstract space, 20x20x20 has no unit, set the starting position of the robot as [-8, -8, -2], the target position as [8, 8, 5], and place random obstacles. The experimental results show that the smoothed path generated by the present application has an improved smoothness of 42.3% compared with the original RRT path, a reduced path length of 15.6%, and a maintained obstacle avoidance success rate of 100%. Compared with traditional smoothing methods (B-spline curve method and moving average filtering method), the present application has better obstacle avoidance ability and path structure reservation effect while maintaining a high smoothness. When the path is executed, the present application reduces the acceleration change and energy consumption of the robot, improves the motion efficiency and stability, and the comparison diagram of each method is shown in Figures 2 to 5 . Among them, Figures 3 to 5 The RRT path in

[0124] Table 1: Advantages and disadvantages of different methods

[0125]

[0126] Another aspect of the present application also provides a path smoothing optimization system based on multi-objective Gaussian mixture regression, comprising a device end, which is configured or executes the path smoothing optimization method.

[0127] The above merely describes specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Furthermore, the technical solutions of each embodiment of the present application can be combined with each other, but it must be based on the realization of the ordinary skilled in the art, when the combination of the technical solutions appears contradictory or unachievable, it should be considered that the combination of the technical solutions does not exist, and is not within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A path smoothing optimization method based on multi-objective Gaussian mixture regression, characterized in that, Includes the following steps: S1. Collect robot motion environment information, establish an environment model containing obstacles and environmental constraints, and use the Fast Exploration Random Tree (RRT) method to generate a collision-free initial path in the environment model. S2. Parameterize the collision-free initial path and assign a label to each path point in the collision-free initial path. Use the parameterized collision-free initial path and the corresponding label to train the constructed multi-objective Gaussian mixture model to obtain the trained multi-objective Gaussian mixture model. S3. Input the parameterized collision-free initial path into the trained multi-objective Gaussian mixture model, and generate a smooth path using the multi-objective Gaussian mixture regression method. S4. Introduce an obstacle repulsion field into the smooth path, calculate the obstacle repulsion force at each path point in the smooth path, and update the position of each path point in combination with the obstacle repulsion force to obtain multiple predicted points of the smooth path. S5. Introduce a path attachment control mechanism, and use the path attachment control mechanism to weightedly fuse the original path and the updated smooth path in S4, so as to keep the structure of the updated smooth path in S4 consistent with the original path. S6. Introduce a global consistency optimization mechanism. Adjust the main direction vector of the smooth path optimized in S5 according to the global consistency optimization mechanism, so that the main direction vector of the original path is consistent with the smooth path obtained in S5, and the final optimized smooth path is obtained. S2 specifically includes the following steps: S21. Define parameters , making Corresponding path starting point, For the corresponding path endpoint, then for each path point in the initial collision-free path. Calculate the corresponding parameter values. This is done to complete the parameterization of the initial collision-free path; then, for each path point... Perform tag assignment; S22. Construct a multi-objective Gaussian mixture model and introduce a joint loss function into the multi-objective Gaussian mixture model; S23. The parameterized collision-free initial path and corresponding label in S21 are used as training data. The multi-objective Gaussian mixture model is trained using the training data and the expectation-maximization algorithm (EM) is used to maximize the joint loss. During the iteration process, the weights of the multi-objective Gaussian mixture model are adjusted according to the joint loss to obtain the trained multi-objective Gaussian mixture model. The joint loss function is as follows: ； in, This is the log-likelihood function of a standard Gaussian Mixture Model (GMM), used to represent how well the GMM fits the data. These are the parameters of a standard Gaussian mixture model (GMM). For classifying losses, For the number of samples, For the first One sample, For the first The label of each sample For the first The predicted values ​​for each sample are used to help maintain structural consistency between the smooth path and the original path; the last item For regularization terms, The number of Gaussian components. For the first A Gaussian distribution, For the first The square of the second norm of a vector with a Gaussian distribution mean. For the first The trace of the covariance matrix of a Gaussian distribution; , and Indicates the weight.

2. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 1, characterized in that, S1 specifically includes the following steps: S11. Construct an obstacle model for the robot's workspace, representing obstacles as geometric objects in three-dimensional space. Each obstacle contains position coordinates and shape parameters. Define the robot's starting point and target point. S12. Set the boundary constraints of the workspace, determine the robot's range of motion and movement limits, and integrate obstacle information with boundary constraints to form a complete environment model; S13. In the environment model, a fast-exploration random tree algorithm is used for path search. A search tree is built from the starting point and new nodes are expanded in random directions. The path is verified to avoid collisions with obstacles. When the tree connects to the target point, a collision-free initial path from the starting point to the end point is obtained by backtracking.

3. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 2, characterized in that, S3 specifically includes the following steps: S31. Input the parameterized collision-free initial path into the trained multi-objective Gaussian mixture model, and calculate the parameters of the trained multi-objective Gaussian mixture model. The conditional distribution of each Gaussian component is determined, and then the parameters are calculated based on the conditional distribution of each Gaussian component. The probability-weighted combination result of each Gaussian component within the component; S32, then calculate the parameters. The expected value of the probability-weighted combination of each Gaussian component is used to obtain the predicted position of the smooth path point, thus completing the generation of the smooth path point.

4. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 3, characterized in that, The parameters The formula for calculating the probability-weighted combination of each Gaussian component is: ； in, Indicates parameters The probability-weighted combination result of each Gaussian component within the component; For the first Conditional distribution under Gaussian components For input parameters Belongs to the The posterior probability of each Gaussian component; The formula for calculating the predicted position of the smooth path point is: ； in, Indicates parameters The corresponding predicted point location; E represents the expected value; For the first The expected value of the conditional distribution under each Gaussian component.

5. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 4, characterized in that, The formula for calculating the repulsive force from the obstacle at each path point is: ； in, Indicates the prediction point The repulsive force from the obstacle, The number of obstacles, For point To the obstacle Euclidean distance, The repulsive force coefficient, For safe distance threshold, To get from the obstacle Point of view , unit vector; The position update of each path point in S4 is represented by a formula, as follows: ； in, This indicates the predicted point after adjustment for the repulsive force of the obstacle. This represents the influence coefficient of the repulsive force field of the obstacle.

6. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 5, characterized in that, The path attachment control mechanism is expressed by the following formula: ； in, This indicates the optimized path point location. For the attached weight function, the attached weight function The formula for calculation is: ； in, For parameters The curvature of the original path. For curvature threshold, when hour, A value close to 0 indicates that the current path is a normal region, allowing for greater adjustments; when... hour, A value close to 1 indicates that the current path is a key feature region, and more original features need to be preserved. This is the adjustment coefficient.

7. The path smoothing optimization method based on multi-objective Gaussian mixture regression according to claim 6, characterized in that, S6 specifically includes the following steps: S61. First, calculate the principal direction vectors of the original path and the smoothed path obtained in S5. The principal direction vectors are obtained by Principal Component Analysis (PCA). The formulas for calculating the principal direction vectors of the two paths are as follows: ； in, This is the main direction vector of the original path. This is the main direction vector of the smooth path obtained in S5; S62. Then, based on the principal direction vectors of the two paths, calculate the direction deviation angle between the original path and the smoothed path obtained in S5. The specific calculation formula is as follows: ； in, This represents the directional deviation angle between the original path and the smoothed path obtained in S5; S63. Construct a rotation matrix based on the direction deviation angles of the original path and the smoothed path obtained in S5. And based on the construction of the rotation matrix Adjust the principal direction vector of the smoothed path obtained in S5 so that the principal direction vector of the original path is consistent with that of the smoothed path obtained in S5, and obtain the smoothed path after secondary optimization, which is expressed by the following formula: ； in, This represents the smoothed path after secondary optimization; S64. Analyze the curvature distribution of the original path, identify key inflection points, and adjust the curvature of the smoothed path after secondary optimization to ensure that the smoothed path remains within the set curvature range in these areas, so that the curvature at the inflection point area does not differ from the curvature of the original path by more than the preset curvature tolerance. This yields the final optimized smooth path.

8. A path smoothing optimization system based on multi-objective Gaussian mixture regression, characterized in that, Includes a device end, which is configured to perform the path smoothing optimization method according to any one of claims 1 to 7.

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