Path Planning Method for Catenary Pantograph Support Maintenance Manipulator Based on Spatial Intelligence Division

Abstract

The present invention relates to the field of robot technology, and discloses a path planning method for a catenary boom maintenance manipulator based on spatial intelligent division. The relationship between each joint and the connecting rod is described by different parameters to establish a robot kinematic model. Based on the robot kinematic model, a simulation analysis of the manipulator's working space is carried out to evaluate whether the manipulator can cover catenary bolts at different positions, and to analyze the reachability of the manipulator's end in the working space under the condition of fixing the manipulator base. The working space area of the catenary bolt operation points is divided according to the distribution of bolt points in the catenary environment. The working space is divided with the minimum movement of the manipulator base. An offline model of the catenary and the manipulator working environment is built, and using the divided working space, through path planning, the maintenance task of the catenary boom is realized. Through the method of the present invention, the manipulator can efficiently and safely complete the bolt tightening task in a complex catenary environment.

Description

Technical Field

[0001] The present invention relates to the technical field of robotics, and particularly to a path planning method for a catenary boom overhaul robot arm based on spatial intelligent partitioning. Background Art

[0002] With the continuous expansion and upgrade of the railway transportation network, the catenary, as a key component of the electrified railway system, its stability and safety are crucial for ensuring the normal operation of the railway. However, various components of the catenary may experience bolt loosening, structural deformation or damage under the influence of environmental changes, natural factors and operational wear, which poses risks to the stable operation of the railway. Currently, traditional catenary maintenance mainly relies on manual labor. This method not only has low efficiency but is also easily affected by subjective factors, making it difficult to meet the large-scale and high-frequency maintenance requirements. Against this background, it is particularly important to introduce a robot arm for catenary maintenance operations. Using a robot arm to replace manual inspection can not only improve the efficiency of maintenance work but also reduce the operational risks and labor intensity of maintenance workers.

[0003] An important task of the robot arm during catenary operations is to complete the tightening of catenary boom bolts. Due to the complex structure of the catenary and the harsh working environment, the tightening of bolts at different positions requires the robot arm to operate in different working spaces. At the same time, since the robot arm is generally installed on the lifting and slewing platform of the maintenance vehicle, the movement of the lifting and slewing platform needs to be minimized during maintenance operations. Therefore, the partitioning of the robot arm's working space is an important link. By accurately partitioning the working space of the robot arm, it can be ensured that it can efficiently complete various maintenance tasks in a restricted space. The reasonable partitioning of the working space can not only improve the operation efficiency of the robot arm but also avoid operation errors caused by overlapping or insufficient working spaces. Summary of the Invention

[0004] The purpose of the present invention is to provide a path planning method for a catenary boom overhaul robot arm based on spatial intelligent partitioning to solve the problems of low efficiency, potential safety hazards and insufficient operation accuracy existing in the current catenary maintenance process. By establishing a DH parameter model, a theoretical basis is provided for subsequent analysis of the robot arm's working space. The Monte Carlo method is applied to analyze the robot arm's working space, and the working space area partitioning of the catenary bolt operation points is calculated in combination with the distribution of the bolt tightening operation points in the catenary environment. The RRT algorithm is used for regional robot arm safety path planning to ensure that the robot arm does not collide with obstacles during the bolt tightening operation, while maximizing the operation efficiency. In this way, the robot arm can efficiently and safely complete the bolt tightening task in a complex catenary environment.

[0005] To achieve the above object, the following technical solutions are adopted:

[0006] A path planning method for the catenary boom maintenance manipulator based on spatial intelligent division, the method includes;

[0007] Describe the relationship between each joint and the connecting rod through different parameters, and establish a robot kinematic model;

[0008] Based on the robot kinematic model, conduct a simulation analysis of the manipulator's workspace to evaluate whether the manipulator can cover the catenary bolts at different positions, and analyze the reachability of the manipulator's end in the workspace under the condition of fixing the manipulator base;

[0009] Based on the simulation analysis of the workspace under the condition of fixing the manipulator base, divide the workspace area of the catenary bolt operation points according to the distribution of the bolt points in the catenary environment;

[0010] Divide the workspace with the minimum movement of the manipulator base;

[0011] Perform offline modeling on the catenary and the manipulator working environment, and use the divided workspace to achieve the maintenance task of the catenary boom through path planning.

[0012] Further, the establishing the robot kinematic model by describing the relationship between each joint and the connecting rod through different parameters includes:

[0013] Rotate the coordinate system {i - 1} around the z i-1 axis by θ i , then move along the direction of z i-1 by a distance of d i-1 , move along the current x i-1 axis by a distance of a i , and rotate the z i axis around the x i axis by α i to obtain the transformation matrix from the coordinate {i - 1} to the coordinate system {i};

[0014] According to the transformation matrix from the coordinate {i - 1} to the coordinate system {i}, determine the transformation matrix between the manipulator end and the base coordinate system;

[0015] Based on the transformation matrix and the transformation matrix, determine the forward kinematic formula of the manipulator.

[0016] Further, the transformation matrix from the coordinate {i - 1} to the coordinate system {i} is expressed as:

[0017]

[0018] In the formula, represents the transformation matrix from the coordinate system {i - 1} to the coordinate system {i}, θ iis the joint angle, indicating the angle between the z-axis (i.e., the rotation axis) of the i-th link coordinate system and the z-axis of the (i - 1)-th link coordinate system. z represents the rotation axis of a link coordinate system, and d i represents the distance measured along the z-axis of the (i - 1)-th link coordinate system from the origin of the (i - 1)-th link to the origin of the i-th link, a i represents the distance between the origin of the (i - 1)-th link coordinate system and the origin of the i-th link coordinate system. Rot represents the rotation matrix used to describe the rotational part of the coordinate system, Trans represents the translation matrix used to describe the translational part of the coordinate system, x represents the position vector, α represents the twist angle between two consecutive z-axes, c represents the abbreviation of the cos function in the rotation matrix, and s represents the abbreviation of the sin function in the rotation matrix.

[0019] Furthermore, the transformation matrix between the end of the robotic arm and the base coordinate system is expressed as:

[0020]

[0021] In the formula, represents the transformation matrix from coordinate system {0} to coordinate system {6}, respectively represent the transformation matrices from coordinate system {0} to coordinate system {1}, from coordinate system {1} to coordinate system {2}, from coordinate system {2} to coordinate system {3}, from coordinate system {4} to coordinate system {5}, and from coordinate system {5} to coordinate system {6}.

[0022] Furthermore, the forward kinematics formula of the robotic arm is expressed as:

[0023]

[0024] In the formula, n x 、n y 、n z represent the components of the rotation axis of the end effector relative to the base coordinate system in the x, y, and z directions. o x 、o y 、o z respectively represent the components of the translation vector of the end effector relative to the base coordinate system in the x, y, and z directions. a x 、a y 、a z respectively represent the offsets of the joint in the x, y, and z directions. p x 、p y 、p z respectively represent the translation distances of the joint.

[0025] The expressions represented by each element in formula (3) are as follows:

[0026] n x= S1S5C6 + C6C 234 C1C5 - S 234 C1S6

[0027] n y = -C6C1S5 + C6C 234 C5C1 - S 234 S1S6

[0028] n z = C 234 S6 + S 234 C5C6

[0029] o x = -S6S1S5 - S6C 234 C1C5 - S 234 C1C6

[0030] o y = S6C1S5 - S6C 234 C1S5 - S 234 C6S1

[0031] o z = C 234 C6 - S 234 C5S6

[0032] a x = C5S1 - C 234 C1S5

[0033] a y = -C1S5 - C 234 S1S5

[0034] a z = -S 234 S5

[0035] p x = d6C5S1 - d6C 234 C1S5 + C1a3C 23 + C1a2C2 + d4S1 + d5S 234 C1 + d2S1 + d3S1

[0036] p y = S1a3C 23 + S1a2C2 - d4C1 - d2C1 - d3C1 - d6C5C1 - d6C 234 S1S5 + d5S 234 S1

[0037] p z = d1 + a3S 234 + a2S2 - d5C 234 - d4S234 S5

[0038] In the formula, C represents the abbreviation of the cosine function in the rotation matrix, S represents the abbreviation of the sine function in the rotation matrix, and S1, S2, S3, S4, S5, and S6 respectively represent the sine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; d1, d2, d3, d4, d5, and d6 respectively represent the offsets of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C1, C2, C3, C4, C5, and C6 respectively represent the cosine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C 23 represents the product of the cosine values of the angles of the second and third joints, and C 234 represents the product of the cosine values of the angles of the second, third, and fourth joints; S 234 represents the product of the sine value of the angle of the second joint and the sine values of the angles of the third and fourth joints; a1, a2, and a3 respectively represent the lengths of the first joint, the second joint, and the third joint.

[0039] Furthermore, based on the robot kinematic model, a workspace simulation analysis of the robotic arm is carried out to evaluate whether the robotic arm can cover the catenary bolts at different positions, and to analyze the reachability of the end of the robotic arm within the workspace under the condition of fixing the base of the robotic arm, including:

[0040] Set the parameters of the Monte Carlo simulation; among them, the parameters of the Monte Carlo simulation include the joint angle range;

[0041] Randomly output a set of N joint angles within the set joint angle range, and the calculation formula is as follows:

[0042] θ = θ min +(θ max -θ min )RAND(N,1) (4)

[0043] In the formula, θ represents, and θ max represents the maximum value of the set joint angle range, θ min represents the minimum value of the set joint angle range, and RAND represents the number of output joint angles;

[0044] Determine the x, y, and z coordinates of the position of the end of the robotic arm according to the forward kinematic formula of the robotic arm;

[0045] Output the x, y, and z coordinates of the position of the end of the robotic arm as a set of coordinate points in three-dimensional space to obtain a scatter plot representing the workspace of the robotic arm;

[0046] Evaluate whether the robotic arm can cover the catenary bolts at different positions based on the scatter plot, and analyze the reachability of the end of the robotic arm within the workspace under the condition of fixing the robotic arm base.

[0047] Furthermore, based on the simulation analysis of the workspace under the condition of fixing the robotic arm base, divide the workspace area of the catenary bolt operation points according to the distribution of bolt points in the catenary environment, including:

[0048] Take the center of the bottom surface of the catenary column as the coordinate origin, define the axis direction of the column as the z-axis, set the direction perpendicular to the paper surface and outward as the x-axis, and set the direction parallel to the catenary flat arm as the y-axis to establish a coordinate system. By measuring the coordinates of each bolt in the catenary column base coordinate system, obtain the specific coordinate values corresponding to each bolt number, and get the coordinate values corresponding to different bolt numbers.

[0049] Furthermore, divide the workspace by minimizing the movement of the robotic arm base, including:

[0050] Determine whether the bolt is located in the upper half of the sphere and outside the unreachable cylinder area according to the judgment basis; wherein, the judgment basis is expressed as:

[0051]

[0052] In the formula, x i , y i , z i represent the x coordinate, y coordinate and z coordinate of the i-th bolt, x cir , y cir , z cir are the x coordinate, y coordinate and z coordinate of the center of the workspace sphere; R cir is the radius of the workspace, R cy is the radius of the unreachable area cylinder within the workspace;

[0053] x cir , y cir , z cir The calculation formula of is:

[0054]

[0055] In the formula, x bias , y bias , z bias are the x coordinate, y coordinate and z coordinate of placing the bolt at the relative position from the center of the workspace sphere;

[0056] If the bolt meets the judgment criteria, classify the bolt into the corresponding workspace area; if the bolt does not meet the judgment criteria, set a new spherical area according to the position of the bolt.

[0057] Furthermore, conduct offline modeling of the catenary and the working environment of the manipulator. Utilize the divided workspace and through path planning, achieve the maintenance tasks of the catenary boom, including:

[0058] Set the starting point q init as the initial point and as the root node of the random tree T;

[0059] In each loop, generate a random sampling point q rand ;

[0060] Sampling: Traverse each node in the random tree T, calculate the Euclidean distance between each node and the random sampling point q rand and find the node q nearest with the closest distance;

[0061] Advance a step size δ from the node q nearest with the closest distance in the direction of the random sampling point q rand to generate a new node q new .

[0062] Detect whether the path from the node q nearest with the closest distance to the new node q new intersects with obstacles. If there is a collision, discard the new node q new and re-enter the sampling process; otherwise, determine that the path is feasible and add the new node q new to the random tree T.

[0063] Calculate the distance from the new node q new to the target point q goal . If the distance is less than the set threshold, determine that the target point has been reached and end the search.

[0064] The beneficial effects of the present invention are:

[0065] (1) Improve the maintenance efficiency: By intelligently dividing the workspace of the manipulator, the manipulator can efficiently complete the fastening tasks of each bolt, reducing the maintenance time.

[0066] (2) Improve the operation accuracy: Precisely divide the workspace of the manipulator and take into account the working ability range of the manipulator itself to ensure that the end of the manipulator can accurately reach the position of each bolt, improving the accuracy of the bolt fastening operation.

[0067] (3) Enhance the operation safety: Avoid collisions between the manipulator and the catenary structure, ensure the safety of the manipulator during the operation process, and reduce the risk of safety accidents. Brief Description of the Drawings

[0068] Figure 1 The figure shows a schematic diagram of a typical catenary structure according to the prior art.

[0069] Figure 2 The figure shows an overall flowchart of a catenary boom maintenance robotic arm path planning method based on spatial intelligent partitioning according to an embodiment of the present invention.

[0070] Figure 3 The figure shows a schematic diagram of the DH parameter coordinate system of UR16e according to an embodiment of the present invention.

[0071] Figure 4 The figure shows a point cloud map of the workspace of UR16e according to an embodiment of the present invention.

[0072] Figure 5 The figure shows a distribution histogram of the point set in the workspace of the robotic arm according to an embodiment of the present invention.

[0073] Figure 6 The figure shows a schematic diagram of the establishment of the catenary coordinate system and the bolt distribution according to an embodiment of the present invention.

[0074] Figure 7 The figure shows a flowchart of the division of the workspace area of the catenary bolt operation point according to an embodiment of the present invention.

[0075] Figure 8 The figure shows a visualization result diagram of the division of the workspace area of the catenary bolt operation point according to an embodiment of the present invention.

[0076] Figure 9 The figure shows an offline model diagram of the catenary and the robotic arm according to an embodiment of the present invention.

[0077] Figure 10 The figure shows a coordinate relationship tree of the offline model according to an embodiment of the present invention.

[0078] Figure 11 The figure shows the robotic arm execution path of the planned target point of bolt S2 according to an embodiment of the present invention. Detailed Description of the Invention

[0079] The following describes the embodiments of the present invention through specific specific examples. Those skilled in the art can easily understand the other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. Various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, without conflict, the following embodiments and the features in the embodiments can be combined with each other.

[0080] The specific implementation manners of the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments.

[0081] Figure 1 The schematic diagram of a typical catenary structure according to the prior art is shown. As Figure 1 shown, the typical catenary structure includes a pillar 1, an inclined boom support 2, a positioning pipe support 3, a positioning pipe 4, an inclined boom 5, a flat boom 6, an insulator 7. The catenary inspection vehicle is on the right side. Among them, the catenary inspection vehicle includes a robotic arm 8, a lifting and slewing platform 9, and a catenary inspection work vehicle 10. During the operation, in order to improve the inspection efficiency of the robotic arm, it is necessary to model the typical catenary, divide the working area, and use the RRT path planning algorithm to perform safe path planning for the UR16e robotic arm to achieve the purpose of efficient and safe inspection.

[0082] Based on this, the embodiment of the present invention provides a path planning method for the catenary boom inspection robotic arm based on spatial intelligent division. As Figure 2 shown, it is the flowchart of this method. The path planning method for the catenary boom inspection robotic arm based on spatial intelligent division includes the following steps:

[0083] S1. Describe the relationship between each joint and the link through different parameters, and establish a robot kinematic model.

[0084] In this embodiment, step S1 is the process of DH modeling and forward kinematic analysis of the robotic arm. Denavit-Hartenberg (DH) parameter modeling describes the relationship between each joint and the link through different parameters, and establishes a robot kinematic model. This method can systematically solve the forward and inverse kinematic problems of the robot, and lay a theoretical foundation for the subsequent analysis of the working space of the robotic arm.

[0085] In some embodiments, UR16e is taken as an example of the robotic arm. According to the method of DH modeling, step S1 specifically includes:

[0086] (1) Determine the z-axis direction of each joint axis and all coordinate systems.

[0087] (2) Determine the common perpendicular or intersection point between joint axis i and joint axis i + 1 as the origin of coordinate system {i}.

[0088] (3) Set the x-axis perpendicular to the direction of joint axis i and joint axis i + 1 to determine the direction of the x-axis.

[0089] By combining the parameters of the UR16e mechanical structure, the coordinate system established on this robotic arm corresponding to the obtained DH parameter table is as Figure 3 shown, and the DH parameter table is shown in Table 1.

[0090] Table 1 DH Parameter Table of UR16e

[0091]

[0092] When calculating the forward kinematics of the robotic arm, it is necessary to calculate the transformation matrix from coordinate system {i - 1} to coordinate system {i} first. According to the definition of DH parameters, the transformation from coordinate system {i - 1} to coordinate system {i} can be divided into the following steps: First, rotate the coordinate system {i - 1} around the z i-1 by θ i , then move along the direction of z i-1 by a distance of d i-1 , then move along the current x i-1 axis by a distance of a i , and finally rotate the z i axis around the x i axis by α i . Therefore, the transformation matrix from coordinate {i - 1} to coordinate system {i} is shown in formula (1).

[0093] According to formula (1), can be obtained and multiplied to get the transformation relationship between the end of the robotic arm and the base coordinate system, and its transformation matrix is shown in formula (2).

[0094]

[0095] In the formula, represents the transformation matrix from coordinate system {i - 1} to coordinate system {i}, θ i is the joint angle, indicating the angle between the z-axis (i.e., the rotation axis) of the i-th link coordinate system and the z-axis of the (i - 1)-th link coordinate system. z represents the rotation axis of a link coordinate system, d i represents the distance measured along the z-axis of the (i - 1)-th link coordinate system from the origin of the (i - 1)-th link to the origin of the i-th link, a i represents the distance between the origin of the (i - 1)-th link coordinate system and the origin of the i-th link coordinate system, Rot represents the rotation matrix used to describe the rotation part of the coordinate system, Trans represents the translation matrix used to describe the translation part of the coordinate system, x represents the position vector, α represents the twist angle between two consecutive z-axes, c represents the abbreviation of the cos function in the rotation matrix, and s represents the abbreviation of the sin function in the rotation matrix.

[0096] Substitute the obtained by formula (1) into formula (2) to get formula (3).

[0097]

[0098] In the formula, n x, n y , n z represent the components of the rotational axis of the end effector relative to the base coordinate system in the x, y, and z directions, o x , o y , o z represent the components of the translation vector of the end effector relative to the base coordinate system in the x, y, and z directions, a x , a y , a z represent the offsets of the joint in the x, y, and z directions, p x , p y , p z represent the translation distances of the joint in the x, y, and z directions respectively.

[0099] The expressions represented by each element in the matrix in formula (3) are as follows:

[0100] n x = S1S5C6 + C6C 234 C1C5 - S 234 C1S6

[0101] n y = -C6C1S5 + C6C 234 C5C1 - S 234 S1S6

[0102] n z = C 234 S6 + S 234 C5C6

[0103] o x = -S6S1S5 - S6C 234 C1C5 - S 234 C1C6

[0104] o y = S6C1S5 - S6C 234 C1S5 - S 234 C6S1

[0105] o z = C 234 C6 - S 234 C5S6

[0106] a x = C5S1 - C 234 C1S5

[0107] a y = -C1S5 - C 234 S1S5

[0108] a z = -S234 S5

[0109] p x = d6C5S1 - d6C 234 C1S5 + C1a3C 23 + C1a2C2 + d4S1 + d5S 234 C1 + d2S1 + d3S1

[0110] p y = S1a3C 23 + S1a2C2 - d4C1 - d2C1 - d3C1 - d6C5C1 - d6C 234 S1S5 + d5S 234 S1

[0111] p z = d1 + a3S 234 + a2S2 - d5C 234 - d4S 234 S5

[0112] In the formula, C represents the abbreviation of the cosine function in the rotation matrix, S represents the abbreviation of the sine function in the rotation matrix, S1, S2, S3, S4, S5, S6 respectively represent the sine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; d1, d2, d3, d4, d5, d6 respectively represent the offsets of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C1, C2, C3, C4, C5, C6 respectively represent the cosine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C 23 represents the product of the cosine values of the angles of the second and third joints, C 234 represents the product of the cosine values of the angles of the second, third, and fourth joints; S 234 represents the product of the sine value of the angle of the second joint and the sine values of the angles of the third and fourth joints; a1, a2, a3 respectively represent the lengths of the first joint, the second joint, and the third joint.

[0113] S2. Perform a simulation analysis of the manipulator workspace based on the robot kinematic model to evaluate whether the manipulator can cover the catenary bolts at different positions, and analyze the reachability of the manipulator end in the workspace under the condition of fixing the manipulator base.

[0114] In this embodiment, step S2 is the process of robotic arm workspace simulation analysis. First, the Monte Carlo method is used to analyze the robotic arm workspace to evaluate whether it can cover the catenary bolts at different positions. The reachability of the robotic arm end in the workspace is analyzed with the robotic arm base fixed.

[0115] In some embodiments, taking UR16e as an example of the robotic arm, the process of applying the Monte Carlo method to solve the workspace of UR16e is as follows:

[0116] (1) Set the parameters of the Monte Carlo simulation, such as the number of samples, sampling range, etc. The joint angle range adopted in this paper is shown in Table 2.

[0117] Table 2 Robotic Arm Joint Angle Motion Range of Monte Carlo Method

[0118]

[0119] (2) Randomly output a set of N joint angles within the set robotic arm joint angle range [θ min , θ max , and its calculation formula is as shown in Formula 4.

[0120] θ = θ min + (θ max - θ min )RAND(N, 1) (4)

[0121] Among them, RAND(N, 1) is a random output function that outputs data with a range of [0, 1] for N rows and 1 column.

[0122] (3) Solve the x, y, and z coordinates of the position of the robotic arm end according to the forward kinematics formula (3) of the robotic arm, and store them.

[0123] (4) Output the calculated position as a set of coordinate points in three-dimensional space, and the set of these points forms a scatter plot representing the robotic arm workspace.

[0124] The point cloud result is as Figure 4 shown. It can be seen that its workspace is approximately hemispherical in shape, and there is an unreachable area in the center. In order to obtain detailed information about this unreachable area and the overall shape, by studying Figure 4 the spatial distribution of the point set, in this embodiment, the distribution of points in different coordinate directions and directions of distances from the origin is studied, and the corresponding point set coordinate distribution histogram is as Figure 5As shown. The histogram further quantifies these distribution characteristics, showing that the point set is mainly concentrated in the range of -0.8 meters to 0.8 meters on the x-axis and y-axis, while on the z-axis, the distribution is mainly concentrated in the range of -0.2 meters to 1.183 meters. In addition, the distribution of the point set along the z-axis is denser in the range of 0.2 meters to 1.2 meters. These analysis results are of great value for understanding the motion limitations of the robotic arm, optimizing the working path, and performing precise path planning and motion control.

[0125] S3. Simulation analysis of the workspace based on a fixed robotic arm base, and dividing the workspace area of the catenary bolt operation points according to the distribution of bolt points in the catenary environment.

[0126] In this embodiment, step S3 is the process of catenary bolt position modeling. Through the simulation analysis of the workspace with a fixed robotic arm base, it is found that its workspace is approximately a hemispherical cylinder with a hollow in the middle. Since the radius of the robotic arm workspace is limited and cannot cover all bolts, it is necessary to divide the workspace area of the catenary bolt operation points according to the distribution of bolt points in the catenary environment.

[0127] In some embodiments, step S3 specifically includes:

[0128] In a typical catenary environment, analyze the distribution of the operation bolt points, and then calculate and divide the workspace area of the bolt operation points. The catenary bolts are mainly distributed in six positions. To facilitate the description of the positions of these bolts, the following method is used to establish a coordinate system in this paper: taking the center of the bottom surface of the catenary column as the coordinate origin, the axis direction of the column is defined as the z-axis, the direction perpendicular to the paper surface and outward is set as the x-axis, and the direction parallel to the catenary flat arm is set as the y-axis, and establish a coordinate system as Figure 6 shown. By measuring the coordinates of bolts S1 to S6 in the catenary column base coordinate system, the specific coordinate values corresponding to each bolt number can be obtained, and finally the coordinate values corresponding to different bolt numbers are shown in Table 3.

[0129] Table 3 Main bolt distribution positions of the catenary

[0130]

[0131] S4. Divide the workspace with the minimum movement of the robotic arm base.

[0132] In this embodiment, step S4 is the process of intelligent division of the working space. To improve the maintenance efficiency of the catenary manipulator, considering that the manipulator base is fixed on the track inspection vehicle and the number of movements of the inspection vehicle is reduced, that is, the number of movements of the manipulator base is reduced, the inspection space of the manipulator is divided. Combining with the manipulator simulation space obtained in step S2, the working space is divided by minimizing the movement of the manipulator base to improve the inspection efficiency.

[0133] In some embodiments, this embodiment proposes an algorithm for dividing the working space area of the catenary bolt operation points. This algorithm first reads the coordinate information of the bolts from the dataset and checks the position of each bolt to determine whether it is located within the defined working space. Specifically, it is checked whether the bolt is located in the upper half of the sphere and outside the unreachable cylindrical area, and this judgment is based on a specific calculation formula (5).

[0134]

[0135] In formula (5), (x i , y i , z i ) represents the coordinates of the i-th bolt, and (x cir , y cir , z cir ) are the coordinates of the center of the working space sphere. R cir is the radius of this working space, which is set to 1m according to the previous description. R cy is the radius of the unreachable area cylinder within this working space, which is set to 0.0576m here.

[0136]

[0137] In formula (6), x bias , y bias , z bias are the relative positions of the bolt placed from the center of the working space sphere. Since there is a cylinder within the working space, this relative position needs to be placed outside the middle unreachable area. In this article, x bias is set to 0.5, y bias is set to 0, and z bias is set to -0.3.

[0138] If the bolt meets the above conditions, it is classified into the corresponding workspace area. Conversely, if the bolt does not meet the conditions, the algorithm defines a new spherical region near the position of the bolt. The algorithm repeats the above steps to judge and classify each bolt coordinate one by one until the processing of the entire set of data is completed. Through this iterative method, the algorithm can gradually construct a detailed workspace division to ensure that each bolt point is reasonably assigned to an appropriate working area. This process not only improves work efficiency but also provides accurate spatial information for subsequent job scheduling and path planning.

[0139] According to Figure 7 the algorithm flow described above, a program is written in Matlab to solve it, and the final division result of the working space area of the catenary bolt operation points is shown in Table 4, and its corresponding visualization result diagram is as shown in Figure 8 shown.

[0140] Table 4 Division Results of the Working Space of Catenary Bolt Operation Points

[0141]

[0142] From Figure 8 and Table 4, it can be seen that at least three independent working spaces are required to cover all bolt operation points. Bolts S1, S2, S3, and S6 are grouped into the same working space, namely Working Space 1, due to their relatively close relative positions in space. Bolts S4 and S5 each form an independent working space because they are far from other bolts. Further observing Figure 8 , it can be found that these working spaces intersect with the components of the catenary. When planning the path of the robotic arm, it is necessary to consider the possible collision between the robotic arm and the catenary components to ensure that no damage is caused to the catenary during the operation.

[0143] S5. Offline model the catenary and the working environment of the robotic arm, and use the divided working space to achieve the maintenance task of the catenary cantilever through path planning.

[0144] In this embodiment, step S5 is a process of safe path planning. First, offline model the catenary and the working environment of the robotic arm, and then use the different working spaces obtained in step S4 to achieve the maintenance task of the catenary cantilever through the RRT path planning algorithm.

[0145] In some embodiments, step S5 specifically includes:

[0146] By using offline modeling technology, models can be efficiently built and collision detection and path planning tasks can be executed. This process requires accurately drawing the mechanical structure model of the catenary to ensure the accuracy of collision detection. In this embodiment, the catenary model is first created in Solidworks software and exported in STL format. Then, in the ROS framework, the Xacro file is used to load the STL model to realize the integration of the catenary model and models such as the robotic arm, and a unified virtual environment is jointly constructed. In this environment, the coordinate relationships between the models are defined, and the necessary visualization and collision attributes are set for simulation analysis. The finally built offline simulation model of the catenary is as shown in Figure 9 and the coordinate relationships of the catenary and the robotic arm defined in the Xacro file are as shown in Figure 10 .

[0147] In different workspaces, the RRT algorithm is used for the path planning of the robotic arm respectively. The process of the RRT algorithm is as follows:

[0148] (1) Set the starting point q init as the initial point and the root node of the random tree T.

[0149] (2) Sampling: In each loop, generate a random sampling point q rand .

[0150] (3) Find the nearest node: Traverse each node in the random tree T, calculate the Euclidean distance between each node and q rand , and find the nearest node q nearest .

[0151] (4) Advance one step: Advance one step δ in the direction from q nearest to q rand to generate a new node q new .

[0152] (5) Collision detection: Detect whether the path from q nearest to q new intersects with obstacles. If there is a collision, discard q new and re-enter the sampling process; otherwise, consider the path feasible and add q new to the random tree T.

[0153] (6) Detect whether the target point is reached: Calculate the distance from q new to the target point q goal . If the distance is less than the set threshold, it is considered that the target point has been reached and the search ends.

[0154] (7) Repeat the above iterative process until q nearest and the target point q goalThe distance between them is lower than the set threshold value.

[0155] In this embodiment, the RRT provided by OMPL is utilized, and tests are carried out using the established offline catenary model. Given the target points as the positions of bolts S1 - S6 on the catenary, the path planning time of different bolts in the catenary environment is tested, and the obtained results are shown in Table 5.

[0156] Table 5 Results of path planning time for different bolts

[0157]

[0158] As can be seen from Table 5, the robotic arm can successfully complete path planning for each bolt target point in the obtained workspace, proving the correctness of the solved workspace. Meanwhile, in order to verify whether the constructed simulation model of the robotic arm and the catenary can effectively perform collision detection and path planning, this embodiment selects bolt S2 located on the catenary positioning pipe as the target point and adopts the RRT path planning algorithm. The generated path is as Figure 11 shown. It can be seen from this that no collision is found in the planned path, indicating the effectiveness of collision detection and path planning based on the intelligent space division algorithm under the offline catenary model.

[0159] The above embodiments are only used to illustrate the present invention and are not intended to limit the present invention. Those of ordinary skill in the relevant technical fields can also make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, all equivalent technical solutions also belong to the scope of the present invention. The patent protection scope of the present invention shall be defined by the claims.

Claims

1. A path planning method for the catenary boom maintenance manipulator based on spatial intelligent division, characterized in that, The method includes: Describing the relationships between each joint and the link through different parameters to establish a robot kinematic model; Performing a simulation analysis of the manipulator workspace based on the robot kinematic model to evaluate whether the manipulator can cover catenary bolts at different positions, and analyzing the reachability of the manipulator end in the workspace with the manipulator base fixed; Based on the simulation analysis of the workspace with the manipulator base fixed, dividing the workspace areas of catenary bolt operation points according to the distribution of bolt points in the catenary environment; Dividing the workspace with the movement of the manipulator base minimized; Performing an offline modeling of the catenary and the manipulator working environment, and using the divided workspace to achieve the maintenance task of the catenary boom through path planning; Based on the simulation analysis of the workspace with the manipulator base fixed, dividing the workspace areas of catenary bolt operation points according to the distribution of bolt points in the catenary environment, including: Taking the center of the bottom surface of the catenary column as the coordinate origin, defining the axis direction of the column as the z-axis, setting the direction perpendicular to the paper surface and outward as the x-axis, and setting the direction parallel to the catenary flat boom as the y-axis to establish a coordinate system. By measuring the coordinates of each bolt in the catenary column base coordinate system, obtaining the specific coordinate values corresponding to each bolt number, and getting the coordinate values corresponding to different bolt numbers; Dividing the workspace with the movement of the manipulator base minimized, including: Determining whether the bolt is located in the upper half of the sphere and outside the unreachable cylinder area according to the judgment criterion; wherein, the judgment criterion is expressed as: where x i , y i , z i represent the x - coordinate, y - coordinate, and z - coordinate of the i - th bolt, and x cir , y cir , z cir are the x - coordinate, y - coordinate, and z - coordinate of the center of the workspace sphere; R cir is the radius of the workspace, and R cy is the radius of the cylinder of the unreachable area within the workspace; x cir , y cir , z cir The calculation formula is: where x bias , y bias , z bias are the x, y, and z coordinates of the relative position of the bolt placed at a distance from the center of the working space sphere; If the bolt meets the judgment criterion, classifying the bolt into the corresponding workspace area; if the bolt does not meet the judgment criterion, setting a new sphere area according to the position of the bolt; Performing an offline modeling of the catenary and the manipulator working environment, and using the divided workspace to achieve the maintenance task of the catenary boom through path planning, including: Set the starting point q init As the initial point and the root node of the random tree T; In each loop, a random sampling point q is generated rand ; Sampling: Traverse each node in the random tree T and calculate the Euclidean distance between each node and the randomly sampled point q rand to find the node q with the closest distance nearest ; From the nearest node q nearest Towards the randomly sampled point q rand Advance one step size δ in the direction to generate a new node q new ; Detect whether the path from the nearest node q nearest to the new node q new intersects with obstacles. If there is a collision, discard the new node q new and re-enter the sampling process; otherwise, determine that the path is feasible and add the new node q new to the random tree T; Calculate the new node q new to the target point q goal If the distance is less than the set threshold, it is determined that the target point has been reached and the search ends.

2. The method for path planning of the catenary wrist arm maintenance manipulator based on spatial intelligent division according to claim 1, wherein, The step of describing the relationships between each joint and the link through different parameters to establish a robot kinematic model includes: Rotate the coordinate system {i - 1} around the z i-1 axis by θ i , and then move along the z i-1 direction by a distance d i-1 , move along the current x i-1 axis by a distance a i , rotate the z i axis around the x i axis by ɑ i to obtain the transformation matrix from the coordinate {i - 1} to the coordinate system {i}; Determining the transformation matrix between the manipulator end and the base coordinate system according to the transformation matrix from coordinate {i - 1} to coordinate system {i}; Based on the transformation matrix and the conversion matrix, determining the forward kinematic formula of the manipulator.

3. The method for path planning of the catenary boom maintenance robot based on spatial intelligent division according to claim 2, characterized in that, The transformation matrix from coordinate {i - 1} to coordinate system {i} is expressed as: In the formula, represents the transformation matrix from coordinate system {i - 1} to coordinate system {i}, and θ i is the joint angle, representing the angle between the z-axis of the i-th link coordinate system and the z-axis of the (i - 1)-th link coordinate system. z represents the rotation axis of a link coordinate system, and d i represents the distance measured along the z-axis of the (i - 1)-th link coordinate system from the origin of the (i - 1)-th link to the origin of the i-th link. a i represents the distance between the origin of the (i - 1)-th link coordinate system and the origin of the i-th link coordinate system. Rot represents the rotation matrix used to describe the rotational part of the coordinate system, Trans represents the translation matrix used to describe the translational part of the coordinate system, x represents the position vector, α represents the twist angle between two consecutive z-axes, c represents the abbreviation of the cosine function in the rotation matrix, and s represents the abbreviation of the sine function in the rotation matrix.

4. The method for path planning of the catenary wrist arm maintenance manipulator based on spatial intelligent division according to claim 3, wherein The conversion matrix between the manipulator end and the base coordinate system is expressed as: In the formula, represents the transformation matrix from coordinate system {0} to coordinate system {6}, respectively represent the transformation matrices from coordinate system {0} to coordinate system {1}, from coordinate system {1} to coordinate system {2}, from coordinate system {2} to coordinate system {3}, from coordinate system {4} to coordinate system {5}, and from coordinate system {5} to coordinate system {6}.

5. The method for path planning of the catenary boom maintenance manipulator based on spatial intelligent division according to claim 4, wherein The forward kinematic formula of the manipulator is expressed as: where n x , n y , n z represent the components of the rotation axis of the end effector relative to the base coordinate system in the x, y, and z directions, o x , o y , o z represent the components of the translation vector of the end effector relative to the base coordinate system in the x, y, and z directions, a x , a y , a z represent the offsets of the joint in the x, y, and z directions, p x , p y , p z represent the translation distances of the joint in the x, y, and z directions, respectively; The expressions represented by each element in formula (3) are as follows: n x = S1S5C6 + C6C 234 C1C5 - S 234 C1S6 n y =-C6C1S5 + C6C 234 C5C1 - S 234 S1S6 n z = C 234 S6 + S 234 C5C6 o x = -S6S1S5 - S6C 234 C1C5 - S 234 C1C6 o y = S6C1S5 - S6C 234 C1S5 - S 234 C6S1 o z = C 234 C6 - S 234 C5S6 a x = C5S1 - C 234 C1S5 a y =-C1S5-C 234 S1S5 a z =-S 234 S5 p x = d6C5S1 - d6C 234 C1S5 + C1a3C 23 + C1a2C2 + d4S1 + d5S 234 C1 + d2S1 + d3S1 p y = S1a3C 23 + S1a2C2 - d4C1 - d2C1 - d3C1 - d6C5C1 - d6C 234 S1S5 + d5S 234 S1 p z = d1 + a3S 234 + a2S2 - d5C 234 - d4S 234 S5 In the formula, C represents the abbreviation of the cosine function in the rotation matrix, S represents the abbreviation of the sine function in the rotation matrix, and S1, S2, S3, S4, S5, and S6 respectively represent the sine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; d1, d2, d3, d4, d5, and d6 respectively represent the offsets of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C1, C2, C3, C4, C5, and C6 respectively represent the cosine values of the angles of the first joint, the second joint, the third joint, the fourth joint, the fifth joint, and the sixth joint; C 23 represents the product of the cosine values of the second and third joint angles, C 234 represents the product of the cosine values of the second, third, and fourth joint angles; S 234 represents the product of the sine value of the second joint angle and the sine values of the third and fourth joint angles; a1, a2, and a3 respectively represent the lengths of the first joint, the second joint, and the third joint.

6. The method for path planning of the catenary wrist arm maintenance manipulator based on spatial intelligent division according to claim 2, wherein, Performing a simulation analysis of the manipulator workspace based on the robot kinematic model to evaluate whether the manipulator can cover catenary bolts at different positions, and analyzing the reachability of the manipulator end in the workspace with the manipulator base fixed, including: Setting the parameters of the Monte Carlo simulation; wherein, the parameters of the Monte Carlo simulation include the joint angle range; Randomly outputting a set of N joint angles within the set joint angle range, and the calculation formula is as follows: θ = θ min +(θ max -θ min )RAND(N,1) (4) where θ represents, θ max represents the maximum value of the set joint angle range, θ min represents the minimum value of the set joint angle range, and RAND represents the number of output joint angles; Determining the x, y, and z coordinates of the position of the manipulator end according to the forward kinematic formula of the manipulator; Output the x, y, and z coordinates of the position at the end of the robotic arm as a set of coordinate points in three-dimensional space to obtain a scatter plot representing the working space of the robotic arm. Based on the scatter plot, evaluate whether the robotic arm can cover the catenary bolts at different positions, and analyze the reachability of the end of the robotic arm within the working space under the condition of fixing the robotic arm base.

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