A Cartesian space trajectory planning method for welding robots based on inverse multi-objective optimization

Abstract

The present invention discloses a method for Cartesian space trajectory planning of a welding robot based on inverse solution multi-objective optimization, including steps 1 to 6, and also including inverse solution multi-objective optimization and optimal solution selection constraint setting process. The present invention proposes an inverse solution multi-objective optimization method, which comprehensively considers the structural size and working condition of the welding robot, is superior to the traditional motion interpolation and uses matlab for simulation; the trajectory planning method of the present invention improves the comprehensiveness of the inverse solution optimization principle, and improves the running rigidity of the welding robot to a certain extent, and combines it with the S-type acceleration and deceleration curve position interpolation and the posture interpolation based on the unit quaternion spherical linear method, ensuring that the welding machine robot completes the expected trajectory while the terminal trajectory, velocity, acceleration curve, posture curve and each joint displacement change curve are continuous and smooth without mutation, thereby improving the stability of the welding robot when working.

Description

Technical Field

[0001] The invention belongs to the technical field of robot Cartesian space trajectory planning, and in particular relates to a welding robot Cartesian space trajectory planning method based on inverse solution multi-objective optimization. Background Art

[0002] With the rapid development of modern industrial technology, industrial production lines are gradually becoming intelligent. Most production lines, such as automobile and shipbuilding, have a harsh working environment when performing welding operations. In order to reduce production costs, improve production efficiency, and ensure welding accuracy, robots have become an indispensable part of their production line welding operations. When robots are working, especially when they are engaged in high-precision work, they need to be verified in advance in terms of motion control and trajectory planning. If actual verification is performed directly, the cost is high and the safety is low. For welding robots, their running trajectory is determined, and the welds of welded parts are generally straight lines and arcs. In order to ensure that the welding robot can accurately complete the welding task along the weld, it is necessary to perform Cartesian space trajectory planning to ensure the stability of the end motion trajectory, thereby improving the welding accuracy and efficiency. However, the optimal choice of the inverse solution is the basis of trajectory planning. Therefore, it is necessary to select appropriate joint variables and combine them with the trajectory planning method so that the welding robot can run according to the expected trajectory and smoothly complete the welding task.

[0003] In patent CN112757306A (publication number), a forward-inverse solution or inverse-forward solution conversion is performed according to the current robot arm posture, and the inverse solution with the smallest norm of the difference between the conversion result and the current robot arm posture is taken as the most suitable set of solutions; trajectory planning is performed using the seventh-order polynomial trajectory planning method.

[0004] In patent CN111113431A (publication number), the robot kinematic model is established using improved DH parameters; according to the position and posture of the robot end at the trajectory point, the robot's six joint angles are solved using a closed solution method to obtain multiple joint angle inverse solutions for each trajectory point; according to the working range of each joint angle of the robot, some joint angle inverse solutions of each trajectory point are removed; based on the principles of "shortest overall trajectory stroke" and "moving more small joints and fewer large joints", a robot inverse solution optimization mathematical model is established; the inverse solution of each trajectory point after screening is converted into nodes, the sequence relationship of the trajectory points is connected to the corresponding nodes, and the starting node S and the ending node T are introduced to establish a directed graph G; the Dijkstra algorithm is used to solve the shortest path from the S node to the T node.

[0005] For the existing inverse optimization principles, only the principle of "minimum joint displacement" is considered, or the principle of "minimum joint displacement" is combined with the principle of "moving small joints more and moving large joints less" to perform inverse optimization, but the structure and working conditions of the robot are ignored, so that the optimal inverse solution is not comprehensive; the conventional inverse optimization method mainly considers the principle of "shortest stroke" and the principle of "moving small joints more and moving large joints less" to select joint variables. However, this method is not comprehensive and does not consider the structural size of the robot and the actual working conditions of the robot.

[0006] To this end, we propose a Cartesian space trajectory planning method for welding robots based on inverse multi-objective optimization to solve the problems existing in the existing technology. Summary of the invention

[0007] The object of the present invention is to provide a welding robot Cartesian space trajectory planning method based on inverse multi-objective optimization to solve the problems in the prior art mentioned in the above background technology.

[0008] To achieve the above object, the present invention adopts the following technical solutions:

[0009] A Cartesian space trajectory planning method for a welding robot based on inverse solution multi-objective optimization, comprising:

[0010] Step 1: Establish the kinematic model of the welding robot according to the improved DH parameter method;

[0011] Step 2: The robot end trajectory is obtained by using an interpolation algorithm based on a series of trajectory points obtained by discretizing the weld trajectory. Therefore, a certain end trajectory is equivalent to a finite number of trajectory points. Since the welding robot is a robot with 6 free series connections and the rear axes intersect at one point, the analytical method is used to perform inverse solution calculations to obtain 8 sets of joint variables.

[0012] Step 3: Constrain the 8 groups of joint variables to be within the angle limit range of each joint;

[0013] Step 4: In view of the fact that the previous inverse optimization principle is not comprehensive and does not take into account the robot's structural dimensions and actual working conditions, the operating stiffness index k is set based on the robot's structural dimensions and working conditions. sg And the improved joint rotation causes the subsequent link movement space range performance index S gj , combining the two with the principle of “minimum joint displacement”, the inverse multi-objective optimization index is set as ω:

[0014]

[0015] Step 5: Circular interpolation based on S-shaped acceleration and deceleration curve;

[0016] Step 6. Through MATLAB simulation, relevant data are obtained, mainly analyzing the arc trajectory. It can be seen that the stability of the welding robot's terminal trajectory, speed, acceleration, and posture curve is guaranteed.

[0017] Preferably, step 4 middle;

[0018] Where p is the weight of the two influencing indicators, θ j is the current joint angle, θ i,j is the jth joint variable of the i-th group of the trajectory point.

[0019] Preferably, step 5 comprises the following steps:

[0020] Step S1: By setting T k =t k -t k-1 (k=1,...,7), represents the time of each stage, and introduces the variable τ, let τ k =tt k-1 , as the relative time with the start time of each time period as the zero point, and set J as the acceleration of the acceleration and deceleration stage; set a max is the maximum acceleration, v max is the maximum speed, v s is the initial velocity, v1 is the initial velocity; at the same time, T1 = T3 = T5 = T7, T2 = T6. By analyzing each process, we can get the acceleration function, velocity function and displacement function of each time period;

[0021] To determine the running time of each stage, you need to set the displacement, start and end speed, maximum speed, maximum acceleration, and jerk of the S-curve. The running time of each stage is as follows:

[0022]

[0023]

[0024]

[0025] The normalized time l(t) operator plays a role in adjusting the step size in the interpolation motion. Where S(t) is the displacement of the S-shaped acceleration / deceleration curve that changes with time, and L is the distance between the starting and ending points;

[0026] Step S2: the conventional weld shape of the welding robot, and arc trajectory planning of the welding robot in Cartesian space;

[0027] Extract the straight weld and determine the starting point p0 (x0, y0, z0) and the end point p0 of the end trajectoryn (x n ,y n , z n ) coordinates; taking the normalized time operator based on the S-shaped acceleration and deceleration curve as the interpolation step, the coordinates of the i-th interpolation point p i (x i ,y i , z i ) is:

[0028]

[0029] Extract the arc weld, set the coordinates of the arc start and end points to p1 (x1, y1, z1), p3 (x3, y3, z3), and the middle point to p2 (x2, y2, z2). According to the construction method of the space arc, determine the transformation matrix between the coordinate system {C} and the coordinate system {B} Discrete the coordinates of each point of the arc weld:

[0030] x ic = r·cos(l(i)·dir·θ 13 )

[0031] y ic = r·sin(l(i)·dir·θ 13 )

[0032] z ic =0

[0033]

[0034] Set the posture matrix of the start and end points of the weld, and find the corresponding quaternions q1 and q2. According to the spherical linear interpolation SLERP method and the normalized time operator l(t), the interpolation of the posture is shown in the following formula:

[0035]

[0036] Preferably, the formulas of the acceleration function, velocity function, and displacement function in each time period in step S1 are as follows:

[0037]

[0038]

[0039]

[0040] Preferably, it also includes the inverse solution multi-objective optimization and optimal solution selection constraint setting process:

[0041] Step A1, constraining the 8 groups of joint variables to be within the angle limit range of each joint;

[0042] Step A2: Combine the robot's structural dimensions and working conditions to perform inverse multi-objective optimization:

[0043] For welding robots, when implementing welding tasks, the main considerations are the subsequent link movement space caused by joint rotation and the stiffness of the robot arm in actual work. Therefore, taking it as an influencing factor, the stiffness performance index is as follows:

[0044]

[0045] Among them C tt is the translation submatrix of the Cartesian flexibility matrix C, and the expression of C is:

[0046]

[0047] In the formula, J(q) is the Jacobian matrix of the welding robot, which can be determined by the improved DH parameters and changes with the posture of the robot arm. θ It is a joint stiffness matrix and a diagonal matrix. The larger the index, the better the stiffness performance. Based on the principle of shortest stroke, the power is minimized and the welding robot mechanism parameters are not considered. It is shown in the following formula:

[0048]

[0049] Among them l i is the connecting rod length of the first three joints;

[0050] Performance index S of the spatial range of subsequent link movement caused by joint rotation j , which is more comprehensive than the conventional expression and includes the structural parameters of the robot, can be obtained based on the standard DH parameters:

[0051]

[0052] However, considering that the three axes of the welding robot intersect at one point, the two formulas are combined, and based on the improved DH parameters, the performance index S of the first three joints is gj As shown in the following formula, the expression of the last three joints remains unchanged;

[0053]

[0054] The performance index S gj Combined with the principle of “minimum joint displacement”, the joint angle travel optimization model γ is obtained S for:

[0055]

[0056] Unify the order of magnitude and set the stiffness index to ksg =k s 10 -μ , the stiffness index and the joint angle travel optimization model are combined to form the inverse solution multi-objective optimization index ω, as shown in the following formula:

[0057]

[0058] Preferably, in step A2, the code flow for optimal selection of the inverse solution includes:

[0059] Step 1. Input the current joint angle variables θ j , j = 1 to 6;

[0060] Step 2: Use the inverse expression to find the joint variables of the next posture and select the joint variables θ that meet the joint angle limit. i,j , i = 1 ~ n, j = 1 ~ 6;

[0061] Step 3: Substitute the above data into the inverse solution of multi-objective optimization indicators to find the optimization indicators corresponding to each group of joint angles.

[0062] Step 4. Make a comparison. Select i The smallest set of joint angles is the optimal solution for the inverse solution;

[0063] Step 5: Take the selected optimal solution as θ j , and select the optimal solution for the next round of inverse solution.

[0064] Technical effects and advantages of the present invention: Compared with the prior art, the present invention proposes a Cartesian space trajectory planning method for a welding robot based on inverse multi-objective optimization, which has the following advantages:

[0065] 1. The present invention proposes an inverse multi-objective optimization method, which comprehensively considers the structural dimensions and working conditions of the welding robot, constructs a stiffness performance evaluation index, optimizes the performance index of the subsequent connecting rod movement area caused by joint rotation, and combines it with the principle of "minimum joint displacement" to perform the inverse optimal selection. Compared with previous optimization methods, it is more comprehensive, and to a certain extent, improves the variation range of joint angles and the stiffness of the robot at different trajectory points; and combined with trajectory planning, on this basis, the S-type acceleration and deceleration curve is combined with the Cartesian space linear interpolation motion and circular interpolation motion of the welding robot to interpolate the position of the welding robot;

[0066] 2. The present invention is superior to the traditional motion interpolation. The posture interpolation adopts the unit quaternion spherical linear interpolation based on the S-type acceleration and deceleration curve. Matlab is used for simulation to obtain relevant data. The inverse optimization method and the interpolation method are combined to ensure that the welding robot's terminal trajectory, speed, acceleration, posture curve and joint variable curve are continuous and smooth, thereby ensuring the welding quality.

[0067] Other features and advantages of the present invention will be described in the following description, and partly become obvious from the description, or be understood by implementing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 Schematic diagram of an S-shaped acceleration / deceleration curve in an embodiment of the present invention;

[0069] Figure 2 Schematic diagram of a conventional weld in an embodiment of the present invention;

[0070] Figure 3 A flowchart of obtaining relevant data by simulating through matlab in an embodiment of the present invention;

[0071] Figure 4 Schematic diagram of the displacement, velocity and acceleration of the end of the welding robot in an embodiment of the present invention;

[0072] Figure 5 Schematic diagram of the arc trajectory of the end of the welding robot in an embodiment of the present invention;

[0073] Figure 6 Schematic diagram of various joint variables of the welding robot in an embodiment of the present invention;

[0074] Figure 7 A schematic diagram of the posture change of the end of the welding robot in an embodiment of the present invention;

[0075] Figure 8 4 is a comparison diagram of the optimization method of the welding robot in the embodiment of the present invention. DETAILED DESCRIPTION

[0076] The following will be combined with the accompanying drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0077] The present invention provides Figure 1-8 In the embodiment shown:

[0078] A Cartesian space trajectory planning method for a welding robot based on inverse solution multi-objective optimization comprises the following steps:

[0079] 1. Establish the kinematic model of the welding robot based on the improved DH parameter method.

[0080] 2. The robot end trajectory is obtained by using the interpolation algorithm based on a series of trajectory points obtained by discretizing the weld trajectory. Therefore, the trajectory of one end is equivalent to a finite number of trajectory points. Since the welding robot is a robot with 6 free series connections and the rear axles intersect at one point, the analytical method is used to perform inverse calculation to obtain 8 sets of joint variables.

[0081] 3. Constrain its 8 groups of joint variables to be within the angle limit range of each joint.

[0082] 4. The previous inverse optimization principle was not comprehensive and did not consider the robot's structural dimensions and actual working conditions. Combined with the robot's structural dimensions and working conditions, the operating stiffness index k was set. sg And the improved joint rotation causes the subsequent link movement space range performance index S gj , combining the two with the principle of “minimum joint displacement”, the inverse solution multi-objective optimization index is set as ω.

[0083]

[0084] Where p is the weight of the two influencing indicators, θ j is the current joint angle, θ i,j is the jth joint variable of the i-th group of the trajectory point.

[0085] 5. Circular interpolation based on S-type acceleration and deceleration curve

[0086] (1) By Figure 1 Set T k =t k -t k-1 (k=1,...,7), indicating the time of each stage. In addition, variable τ is introduced, assuming τ k =tt k-1 , as the relative time with the start time of each time period as the zero point, and set J as the acceleration of the acceleration and deceleration stage; set a max is the maximum acceleration, v max is the maximum speed, v s is the initial speed, v1 is the initial speed; at the same time, T1 = T3 = T5 = T7, T2 = T6.

[0087] By analyzing the above, we can obtain the acceleration function, velocity function, and displacement function of each time period as shown in formulas (2) to (4):

[0088]

[0089]

[0090]

[0091] To determine the running time of each stage, it is necessary to set the displacement, start and end speed, maximum speed, maximum acceleration, and jerk of the S-curve. The running time of each stage is as shown in formulas (5) to (7):

[0092]

[0093]

[0094]

[0095] The normalized time l(t) operator plays a role in adjusting the step size in the interpolation motion. According to the literature, the normalized time operator Where S(t) is the displacement of the S-shaped acceleration / deceleration curve that changes with time, and L is the distance between the starting and ending points.

[0096] (2) The conventional weld shape of the welding robot is as follows Figure 2 As shown, arc trajectory planning of the welding robot is performed in Cartesian space 3.

[0097] Extract the straight weld and determine the starting point p0 (x0, y0, z0) and the end point p0 of the end trajectory n (x n ,y n , z n ). Taking the normalized time operator based on the S-shaped acceleration and deceleration curve as the interpolation step, the coordinates of the i-th interpolation point p i (x i ,y i , z i ) is:

[0098]

[0099] Extract the arc weld, set the coordinates of the arc start and end points to p1 (x1, y1, z1), p3 (x3, y3, z3), and the middle point to p2 (x2, y2, z2). According to the construction method of the space arc, determine the transformation matrix between the coordinate system {C} and the coordinate system {B} Discrete the coordinates of each point of the arc weld:

[0100] xic = r·cos(l(i)·dir·θ 13 ) (9)

[0101] y ic = r·sin(l(i)·dir·θ 13 ) (10)

[0102] z ic =0 (11)

[0103]

[0104] Set the posture matrix of the start and end points of the weld, and calculate the corresponding quaternions q1 and q2. According to the spherical linear interpolation SLERP method and the normalized time operator l(t), the interpolation of the progressive posture is shown in formula (13):

[0105]

[0106] 6. Use Matlab to simulate and obtain relevant data. The process is as follows: Figure 3 , mainly analyzing the arc trajectory, it can be seen that the stability of the welding robot's terminal trajectory, speed, acceleration, and posture curve is guaranteed, such as Figure 4 to Figure 7 .

[0107] The key points in the technical solution of the present invention are:

[0108] Inverse solution multi-objective optimization, the optimal solution selection constraints are set as follows:

[0109] (1) Constrain the eight groups of joint variables to be within the angle limit range of each joint;

[0110] (2) Combine the robot's structural dimensions and working conditions to perform inverse multi-objective optimization:

[0111] For welding robots, when implementing welding tasks, the main considerations are the subsequent link movement space caused by joint rotation and the stiffness of the robot arm in actual work. Therefore, taking it as an influencing factor, the stiffness performance index is as follows:

[0112]

[0113] Among them C tt is the translation submatrix of the Cartesian flexibility matrix C, and the expression of C is:

[0114]

[0115] In the formula, J(q) is the Jacobian matrix of the welding robot, which can be determined by the improved DH parameters and changes with the posture of the robot arm. θis the joint stiffness matrix and is a diagonal matrix. The larger the index, the better the stiffness performance. For the principle of "moving small joints more and large joints less", the power minimization is considered on the basis of the shortest stroke principle, and the welding robot mechanism parameters are not considered, as shown in formula (3):

[0116]

[0117] Among them l i is the connecting rod length of the first three joints.

[0118] Performance index S of the spatial range of subsequent link movement caused by joint rotation j , which is more comprehensive than the conventional expression and includes the structural parameters of the robot, can be obtained based on the standard DH parameters:

[0119]

[0120] However, considering that the three axes of the welding robot intersect at one point, the performance index S of the first three joints is obtained by combining formulas (4) and (5) based on the improved DH parameter. gj As shown in formula (6), the expressions of the last three joints remain unchanged.

[0121]

[0122] The performance index S gj Combined with the principle of “minimum joint displacement”, the joint angle travel optimization model γ is obtained S for:

[0123]

[0124] Unify the order of magnitude and set the stiffness index to k sg =k s 10 -μ , the stiffness index and the joint angle travel optimization model are combined to form the inverse solution multi-objective optimization index ω, as shown in formula (8):

[0125]

[0126] The code idea for the optimal selection of the inverse solution is as follows:

[0127] Step 1: Input the current joint angle variables θ j , j = 1 to 6;

[0128] Step 2: Use the inverse expression to find the joint variables of the next posture and select the joint variables θ that meet the joint angle limit. i,j , i = 1 ~ n, j = 1 ~ 6;

[0129] Step 3: Substitute the above data into the inverse solution of multi-objective optimization indicators to find the optimization indicators corresponding to each group of joint angles.

[0130] Step 4: Make a comparison.

[0131] Select i The smallest set of joint angles is the optimal solution for the inverse solution.

[0132] Step 5: Take the selected optimal solution as θ j , and select the optimal solution for the next round of inverse solution.

[0133] Table 1 Analysis of weights and robot impact factors

[0134]

[0135]

[0136] The multi-objective optimization index is more comprehensive, and at the same time, it is combined with the performance index S of the subsequent link movement space range caused by joint rotation. j By comparison, it can be seen that the change range of the joint variables of the rear three axes is improved, and its stiffness is improved to a certain extent, such as Figure 7 and Figure 8 As shown;

[0137] In summary, the trajectory planning method of the present invention improves the comprehensiveness of the inverse solution optimization principle and improves the running stiffness of the welding robot to a certain extent. At the same time, it is combined with the S-type acceleration and deceleration curve position interpolation and the posture interpolation based on the unit quaternion spherical linear method to ensure that the terminal trajectory, velocity, acceleration curve, posture curve and displacement change curves of each joint of the welding robot are continuous and smooth without mutation while completing the expected trajectory, thereby improving the stability of the welding robot when working;

[0138] The present invention proposes an inverse solution multi-objective optimization method, which comprehensively considers the structural dimensions and working conditions of the welding robot, constructs a stiffness performance evaluation index, optimizes the performance index of the subsequent connecting rod movement area caused by joint rotation, and combines it with the "minimum joint displacement" principle to perform the inverse solution optimal selection. Compared with previous optimization methods, it is more comprehensive, and to a certain extent, improves the variation range of joint angles and the stiffness of the robot at different trajectory points; and combined with trajectory planning, on this basis, the S-type acceleration and deceleration curve is combined with the Cartesian space linear interpolation motion and circular interpolation motion of the welding robot to interpolate the position of the welding robot;

[0139] The invention is superior to the traditional motion interpolation. The posture interpolation adopts the unit quaternion spherical linear interpolation based on the S-type acceleration and deceleration curve. Matlab is used for simulation to obtain relevant data. The inverse solution optimization method and the interpolation method are combined to ensure that the welding robot's terminal trajectory, speed, acceleration, posture curve and joint variable curve are continuous and smooth, thereby ensuring the welding quality.

[0140] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A Cartesian space trajectory planning method for a welding robot based on inverse multi-objective optimization, characterized in that: include: Step 1: Establish the kinematic model of the welding robot according to the improved DH parameter method; Step 2: The robot end trajectory is obtained by using an interpolation algorithm based on a series of trajectory points obtained by discretizing the weld trajectory. Therefore, a certain end trajectory is equivalent to a finite number of trajectory points. Since the welding robot is a robot with 6 free series connections and the rear axes intersect at one point, the analytical method is used to perform inverse solution calculations to obtain 8 sets of joint variables. Step 3: Constrain the 8 groups of joint variables to be within the angle limit range of each joint; Step 4: In view of the fact that the previous inverse optimization principle is not comprehensive and does not take into account the robot's structural dimensions and actual working conditions, the operating stiffness index k is set based on the robot's structural dimensions and working conditions. sg And the improved joint rotation causes the subsequent link movement space range performance index S gj , combining the two with the principle of "minimum joint displacement", setting the inverse solution multi-objective optimization index as ω: Where p is the weight of the two influencing indicators, θ j is the current joint angle, θ i,j is the jth joint variable of the i-th group of the trajectory point; Step 5: Circular interpolation based on S-shaped acceleration and deceleration curve; Step 6. Through MATLAB simulation, relevant data are obtained, mainly analyzing the arc trajectory. It can be seen that the stability of the welding robot's terminal trajectory, speed, acceleration, and posture curve is guaranteed.

2. The method for Cartesian space trajectory planning of a welding robot based on inverse solution multi-objective optimization according to claim 1, characterized in that: Step 5 includes the following steps: Step S1: By setting T k =t k -t k-1 (k=1,...,7), represents the time of each stage, and introduces the variable τ, let τ k =tt k-1 , as the relative time with the start time of each time period as the zero point, and set J as the acceleration of the acceleration and deceleration stage; set a max is the maximum acceleration, v max is the maximum speed, v s is the initial velocity, v1 is the initial velocity; at the same time, T1 = T3 = T5 = T7, T2 = T6. By analyzing each process, we can get the acceleration function, velocity function and displacement function of each time period; To determine the running time of each stage, you need to set the displacement, start and end speed, maximum speed, maximum acceleration, and jerk of the S-curve. The running time of each stage is as follows: The normalized time l(t) operator plays a role in adjusting the step size in the interpolation motion. Where S(t) is the displacement of the S-shaped acceleration / deceleration curve that changes with time, and L is the distance between the starting and ending points; Step S2: the conventional weld shape of the welding robot, and arc trajectory planning of the welding robot in Cartesian space; Extract the straight weld and determine the starting point p0 (x0, y0, z0) and the ending point pn (x n ,yn,z n ) coordinates; the normalized time operator based on the S-shaped acceleration and deceleration curve is used as the interpolation step, then the coordinate pi (x i , yi, z i ) is: Extract the arc weld, set the coordinates of the arc start and end points to p1 (x1, y1, z1), p3 (x3, y3, z3), and the middle point to p2 (x2, y2, z2). According to the construction method of the space arc, determine the transformation matrix between the coordinate system {C} and the coordinate system {B} Discrete the coordinates of each point of the arc weld: x ic =r·cos(l(i)·dir·θ 13 ) y ic =r·sin(l(i)·dir·θ 13 ) z ic ＝0 Set the posture matrix of the start and end points of the weld, and find the corresponding quaternions q1 and q2. According to the spherical linear interpolation SLERP method and the normalized time operator l(t), the interpolation of the posture is shown in the following formula:

3. The method for Cartesian space trajectory planning of a welding robot based on inverse solution multi-objective optimization according to claim 2, characterized in that: The formulas of the acceleration function, velocity function, and displacement function in each time period in step S1 are as follows:

4. The method for Cartesian space trajectory planning of a welding robot based on inverse solution multi-objective optimization according to claim 1, characterized in that: It also includes the inverse solution multi-objective optimization and the optimal solution selection constraint setting process: Step A1, constraining the 8 groups of joint variables to be within the angle limit range of each joint; Step A2: Combine the robot's structural dimensions and working conditions to perform inverse multi-objective optimization: For welding robots, when implementing welding tasks, the main considerations are the subsequent link movement space caused by joint rotation and the stiffness of the robot arm in actual work. Therefore, taking it as an influencing factor, the stiffness performance index is as follows: Among them C tt is the translation submatrix of the Cartesian flexibility matrix C, and the expression of C is: In the formula, J(q) is the Jacobian matrix of the welding robot, which can be determined by the improved DH parameters and changes with the posture of the robot arm. θ It is a joint stiffness matrix and a diagonal matrix. The larger the index, the better the stiffness performance. Based on the principle of shortest stroke, the power is minimized and the welding robot mechanism parameters are not considered. It is shown in the following formula: Among them l i is the connecting rod length of the first three joints; Performance index S of the spatial range of subsequent link movement caused by joint rotation j , which is more comprehensive than the conventional expression and includes the structural parameters of the robot, can be obtained based on the standard DH parameters: However, considering that the three axes of the welding robot intersect at one point, the two formulas are combined, and based on the improved DH parameters, the performance indicators of the first three joints are As shown in the following formula, the expression of the last three joints remains unchanged; The performance index S gj Combined with the principle of "minimum joint displacement", the joint angle travel optimization model γ is obtained S for: Unify the order of magnitude and set the stiffness index to k sg =k s 10 -μ , the stiffness index and the joint angle travel optimization model are combined to form the inverse solution multi-objective optimization index ω, as shown in the following formula:

5. The method for Cartesian space trajectory planning of a welding robot based on inverse solution multi-objective optimization according to claim 4, characterized in that: In step A2, the code flow for inverse solution optimal selection includes: Step 1. Input the current joint angle variables θ j , j = 1 to 6; Step 2: Use the inverse expression to find the joint variables of the next posture and select the joint variables θ that meet the joint angle limit. i,j , i = 1 ~ n, j = 1 ~ 6; Step 3: Substitute the above data into the inverse solution of multi-objective optimization indicators to find the optimization indicators corresponding to each group of joint angles. Step 4. Make a comparison. Select i The smallest set of joint angles is the optimal solution for the inverse solution; Step 5: Take the selected optimal solution as θ j , and select the optimal solution for the next round of inverse solution.

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