Trajectory planning method for rocket tank weld radiographic testing robot

Abstract

The rocket tank weld ray detection robot trajectory planning method solves the problems of complex and low efficiency of the rocket tank weld digital ray detection robot trajectory planning method, and belongs to the field of robot trajectory planning and optimization. The D-H method is used to establish the robot kinematics model, and the laser tracker is combined with the robot inverse kinematics algorithm to solve the robot D-H parameter error value, the robot kinematics model is compensated, and the more accurate robot kinematics model is obtained. According to the detection process, the weld detection pose points are collected, and then the inverse kinematics algorithm of the robot is used to obtain 8 sets of joint solutions corresponding to each pose point, a series of joint solution sets with the minimum joint amount change are iteratively solved through the particle swarm algorithm, and finally, based on the joint solution set with the minimum change amount, the quintic polynomial interpolation algorithm is used for trajectory planning, and the efficient robot detection trajectory is obtained.

Description

Technical Field

[0001] This invention relates to a trajectory planning method for a robot for radiographic inspection of weld seams in rocket propellant tanks, belonging to the field of robot trajectory planning and optimization. Background Technology

[0002] Radiographic testing, as a general-purpose testing technology, is widely used in industries such as aviation, aerospace, nuclear industry, new energy, electronic components, special equipment, shipbuilding, railway, and automobiles. The objects inspected include circuit boards, battery modules, castings, 3D printed parts, welded parts, and powders. Currently, radiographic testing is the primary method used by domestic rocket propellant tank manufacturing units for weld inspection. However, with the increasing frequency and intensity of rocket propellant tank development and launch missions, the workload is constantly increasing. Weld inspection of the bottom, cylindrical sections, and ring parts of rocket propellant tanks suffers from low automation, requiring manual inspection by multiple personnel, which is cumbersome, inefficient, and cannot meet the fast-paced development demands of current multi-model projects.

[0003] Trajectory planning is the foundation of current multi-robot X-ray inspection systems. The quality of trajectory planning directly affects the efficiency and quality of X-ray inspection. Robot trajectory planning involves mapping from task space to joint space, and this mapping is non-linear, making robot trajectory planning quite complex. Summary of the Invention

[0004] To address the issues of complex and inefficient trajectory planning methods for digital radiographic inspection robots of rocket propellant tank welds, this invention provides a trajectory planning method for such robots.

[0005] The present invention provides a trajectory planning method for a robot for radiographic inspection of weld seams in rocket propellant tanks, characterized in that the method comprises:

[0006] Step 1: Determine the corresponding DH parameter value by using the model of the rocket propellant tank weld radiographic inspection robot, and establish the robot kinematic model based on the DH parameter;

[0007] Step 2: Select random pose points of the robot kinematic model, move the actual robot to the corresponding joint position, and then use a laser tracker to measure and solve the error value of the DH parameter. Determine whether the error value meets the error condition. If not, compensate and correct the DH parameter according to the solved error value. Rebuild the robot kinematic model according to the corrected DH parameter, and then repeat Step 2 until the error condition is met, and then proceed to Step 3.

[0008] Step 3: Based on the robot's kinematic model and the rocket's propellant tank 3D product model, determine the weld inspection pose points according to the radiographic inspection process;

[0009] Step 4: Based on the weld seam detection pose points, use the inverse kinematics algorithm to solve for the corresponding 8 sets of robot joint solutions;

[0010] Step 5: Import the 8 sets of robot joint solutions into the particle swarm optimization algorithm model as the initial population, perform iterative solutions, and obtain the set of joint solutions with the smallest joint change after the iteration conditions are met.

[0011] Step 6: Perform trajectory planning based on the set of joint solutions with the smallest joint changes to obtain the planned robot trajectory.

[0012] Preferably, step 1 includes:

[0013] The DH parameters are determined based on the model of the X-ray inspection robot, where the DH parameters include the robot's Z-axis rotation. i-1 The axis is X i-1 Axis Steering X i Joint angle θ of the axis i From X i-1 Axis to X i Axial along Z i-1 The connecting rod offset d of the shaft i From Z i-1 Axis to Z i Axis along X i The length a of the connecting rod of the shaft i and around X i The axis is Z i-1 Axis Steering Z i Joint angle α of the shaft i , i = 1, 2, 3, 4, 5, 6;

[0014] Based on the DH parameters, the DH method is used to perform kinematic modeling of the robot, resulting in a robot kinematic model, which includes:

[0015] The homogeneous transformation matrix between the coordinate systems of the link at the i-th joint and the coordinate systems of the link at the (i+1)-th joint. i T i+1 :

[0016]

[0017] Where i = 1, 2, 3, 4, 5;

[0018] Homogeneous transformation matrix of robot end effector in base coordinate system 0 T6 is:

[0019]

[0020] Among them, [n x n y n z ]T , [o x o y o z ] T , [a x a y a z ] T These are the rotational attitude parameters of the robot's end effector in the X, Y, and Z axes of the base coordinate system, respectively. x p y p z ] T These are the position parameters of the robot's end effector;

[0021] The robot end effector's pose parameters in the robot's base coordinate system are P = [x, y, z, α]. k ,β,γ] T (x, y, z) are the position coordinates of the robot's end effector; x = p x y = p y z = p z ,

[0022] Preferably, step 4 includes:

[0023] Determine the pose matrix based on the weld seam detection pose points. 0 T6 uses an algebraic method to solve the inverse kinematics problem, separating variables one by one to obtain the joint values. Specifically, the method involves successively left-multiplying matrices to simplify the equations and solve for the joint angles θ. i For i = 1, 2, 3, 4, 5, 6, the simplified equation is:

[0024]

[0025] Preferably, the method for determining the X-ray inspection process in step 3 is as follows: determine

[0026] The distance f from the X-ray machine to the surface of the rocket propellant tank weld is determined based on the distance b from the product to the imaging plate and the focal spot size d of the X-ray machine.

[0027]

[0028] Preferably, the distance b from the product to the imaging plate is greater than 100mm, the focal spot size d of the X-ray machine is 0.4mm, and the distance f from the X-ray machine to the surface of the rocket propellant tank weld is 500mm.

[0029] Preferably, in step 5, the particle swarm optimization algorithm model is as follows:

[0030]

[0031]

[0032] Where ω is the inertia weight, r1 and r2 are random numbers distributed in the interval [0,1], k is the current iteration number, pbest is the individual optimal particle position, gbest is the global optimal particle position, and c1 and c2 are constants; Let be the particle velocity in the k-th iteration; Let be the particle position in the k-th iteration.

[0033] Preferably, step 5 includes:

[0034] Step 51: Use 8 sets of robot joint solutions as the initial population P, with the number of particles S. The position vector of each particle is composed of the joint solutions corresponding to each weld detection pose point. The dimension of the particle's position vector is m. Then, perform initialization settings and set the joint solution set corresponding to each weld detection pose point.

[0035] Step 52: Establish a fitness function, using the joint motion of the joint solution at the detection point corresponding to each particle in the particle swarm optimization algorithm as the fitness value. Through iterative iteration of the particle swarm optimization algorithm, obtain the globally optimal solution that continuously decreases the fitness value. The fitness function is:

[0036]

[0037] Where m is the total number of weld seam detection pose points, fitness is the fitness value, and y i Let i be the joint solution corresponding to the i-th weld detection pose point;

[0038] Step 53: Update the velocity and position of each particle using the particle swarm optimization model;

[0039] Step 54: If the current fitness value calculated by the particle is greater than pbest, then the current fitness value is taken as pbest and the current position of the particle is updated; if the current fitness value calculated by the particle is greater than gbest, then the current fitness value is taken as the global extreme solution and the global optimal solution is updated.

[0040] Step 55: Verify the termination condition. If the condition is met, obtain the set of joint solutions with the smallest joint change; otherwise, go to step 53.

[0041] As a preferred approach, trajectory planning is performed using a fifth-order polynomial interpolation algorithm and maximum acceleration constraints on the joint solution set with the smallest obtained joint changes, resulting in the planned robot trajectory.

[0042] The equation for the fifth-order polynomial interpolation algorithm is as follows:

[0043]

[0044] Where θ(t) represents the joint angle value at time t, and ak0 ak1 ak2 ak3 ak4 ak5 are the equation coefficients;

[0045] The maximum acceleration constraint is:

[0046]

[0047] Where q represents the maximum joint angular acceleration.

[0048] The beneficial effects of this invention are as follows: Within the effective workspace of the robot and under certain constraints, this invention selects optimization variables and determines its feasible region. Based on the idea of ​​motion stability, the optimization objective is to minimize the total change in the angular displacement of each joint of the robot throughout the entire process, searching for the optimal value of the detection pose point, and thus obtaining the optimal detection trajectory. This invention uses the DH method to establish a kinematic model of the rocket tank weld radiographic inspection robot, and uses a laser tracker combined with the robot inverse kinematics algorithm to solve for the robot DH parameter error value, and compensates for the robot kinematic model to obtain a more accurate robot kinematic model. This invention collects detection pose points according to the rocket tank weld radiographic inspection process. Through a series of collected detection pose points, combined with the robot inverse kinematics algorithm, eight sets of joint solutions corresponding to each pose point are obtained. Then, the particle swarm optimization algorithm is used to iteratively solve for a series of joint solutions with the smallest joint quantity change. Finally, based on the joint solution set with the smallest change, a fifth-order polynomial interpolation algorithm is used for trajectory planning to obtain a highly efficient robot detection trajectory. To address the common problems of high labor intensity, poor reliability, and low efficiency in trajectory planning for digital radiographic inspection robots of rocket propellant tank welds, this invention proposes a trajectory planning and optimization method for such robots. Simulation and experiments demonstrate that this method significantly improves labor intensity, reliability, and inspection efficiency, providing a reliable trajectory planning and optimization method for current rocket propellant tank weld radiographic inspection robots. Attached Figure Description

[0049] Figure 1 A flowchart illustrating an embodiment of the present invention;

[0050] Figure 2 This is a flowchart of the robot error compensation process of the present invention;

[0051] Figure 3 This is a flowchart of the particle swarm optimization algorithm of the present invention;

[0052] Figure 4 This is an iterative graph of the fitness values ​​in the particle swarm optimization algorithm of this invention;

[0053] Figure 5 This is a robot trajectory diagram planned by the fifth-order polynomial interpolation algorithm of this invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0057] like Figure 1 As shown, the trajectory planning method for the rocket propellant tank weld radiographic inspection robot of this embodiment includes:

[0058] Step 1: Determine the corresponding DH parameter values ​​by using the model of the robot for radiographic inspection of rocket propellant tank welds, and establish the robot's kinematic model using the DH method based on the DH parameters:

[0059] The DH parameters are determined based on the model of the X-ray inspection robot, where the DH parameters include the robot's Z-axis rotation. i-1 The axis is X i-1 Axis Steering X i Joint angle θ of the axis i From X i-1 Axis to X i Axial along Z i-1 The connecting rod offset d of the shaft i From Z i-1 Axis to Z i Axis along X i The length a of the connecting rod of the shaft i and around X i The axis is Z i-1 Axis Steering Z i Joint angle α of the shaft i , i = 1, 2, 3, 4, 5, 6;

[0060] Based on the DH parameters, the DH method is used to perform kinematic modeling of the robot. This method establishes a 4*4 homogeneous transformation matrix for the link coordinate system at each joint of the robot, representing its relationship with the previous link coordinate system, thus obtaining the robot's kinematic model. The robot kinematic model includes:

[0061] The homogeneous transformation matrix between the coordinate systems of the link at the i-th joint and the coordinate systems of the link at the (i+1)-th joint. i T i+1:

[0062]

[0063] Where i = 1, 2, 3, 4, 5;

[0064] Homogeneous transformation matrix of robot end effector in base coordinate system 0 T6 is:

[0065]

[0066] Among them, [n x n y n z ] T , [o x o y o z ] T , [a x a y a z ] T These are the rotational attitude parameters of the robot's end effector in the X, Y, and Z axes of the base coordinate system, respectively. x p y p z ] T These are the position parameters of the robot's end effector;

[0067] The robot end effector's pose parameters in the robot's base coordinate system are P = [x, y, z, α]. k ,β,γ] T (x, y, z) are the position coordinates of the robot's end effector; x = p x y = p y z = p z , (α k (β, γ) represents the angle between the robot's end effector and the three coordinate axes of the base coordinate system.

[0068] Step 2: Select random pose points of the robot's kinematic model, move the actual robot to the corresponding joint positions, and then use a laser tracker to measure and solve for the error value of the DH parameters. Determine whether the error value meets the error condition. If not, compensate and correct the DH parameters based on the solved error value. Rebuild the robot kinematic model based on the corrected DH parameters, and repeat Step 2 until the error condition is met, then proceed to Step 3. The specific implementation of Step 2 in this embodiment is as follows:

[0069] Step 21: Select random pose points of the robot's kinematic model and record the joint angle values ​​and robot pose parameter values ​​at this time;

[0070] Step 22: Using the recorded joint angle values ​​of the robot's kinematic model, control the robot to move to the corresponding joint position using the robot teach pendant;

[0071] Step 23: Measure the robot's end effector pose using a laser tracker. Compare the measured pose parameters with the recorded robot kinematic model pose parameters to obtain the DH parameter error. Simultaneously, observe whether the error condition is met. If not, compensate the obtained DH parameter error into the robot kinematic model, and then repeat step 21. Figure 2 The diagram shows the robot error compensation process, which uses a parameter calibration method to calibrate and compensate for the robot's absolute accuracy. First, the DH method is used to construct the robot's kinematic model. For industrial robots, errors in the parameters of each link will cause inaccurate end-effector position movement; therefore, it is necessary to accurately express the transformation relationships between each joint based on the kinematic model, and then construct an error model. Second, a laser tracker is used to measure the current position of the robot's end effector and compare it with the theoretical value to obtain the error value. This value is then substituted into the error model to obtain the kinematic parameter error. Finally, robot error compensation is performed, setting the identified true parameter values ​​into the kinematic model to improve positioning accuracy.

[0072] Step 3: Based on the robot's kinematic model and the rocket propellant tank's 3D product model, determine the weld inspection pose points according to the radiographic inspection process; specifically including:

[0073] Based on the principle of optimal radiographic inspection sensitivity, the single-wall radiographic method recommended in GJB1187A-2019 "Radiographic Inspection" is adopted, with the X-ray machine inside and the imaging plate outside, and the X-ray beam from the center of the X-ray machine perpendicular to the center area of ​​the weld. According to GB / T35388-2017 "Non-destructive Testing - Digital Imaging Inspection Methods for X-rays," the distance f from the X-ray machine to the surface of the rocket propellant tank weld, the focal length d of the X-ray machine, and the distance b from the product to the imaging plate should meet the following requirements:

[0074]

[0075] To ensure the safety of the rocket propellant tank and the robot during the inspection process, the distance b from the product to the imaging plate is greater than 100mm, and the focal spot size d of the X-ray machine is 0.4mm. Calculated using the above formula, the distance f from the X-ray source to the product surface should be greater than 130mm. Since the cone angle of the directional X-ray tube is 40 degrees, to increase the length of a single exposure while ensuring the thickness of X-ray penetration, the distance f from the X-ray machine to the surface of the rocket propellant tank weld is set to 500mm.

[0076] By using a robot kinematic model and a rocket propellant tank 3D model that meet the error conditions, and combining them with the set process conditions, all weld inspection pose points of the robot kinematic model are selected, and the parameter values ​​of all weld inspection pose points are recorded.

[0077] Step 4: Based on the weld seam detection pose points, use the inverse kinematics algorithm to solve for the corresponding 8 sets of robot joint solutions:

[0078] By obtaining all the weld seam detection pose points, and combining them with the robot inverse kinematics algorithm, the corresponding joint solution sets are solved: the inverse kinematics solution problem is based on the pose matrix. 0 T6, derives the angles θ that each joint of the robot's end effector needs to change when it is at the detection pose point. i The process (i = 1, 2, 3, 4, 5, 6); this implementation method uses an algebraic solution to complete the inverse kinematics solution, solving for each variable one by one to obtain the values ​​of each joint. Specifically, the method involves successive left multiplication of the matrix, simplifying the equation to obtain the following equation:

[0079] ( 0 T1) -10 T6 = 1 T2 2 T3 3 T4 4 T5 5 T6

[0080] ( 1 T2) -1 ( 0 T1) -10 T6 = 2 T3 3 T4 4 T5 5 T6

[0081] Step 5: Import the 8 sets of robot joint solutions into the particle swarm optimization algorithm model as the initial population, and perform iterative solutions. After satisfying the iteration conditions, obtain the set of joint solutions with the smallest joint change.

[0082] In step 5, the particle swarm optimization model is as follows:

[0083]

[0084]

[0085] Where ω is the inertia weight, r1 and r2 are random numbers distributed in the interval [0,1], k is the current iteration number, pbest is the individual optimal particle position, gbest is the global optimal particle position, and c1 and c2 are constants; Let be the particle velocity in the k-th iteration; Let be the particle position in the k-th iteration.

[0086] The training iteration process of the particle swarm optimization algorithm to solve for the joint solution set corresponding to the optimal weld detection pose point is as follows:

[0087] Step 51: Assume there are m total weld seam detection pose points, and the detection order is ordered. Each weld seam detection pose point has 8 joint solutions. The goal is to extract one joint solution from all pose points to minimize the robot's joint motion during the entire detection process. In the particle swarm optimization algorithm, a population P is first initialized with S particles. The position vector of each particle consists of the joint solutions corresponding to each pose point, and the dimension of the particle's position vector is m. Then, initialization settings are performed to define the joint solution sets corresponding to each weld seam detection pose point.

[0088] Step 52: Establish a fitness function. The initial fitness value of each particle is calculated by treating the initial position as the individual extreme value. Then, the optimal position solution of the population is calculated. From the perspective of optimization, it is to find a joint solution in each of the m weld detection pose points, satisfying that the total joint motion is minimized when the m joint solutions are calculated in the detection order.

[0089] To enable the initial solution to gradually evolve towards the optimal solution, this invention uses the joint motion of the joint solution at the detection point corresponding to each particle in the particle swarm optimization algorithm as the fitness value. Through iterative iteration of the particle swarm optimization algorithm, a globally optimal solution that continuously reduces the fitness value is obtained. The established fitness function is as follows:

[0090]

[0091] Where m is the total number of weld seam detection pose points, fitness is the fitness value, and y i Let i be the joint solution corresponding to the i-th weld detection pose point.

[0092] Step 53: Each particle is updated using the particle swarm optimization formula, including the particle's velocity and position.

[0093] Step 54: Compare the current fitness value of the particle with pbest. If the former is greater than the latter, then use the current fitness value as pbest and update the particle's current position.

[0094] Step 55: Simultaneously compare the current fitness value with gbest. If the former is greater than the latter, then take the current fitness value as the global extreme solution and update the global optimal solution.

[0095] Step 56: Verify the termination condition. If the condition is met, the optimization ends; otherwise, proceed to step 53 to continue the calculation.

[0096] like Figure 3The diagram shows the flowchart of the particle swarm optimization (PSO) search algorithm. The population initialization module initializes the particle positions X and velocities V. The fitness calculation module calculates the individual fitness value according to the fitness calculation formula. The optimal particle update module updates the optimal particle based on the new particle positions. The non-dominated solution update module filters non-dominated solutions based on the new particle dominance relationships. The particle velocity and position update module updates the particle velocity and position based on the optimal particle position and the global particle positions.

[0097] like Figure 4 The graph shows the fitness values ​​for the particle swarm optimization (PSO) algorithm. In step 5, the PSO parameters are set as follows: inertia weight ω, learning factors c1 and c2, maximum particle velocity, and maximum number of iterations. First, an adaptively adjusted linearly decreasing inertia weight is selected, with a typical weight value of ω. max =0.9, ω min =0.4, and the initial weight ω is set to 0.9. The learning factor satisfies c1+c2=4, and the number of iterations is small when c1=2, but large when c1=2, showing symmetry; the failure rate is large at the two endpoints. Therefore, c1=c2=2, and the maximum particle velocity is set to 0.5 according to the required resolution between the current position and the best position. Finally, to prevent continuous iterations from failing to reach the convergence state and to observe the convergence number of iterations of the particle swarm algorithm of this invention, the maximum number of iterations of the algorithm is determined to be 100.

[0098] Step 6: Based on the joint solution set with the smallest joint changes, perform trajectory planning using a fifth-order polynomial interpolation algorithm and maximum acceleration constraints to obtain the planned robot trajectory:

[0099] like Figure 5 For the robot trajectory planned using a fifth-order polynomial interpolation algorithm, the motion trajectory of the rocket propellant tank weld X-ray inspection robot needs to be relatively smooth and continuous. This implementation uses a fifth-order polynomial algorithm for interpolation calculations. The fifth-order polynomial is a time function of the joint angles. Its first and second differentiability are time functions of the joint angular velocity and joint angular acceleration. Furthermore, according to the fifth-order polynomial interpolation algorithm, the joint acceleration may tend to infinity. This implementation adds maximum acceleration constraints for each joint during the planning process based on the robot model.

[0100] The equation for the fifth-order polynomial interpolation algorithm is as follows:

[0101]

[0102] Where θ(t) represents the joint angle value at time t, and ak0 ak1 ak2 ak3 ak4 ak5 are the equation coefficients;

[0103] The maximum acceleration constraint is:

[0104]

[0105] Where q represents the maximum joint angular acceleration.

[0106] Compared to cubic polynomial interpolation, quintic polynomial interpolation adds constraints on the start and end points, as follows:

[0107]

[0108] Where θ(t0) and θ(t) f () represents the joint angle between the starting point and the target point. Indicates the joint angular velocity at the starting point and the target point. Let represent the joint angular accelerations at the starting and target points, satisfying the maximum angular acceleration constraint. Setting the starting time to 0, the solution is:

[0109]

[0110] Step 7: By using the DH method to establish the robot kinematic model, and combining it with the trajectory with the minimum joint motion planned by the fifth-order polynomial interpolation algorithm, establish the profinet communication between the kinematic model and the robot controller. Connect the time functions of each joint angle with the joint variables in the robot controller to realize the combination of trajectory simulation and actual X-ray inspection process, thereby effectively solving the trajectory planning problem of the X-ray inspection robot for rocket tank welds.

[0111] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A trajectory planning method for a robot used for radiographic inspection of rocket propellant tank welds, characterized in that, The method includes: Step 1: Determine the corresponding DH parameter value by using the model of the rocket propellant tank weld radiographic inspection robot, and establish the robot kinematic model based on the DH parameter; Step 2: Select random pose points of the robot kinematic model, move the actual robot to the corresponding joint position, and then use a laser tracker to measure and solve the error value of the DH parameter. Determine whether the error value meets the error condition. If not, compensate and correct the DH parameter according to the solved error value. Rebuild the robot kinematic model according to the corrected DH parameter, and then repeat Step 2 until the error condition is met, and then proceed to Step 3. Step 3: Based on the robot's kinematic model and the rocket's propellant tank 3D product model, determine the weld inspection pose points according to the radiographic inspection process; Step 4: Based on the weld seam detection pose points, use the inverse kinematics algorithm to solve for the corresponding 8 sets of robot joint solutions; Step 5: Import the 8 sets of robot joint solutions into the particle swarm optimization algorithm model as the initial population, perform iterative solutions, and obtain the set of joint solutions with the smallest joint change after the iteration conditions are met. Step 6: Perform trajectory planning based on the set of joint solutions with the smallest joint changes to obtain the planned robot trajectory; Step 1 includes: The DH parameters are determined based on the model of the X-ray inspection robot, where the DH parameters include the robot's Z-axis rotation. i-1 The axis is X i-1 Axis Steering X i Joint angle of the shaft From X i-1 Axis to X i Axial along Z i-1 Shaft connecting rod offset From Z i-1 Axis to Z i Axis along X i Length of the connecting rod of the shaft and around X i The axis is Z i-1 Axis Steering Z i Joint angle of the shaft , ; Based on the DH parameters, the DH method is used to perform kinematic modeling of the robot, resulting in a robot kinematic model, which includes: The homogeneous transformation matrix between the coordinate systems of the link at the i-th joint and the coordinate systems of the link at the (i+1)-th joint. : ； in, ; Homogeneous transformation matrix of robot end effector in base coordinate system for: ； in, , , These are the rotational attitude parameters of the robot's end effector in the base coordinate system along the X, Y, and Z axes, respectively. These are the position parameters of the robot's end effector; pose parameters of the robot end effector in the robot base coordinate system , The coordinates of the robot's end effector; , , , , , .

2. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 1, characterized in that, Step 4 includes: Determine the pose matrix based on the weld detection pose points. The inverse kinematics solution is obtained by using an algebraic method, separating variables one by one to obtain the joint values. Specifically, the joint angles are solved by successively multiplying matrices on the left to simplify the equations. , The simplified equation is: 。 3. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 1, characterized in that, The method for determining the X-ray inspection process in step 3 is as follows: [Determine...] The distance f from the X-ray machine to the surface of the rocket propellant tank weld is determined based on the distance b from the product to the imaging plate and the focal spot size d of the X-ray machine. 。 4. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 3, characterized in that, The distance b from the product to the imaging plate is greater than 100mm, the focal spot size d of the X-ray machine is 0.4mm, and the distance f from the X-ray machine to the surface of the rocket propellant tank weld is 500mm.

5. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 1, characterized in that, In step 5, the particle swarm optimization algorithm model is as follows: ； ； in, For inertial weights, and The random numbers are distributed in the interval [0,1]. This represents the current iteration number. `gbest` represents the optimal position for an individual particle, while `gbest` represents the globally optimal particle position. and It is a constant; For the first The particle velocity in the next iteration; For the first The particle position in the next iteration.

6. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 5, characterized in that, Step 5 includes: Step 51: Use 8 sets of robot joint solutions as the initial population P, with the number of particles S. The position vector of each particle is composed of the joint solutions corresponding to each weld detection pose point. The dimension of the particle's position vector is m. Then, perform initialization settings and set the joint solution set corresponding to each weld detection pose point. Step 52: Establish a fitness function, using the joint motion of the joint solution corresponding to each particle in the particle swarm optimization algorithm as the fitness value. Through iterative processing using the particle swarm optimization algorithm, obtain the globally optimal solution that continuously decreases the fitness value. The fitness function is: ； Where m is the total number of weld inspection pose points. For fitness value, For the first The joint solution corresponding to the pose point of each weld seam inspection; Step 53: Update the velocity and position of each particle using the particle swarm optimization model; Step 54: If the current fitness value calculated by the particle is greater than pbest, then the current fitness value is taken as pbest and the current position of the particle is updated; if the current fitness value calculated by the particle is greater than gbest, then the current fitness value is taken as the global extreme solution and the global optimal solution is updated. Step 55: Verify the termination condition. If the condition is met, obtain the set of joint solutions with the smallest joint change; otherwise, go to step 53.

7. The trajectory planning method for the rocket propellant tank weld radiographic inspection robot according to claim 1, characterized in that, Based on the set of joint solutions with the minimum joint changes, a fifth-order polynomial interpolation algorithm and a maximum acceleration constraint are used to plan the trajectory, resulting in the planned robot trajectory. The equation for the fifth-order polynomial interpolation algorithm is as follows: ； in, This represents the joint angle value at time t. These are the equation coefficients; The maximum acceleration constraint is: ； in, This represents the maximum joint angular acceleration.

8. A computer-readable storage device storing a computer program, characterized in that, When the computer program is executed, it implements the trajectory planning method for the rocket propellant tank weld radiographic inspection robot as described in any one of claims 1 to 7.

9. A trajectory planning device for a rocket propellant tank weld radiographic inspection robot, comprising a storage device, a processor, and a computer program stored in the storage device and executable on the processor, characterized in that, The processor executes the computer program to implement the trajectory planning method for the rocket propellant tank weld radiographic inspection robot as described in any one of claims 1 to 7.

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