A Fast Method for Extracting Joint Angles of Robotic Arms Based on GRU Neural Network and Fireworks Algorithm

Abstract

This invention discloses a method for rapid extraction of robotic arm joint angles based on a GRU neural network and a firework algorithm. The method includes: obtaining the end effector pose of an industrial robot; training a GRU neural network model based on the end effector pose and actual joint angles; inputting the end effector pose to be extracted and outputting the extracted predicted joint angles; and using the firework algorithm to obtain the optimal joint angles, thus achieving rapid extraction of the robotic arm joint angles. This invention extracts more accurate joint angles, reduces abrupt changes in joint angles between adjacent poses during industrial robot movement, and, combined with the firework algorithm, obtains accurate inverse kinematics of the robot joint angles adapted to the end effector pose, achieving rapid extraction of the robotic arm joint angles.

Description

Technical Field

[0001] This invention relates to a method for rapid extraction of joint angles of a robotic arm, relating to the field of robot motion control, and specifically to a method for rapid extraction of joint angles of a robotic arm based on a GRU neural network and a firework algorithm. Background Technology

[0002] Kinematics is the foundation of robot motion control. Solving the robot's end-effector pose given the angles of its joints is called forward kinematics. Forward kinematics has a unique solution. Inverse kinematics, on the other hand, involves solving for the robot's joint angles based on its end-effector pose. Even with a determined end-effector pose, the joint angles are not unique; multiple sets of joint angles may correspond to that pose. There are various methods for solving inverse kinematics, including geometric, algebraic, and numerical methods. Geometric and algebraic methods are collectively known as analytical methods. Using analytical methods for inverse kinematics requires satisfying the Pieper criterion. Numerical methods for solving inverse kinematics may get trapped in local optima or singular values.

[0003] To solve the inverse kinematics of a robot's motion, a method combining spinor exponential product with geometric and algebraic methods is proposed to overcome the singularity problem in robot kinematics, but the solution process is relatively complex. A method using quantum particle swarm optimization (BP neural network) to solve the inverse kinematics is also proposed, but this method can only be based on a linear robot motion space and requires a large amount of data as a training set. An improved chaotic sparrow search algorithm is used to solve the inverse kinematics problem of a redundant robot arm, greatly improving the accuracy of the solution. However, this method is limited by the initial pose, and the solution for the robot's inverse kinematics is not unique.

[0004] The motion of an industrial robot is a continuous process of joint changes, and the changes of each joint are continuously related. Directly solving the inverse kinematics of a specified end-effector pose can lead to large joint angle changes, even over short distances, which is detrimental to motion planning. Backpropagation (BP) neural networks and recurrent circular network (RBF) neural networks cannot track the continuous joint changes of an industrial robot and therefore cannot solve this problem. Recurrent neural networks can handle temporal memory information, but they are prone to losing their ability to learn from previous information, resulting in gradient explosion or vanishing gradient problems. Long Short-Term Memory (LSTM) networks can effectively solve the long-term dependence on historical information and avoid gradient explosion or vanishing gradients. However, LSM networks have a relatively complex structure, high computational complexity, and slow computational efficiency. Summary of the Invention

[0005] To address the problems existing in the background technology, the present invention provides a method for rapid extraction of joint angles of robotic arms based on GRU neural network and fireworks algorithm.

[0006] The technical solution adopted in this invention is:

[0007] The present invention provides a method for fast extraction of joint angles of a robotic arm based on a GRU neural network and a fireworks algorithm, comprising:

[0008] 1) During the movement of the industrial robot, the end pose of the industrial robot is obtained by using the forward kinematics analysis method based on the movement trajectory of the industrial robot.

[0009] 2) The end-effector pose and actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model to train the model and obtain the trained neural network model.

[0010] 3) Input the end-effector pose of the industrial robot to be extracted into the trained model, and output the predicted joint angles of the extracted industrial robot.

[0011] 4) After applying the Fireworks Algorithm to the predicted joint angles of the industrial robot in step 3), the optimal joint angles of the industrial robot are obtained, thus realizing the rapid extraction of the joint angles of the robotic arm of the industrial robot.

[0012] In step 1), the end effector pose of the industrial robot includes the end effector position and attitude angles. The end effector position includes the X-axis coordinate (x), Y-axis coordinate (y), and Z-axis coordinate (z) of the end effector. The attitude angles include the roll angle α, pitch angle β, and yaw angle γ of the end effector, as detailed below:

[0013]

[0014]

[0015]

[0016]

[0017] in, and These represent the transformation matrices of the end effector of the industrial robot relative to the base. The elements in the first row and first column, the first row and second column, the first row and third column, the first row and fourth column, the second row and third column, the second row and fourth column, the third row and third column, and the third row and fourth column.

[0018] An industrial robot is controlled by a teach pendant to operate along a planned trajectory. During the robot's movement, its end effector posture and corresponding joint angles are acquired and recorded from the teach pendant. A forward kinematic model of the industrial robot is established using the DH parameter method, and then the transformation matrix from the robot base to the end effector is obtained.

[0019] The transformation matrix of the end effector of the industrial robot relative to the base Specifically as follows:

[0020]

[0021]

[0022] in, and Let θ represent the transformation matrices between the base and the first robotic arm, the first robotic arm and the second robotic arm, the (i-1)th robotic arm and the ith robotic arm, and the (n-1)th robotic arm and the nth robotic arm, respectively, where n represents the total number of robotic arms / joints of the industrial robot; i a represents the actual angle of the i-th joint of the industrial robot; i-1 α represents the length of the line segment representing the common perpendicular between the two axes of the (i-1)th robotic arm; i-1 This represents the included angle between the axes of the two ends of the (i-1)th robotic arm.

[0023] Industrial robots are serial robots, with a basic structure consisting of a series of jointed links. The forward kinematics analysis of an industrial robot is essentially a decomposition of the positional relationships between these links. By establishing coordinate systems at the ends of the links, the positional relationships between them can be described by coordinate system transformations. The process of transforming the coordinate system from i-1 to coordinate system i can be decomposed into four sub-transformations: [the transformations occur around the x-axis]. i-1 Axis rotation angle α i-1 , along x i-1 Axis movement distance a i-1 Rotation angle θ around the z-axis i The distance d along the z-axis i For two adjacent links, use a i-1 α i-1 θ i and d i Describe their relationship. θ i Indicates two common perpendiculars a i-1 and a i The angle between them, d i Indicates two common perpendiculars a i-1 and a i The distance between them.

[0024] In step 2), the end-effector pose and the actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model for training. Specifically, during each iteration of training, the end-effector pose of the industrial robot at the t-th position in the motion trajectory and the hidden state h of the GRU neural network model obtained during the iteration training at the (t-1)-th position of the industrial robot are used. t-1 As input to the GRU (Gated Recurrent Unit) neural network model, the GRU neural network model outputs the predicted joint angles at the t-th position of the industrial robot and the hidden state h at that position. t At the initial position, the hidden state h0 is set to zero.

[0025] During each training iteration, the mean squared errors of the predicted joint angles of the industrial robot at the current position output by the gated recurrent unit (GRU) neural network model and the actual joint angles in step 1) are compared. The mean squared error loss function is used as the loss function MSE of the GRU neural network model, as follows:

[0026]

[0027] Where n represents the total number of robotic arms in the industrial robot; G(t) i ) represents the predicted joint angle of the industrial robot output by the GRU neural network model after processing the t-th end-effector position of the input, i.e., the robot inverse solution, θ. i This represents the angle of the i-th actual joint of the industrial robot.

[0028] When the loss function MSE reaches its minimum or the number of training iterations reaches its preset maximum, training stops, and a gated recurrent unit (GRU) neural network model is obtained after training.

[0029] In step 4), the predicted joint angles of the industrial robot in step 3) are used to obtain the optimal joint angles of the industrial robot by applying the fireworks algorithm. Specifically, N fireworks are first generated in the neighborhood of each predicted joint angle. Each fireworks has n dimensions, where n represents the total number of joints of the industrial robot. Then, the fitness value of each fireworks is calculated. Based on the fitness value, the explosion radius and number of explosions of each fireworks are calculated, thereby generating explosion sparks around each fireworks. The iteration is performed based on the fitness values ​​of each fireworks and explosion sparks until the iteration termination condition is met. Then, the current fireworks are output as the optimal joint angle, thus realizing the rapid extraction of joint angles.

[0030] In practice, the neighborhood range for predicting joint angles is as follows:

[0031] f i =i*4°

[0032] Among them, f i This represents the neighborhood range of the i-th predicted joint angle of the industrial robot.

[0033] The calculation of the fitness value for each firework involves first obtaining the end-effector pose of the industrial robot corresponding to the firework using forward kinematics analysis, and then calculating the fitness value of the firework, as detailed below:

[0034] f(θ * )=min(λ(|x * -x|+|y * -y|+|z * -z|)+(|α * -α|+|β * -β|+|γ * -y|))

[0035] Where, f(θ) * ) represents fireworks θ * The fitness value; λ represents the weight of the position coordinates; x * y * z * α * β * and γ * Representing fireworks θ * The corresponding X-axis coordinates, Y-axis coordinates, Z-axis coordinates, roll angle, pitch angle, and yaw angle of the industrial robot end effector are given. x, y, z, α, β, and γ represent the predicted joint angles of the industrial robot end effector corresponding to the X-axis coordinates, Y-axis coordinates, Z-axis coordinates, roll angle, pitch angle, and yaw angle, respectively.

[0036] The explosion radius and number of explosions for each firework are calculated based on the fitness value, as follows:

[0037]

[0038]

[0039] Among them, A k Let A be the explosion radius of the k-th firework. k S is a vector representing the different explosion radii at different joints; k Let K be the number of sparks generated by the explosion of the k-th firework. This represents the k-th firework. fitness value; Y min and Y max These represent the minimum and maximum fitness values ​​for each of the current fireworks. d represents the preset explosion vector, m represents the preset explosion constant, and ε represents the preset explosion parameter. ε is a minimum value to prevent the formula from being meaningless.

[0040] Based on the explosion radius and number of explosions of each firework, explosion sparks are randomly generated within the explosion radius of the firework. It is also necessary to perform boundary detection on the explosion sparks to ensure that the range of the explosion sparks is within the preset neighborhood.

[0041] The process iterates based on the fitness values ​​of each firework and explosion spark until an iteration termination condition is met, at which point the current firework is output as the optimal joint angle. Specifically, the fitness values ​​of each firework and each explosion spark it generates are calculated. The firework or explosion spark with the lowest fitness value is selected as the next generation firework. Then, a roulette wheel selection method is used to select the remaining N-1 firework. When the fitness value of the selected firework is less than a preset threshold, the iteration stops, and the currently selected firework is output as the optimal joint angle. When the fitness value of the selected firework is greater than or equal to the preset threshold, the same operation of predicting the joint angle is repeated for the next generation firework until the fitness value of the selected firework is less than the preset threshold or the iteration reaches the maximum preset number of iterations, thus satisfying the iteration termination condition. The loop is then exited, and the current firework is output as the optimal joint angle.

[0042] The beneficial effects of this invention are:

[0043] This invention combines the forward kinematics model of an industrial robot with the motion process of task planning, collects kinematic data of the industrial robot, and uses a memory-based GRU neural network model to perform inverse kinematics modeling and solution, obtaining preliminary robot inverse kinematics results. These results are more accurate than those obtained by traditional BP neural networks, RBF neural networks, and other algorithms, reducing abrupt changes in joint angles between adjacent poses during robot movement. Based on these results, and combined with the Fireworks algorithm, an accurate solution is quickly searched within the robot's workspace neighborhood to obtain precise inverse solutions for robot joint angles that adapt to the end effector posture of the industrial robot. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the connecting rod DH parameters;

[0045] Figure 2 This is a flowchart of the method of the present invention;

[0046] Figure 3 This is a schematic diagram of a GRU neural network. Detailed Implementation

[0047] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] like Figure 2As shown, the method for fast extraction of joint angles of a robotic arm based on GRU neural network and fireworks algorithm of the present invention includes:

[0049] 1) During the movement of the industrial robot, the end pose of the industrial robot is obtained by using the forward kinematics analysis method based on the movement trajectory of the industrial robot.

[0050] In step 1), the end effector pose of the industrial robot includes the end effector position and attitude angles. The end effector position includes the X-axis coordinate (x), Y-axis coordinate (y), and Z-axis coordinate (z) of the end effector. The attitude angles include the roll angle α, pitch angle β, and yaw angle γ of the end effector, as detailed below:

[0051]

[0052]

[0053]

[0054]

[0055] in, and These represent the transformation matrices of the end effector of the industrial robot relative to the base. The elements in the first row and first column, the first row and second column, the first row and third column, the first row and fourth column, the second row and third column, the second row and fourth column, the third row and third column, and the third row and fourth column.

[0056] A teach pendant is used to control an industrial robot to operate along a planned trajectory. During the robot's movement, the teach pendant collects and records its end-effector posture and corresponding joint angles. For example... Figure 1 As shown, the forward kinematics model of the industrial robot is established using the DH parameter method, and then the transformation matrix from the robot base to the robot end effector is obtained.

[0057] Transformation matrix of the end effector of an industrial robot relative to its base Specifically as follows:

[0058]

[0059]

[0060] in, and Let θ represent the transformation matrices between the base and the first robotic arm, the first robotic arm and the second robotic arm, the (i-1)th robotic arm and the ith robotic arm, and the (n-1)th robotic arm and the nth robotic arm, respectively, where n represents the total number of robotic arms / joints of the industrial robot; ia represents the actual angle of the i-th joint of the industrial robot; i-1 α represents the length of the line segment representing the common perpendicular between the two axes of the (i-1)th robotic arm; i-1 This represents the included angle between the axes of the two ends of the (i-1)th robotic arm.

[0061] Industrial robots are serial robots, with a basic structure consisting of a series of jointed links. The forward kinematics analysis of an industrial robot is essentially a decomposition of the positional relationships between these links. By establishing coordinate systems at the ends of the links, the positional relationships between them can be described by coordinate system transformations. The process of transforming the coordinate system from i-1 to coordinate system i can be decomposed into four sub-transformations: [the transformations occur around the x-axis]. i-1 Axis rotation angle α i-1 , along x i-1 Axis movement distance a i-1 Rotation angle θ around the z-axis i The distance d along the z-axis i For two adjacent links, use a i-1 α i-1 θ i and d i Describe their relationship. θ i Indicates two common perpendiculars a i-1 and a i The angle between them, d i Indicates two common perpendiculars a i-1 and a i The distance between them.

[0062] 2) The end-effector pose and actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model for training, resulting in a trained neural network model, such as... Figure 3 As shown.

[0063] In step 2), the end-effector pose and actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model for training. Specifically, during each iteration of training, the end-effector pose of the industrial robot at position t in the motion trajectory and the hidden state h of the GRU neural network model obtained during the iteration training at position t-1 are used. t-1 As input to the GRU (Gated Recurrent Unit) neural network model, the GRU neural network model outputs the predicted joint angles at the t-th position of the industrial robot and the hidden state h at that position. t At the initial position, the hidden state h0 is set to zero.

[0064] During each training iteration, the mean squared errors of the predicted joint angles of the industrial robot at the current position output by the gated recurrent unit (GRU) neural network model and the actual joint angles in step 1) are compared. The mean squared error loss function is used as the loss function MSE of the GRU neural network model, as follows:

[0065]

[0066] Where n represents the total number of robotic arms in the industrial robot; G(t) i ) represents the predicted joint angle of the industrial robot output by the GRU neural network model after processing the t-th end-effector position of the input, i.e., the robot inverse solution, θ. i This represents the angle of the i-th actual joint of the industrial robot.

[0067] When the loss function MSE reaches its minimum or the number of training iterations reaches its preset maximum, training stops, and a gated recurrent unit (GRU) neural network model is obtained after training.

[0068] 3) Input the end-effector pose of the industrial robot to be extracted into the trained model, and output the predicted joint angles of the extracted industrial robot.

[0069] 4) After applying the Fireworks Algorithm to the predicted joint angles of the industrial robot in step 3), the optimal joint angles of the industrial robot are obtained, thus realizing the rapid extraction of the joint angles of the robotic arm of the industrial robot.

[0070] In step 4), the predicted joint angles of the industrial robot in step 3) are used to obtain the optimal joint angles of the industrial robot. Specifically, N fireworks are generated in the neighborhood of each predicted joint angle. Each fireworks has n dimensions, where n represents the total number of joints of the industrial robot. Then, the fitness value of each fireworks is calculated. Based on the fitness value, the explosion radius and number of explosions of each fireworks are calculated, thereby generating explosion sparks around each fireworks. The iteration is performed based on the fitness values ​​of each fireworks and explosion sparks until the iteration termination condition is met. Then, the current fireworks are output as the optimal joint angle, thus realizing the rapid extraction of joint angles.

[0071] In practice, the neighborhood range for predicting joint angles is as follows:

[0072] f i =i*4°

[0073] Among them, f i This represents the neighborhood range of the i-th predicted joint angle of the industrial robot.

[0074] The fitness value for each firework is calculated by first obtaining the end-effector pose of the industrial robot corresponding to the firework using forward kinematics analysis, and then calculating the fitness value of the firework, as follows:

[0075] f(θ * )=min(λ(|x * -x|+|y * -y|+|z * -z|)+(|α * -α|+|β * -β|+|γ * -y|))

[0076] Where, f(θ) * ) represents fireworks θ * The fitness value; λ represents the weight of the position coordinates; x * y * z * α * β * and γ * Representing fireworks θ * The corresponding X-axis coordinates, Y-axis coordinates, Z-axis coordinates, roll angle, pitch angle, and yaw angle of the industrial robot end effector are given. x, y, z, α, β, and γ represent the predicted joint angles of the industrial robot end effector corresponding to the X-axis coordinates, Y-axis coordinates, Z-axis coordinates, roll angle, pitch angle, and yaw angle, respectively.

[0077] The explosion radius and number of explosions for each firework are calculated based on the fitness value, as follows:

[0078]

[0079]

[0080] Among them, A k Let A be the explosion radius of the k-th firework. k S is a vector representing the different explosion radii at different joints; k Let K be the number of sparks generated by the explosion of the k-th firework. This represents the k-th firework. fitness value; Y min and Y max These represent the minimum and maximum fitness values ​​for each of the current fireworks. d represents the preset explosion vector, m represents the preset explosion constant, and ε represents the preset explosion parameter. ε is a minimum value to prevent the formula from being meaningless.

[0081] Based on the explosion radius and number of explosions of each firework, explosion sparks are randomly generated within the explosion radius of the firework. It is also necessary to perform boundary detection on the explosion sparks to ensure that the range of the explosion sparks is within the preset neighborhood.

[0082] The iteration process is performed based on the fitness values ​​of each firework and its generated sparks until the iteration termination condition is met. The current firework is then output as the optimal joint angle. Specifically, the fitness values ​​of each firework and its generated sparks are calculated. The firework or spark with the lowest fitness value is selected for the next generation of firework. A roulette wheel selection method is then used to select the remaining N-1 firework. If the fitness value of the selected firework is less than a preset threshold, the iteration stops, and the currently selected firework is output as the optimal joint angle. If the fitness value of the selected firework is greater than or equal to the preset threshold, the same operation of predicting joint angles continues for the next generation of firework until the fitness value of the selected firework is less than the preset threshold or the iteration reaches the maximum preset number of iterations, thus meeting the iteration termination condition. The loop exits, and the current firework is output as the optimal joint angle.

[0083] Specific embodiments of the present invention are as follows:

[0084] This invention uses the FANUC P_250iA painting robot. This robot is an industrial 6-axis serial robot. First, the robot is modeled using DH parameters, such as... Figure 1 As shown in Table 1 below, the DH parameters of the robot are obtained:

[0085] Table 1

[0086]

[0087] The transformation matrix is ​​constructed based on the DH parameter list. The end position and attitude angle are derived from the transformation matrix. Simulation is performed in MATLAB to verify the correctness of the DH parameters and transformation matrix.

[0088] Obtain the existing human-taught program from the robot teach pendant, run the program, and control the robot to move according to the program. Collect and record the end effector pose and corresponding joint angles from the teach pendant. Select 10,000 points with approximately fixed end effector position intervals from the collected records. Use the end effector pose (x, y, z, α, β, γ) corresponding to the points as input and the corresponding joint angles (θ1, θ2, θ3, θ4, θ5, θ6) as output to train the GRU neural network model, obtaining the trained model. The GRU neural network model is as follows. Figure 3 As shown, the actual end-effector pose of the robot is input into the training model to obtain a preliminary inverse kinematic solution for the robot.

[0089] The initial inverse joint angles are used to release 20 fireworks using a fireworks algorithm. The neighborhood size of each fireworks ranges from the first to the sixth joint of the painting robot as [4°, 8°, 12°, 16°, 20°, 24°]. The fitness value of each fireworks is calculated, with λ set to 0.5. The explosion radius and number of explosions are calculated, with d set to [2°, 4°, 6°, 8°, 10°, 12°], N set to 20, and ε set to 0.001. Explosion sparks are randomly generated within the explosion radius of each fireworks based on the number of explosions. It is checked whether the range of each explosion spark is within its neighborhood size. The fireworks or explosion sparks with the lowest fitness are selected for the next generation of fireworks. The remaining fireworks are calculated using a roulette wheel method to obtain the remaining 19 fireworks. The position and number of fireworks are iteratively calculated. At each iteration, it is checked whether the number of iterations reaches 300 or the fitness function value is less than 0.1. If the above conditions are met, the loop is exited, and the current joint angle value is selected as the joint angle value relative to the current robot end effector posture.

Claims

1. A method for fast extraction of joint angles of a robotic arm based on GRU neural network and fireworks algorithm, characterized in that, include: 1) During the movement of the industrial robot, the end-effector pose is obtained by using forward kinematics analysis based on the robot's motion trajectory; 2) The end-effector pose and actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model to train the model and obtain the trained neural network model. 3) Input the end-effector pose of the industrial robot to be extracted into the trained model, and output the predicted joint angles of the extracted industrial robot. 4) After applying the fireworks algorithm to the predicted joint angles of the industrial robot in step 3), the optimal joint angles of the industrial robot are obtained, realizing the rapid extraction of the joint angles of the robotic arm of the industrial robot. In step 2), the end-effector pose and the actual joint angles of the industrial robot are used as the input and output of the gated recurrent unit (GRU) neural network model for training. Specifically, during each iteration of training, the end-effector pose of the industrial robot at the t-th position in the motion trajectory and the hidden state of the GRU neural network model obtained during the iteration training at the (t-1)-th position of the industrial robot are used. As input to the GRU (Gated Recurrent Unit) neural network model, the GRU neural network model outputs the predicted joint angles at the t-th position of the industrial robot and the hidden state at that position. In the initial position, the state is hidden. Set all values ​​to zero; In step 4), the predicted joint angles of the industrial robot in step 3) are used to obtain the optimal joint angles of the industrial robot by applying the fireworks algorithm. Specifically, N fireworks are generated in the neighborhood of each predicted joint angle. Each fireworks has n dimensions, where n represents the total number of joints of the industrial robot. Then, the fitness value of each fireworks is calculated. Based on the fitness value, the explosion radius and number of explosions of each fireworks are calculated, thereby generating explosion sparks around each fireworks. The iteration is performed based on the fitness values ​​of each fireworks and explosion sparks until the iteration termination condition is met. Then, the current fireworks are output as the optimal joint angle, thus realizing the rapid extraction of joint angles. The calculation of the fitness value for each firework involves first obtaining the end-effector pose of the industrial robot corresponding to the firework using forward kinematics analysis, and then calculating the fitness value of the firework, as detailed below: ； in, Fireworks fitness value; The weights representing the position coordinates; , , , , and They represent fireworks. The corresponding X-axis coordinates, Y-axis coordinates, Z-axis coordinates, roll angle, pitch angle, and yaw angle of the industrial robot end effector. , and These represent the X-axis coordinate, Y-axis coordinate, Z-axis coordinate, roll angle, pitch angle, and yaw angle of the industrial robot end effector, respectively, corresponding to the predicted joint angles of the industrial robot. The explosion radius and number of explosions for each firework are calculated based on the fitness value, as follows: ； ； in, Let be the explosion radius of the k-th firework; Let K be the number of sparks generated by the explosion of the k-th firework. This represents the k-th firework. fitness value; and These represent the minimum and maximum fitness values ​​for each of the current fireworks. =min , =max ; d represents the preset explosion vector, m represents the preset explosion constant, Indicates the preset explosion parameters; Based on the blast radius and number of explosions of each firework, explosive sparks are generated within the blast radius of the firework.

2. The method for rapid extraction of robotic arm joint angles based on GRU neural network and fireworks algorithm according to claim 1, characterized in that: In step 1), the end effector pose of the industrial robot includes the end effector position and attitude angle. The end effector position includes the X-axis coordinate (x), Y-axis coordinate (y), and Z-axis coordinate (z) of the end effector, and the attitude angle includes the roll angle of the end effector. Pitch angle and deflection angle The details are as follows: ， ， ； ； ； ； in, , , , , , , and These represent the transformation matrices of the end effector of the industrial robot relative to the base. The elements in the first row and first column, the first row and second column, the first row and third column, the first row and fourth column, the second row and third column, the second row and fourth column, the third row and third column, and the third row and fourth column.

3. The method for rapid extraction of robotic arm joint angles based on GRU neural network and fireworks algorithm according to claim 2, characterized in that: The transformation matrix of the end effector of the industrial robot relative to the base Specifically as follows: ； ； in, , , and Let n represent the transformation matrices between the base and the first robotic arm, the first robotic arm and the second robotic arm, the (i-1)th robotic arm and the ith robotic arm, and the (n-1)th robotic arm and the nth robotic arm, respectively, where n represents the total number of robotic arms in the industrial robot. This represents the actual angle of the i-th joint of the industrial robot; The length of the line segment representing the common perpendicular between the two axes of the (i-1)th robotic arm; This represents the included angle between the axes of the two ends of the (i-1)th robotic arm.

4. The method for fast extraction of robotic arm joint angles based on GRU neural network and fireworks algorithm according to claim 1, characterized in that: During each training iteration, the mean squared errors of the predicted joint angles of the industrial robot at the current position output by the gated recurrent unit (GRU) neural network model and the actual joint angles in step 1) are compared. The mean squared error loss function is then used as the loss function of the GRU neural network model. The details are as follows: ； Where n represents the total number of robotic arms of the industrial robot; This represents the predicted joint angle of the industrial robot output by the GRU (Gated Recurrent Unit) neural network model after processing the t-th end-effector position of the input. This represents the actual angle of the i-th joint of the industrial robot; When the loss function When the value reaches the minimum or the number of training iterations reaches the preset maximum, training stops, and the trained GRU neural network model is obtained.

5. The method for fast extraction of robotic arm joint angles based on GRU neural network and fireworks algorithm according to claim 1, characterized in that: The process iterates based on the fitness values ​​of each firework and explosion spark until an iteration termination condition is met, at which point the current firework is output as the optimal joint angle. Specifically, the fitness values ​​of each firework and each explosion spark it generates are calculated. The firework or explosion spark with the lowest fitness value is selected as the next generation firework. Then, a roulette wheel selection method is used to select the remaining N-1 firework. When the fitness value of the selected firework is less than a preset threshold, the iteration stops, and the currently selected firework is output as the optimal joint angle. When the fitness value of the selected firework is greater than or equal to the preset threshold, the same operation of predicting the joint angle is repeated for the next generation firework until the fitness value of the selected firework is less than the preset threshold or the iteration reaches the maximum preset number of iterations, thus satisfying the iteration termination condition. The loop is then exited, and the current firework is output as the optimal joint angle.

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