Five-degree-of-freedom mechanical arm inverse motion method and system based on improved melolontha optimization algorithm
By improving the dung beetle optimization algorithm and combining it with the genetic algorithm to optimize the neural network model, the singularity and convergence problems in the inverse kinematics solution of the robotic arm were solved, achieving high-precision and high-efficiency inverse kinematics solution, which is suitable for five-degree-of-freedom robotic arms in warehousing and logistics scenarios.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2026-05-07
- Publication Date
- 2026-07-21
Smart Images
Figure CN122425690A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mechanical automation technology, specifically relating to a method and system for the inverse motion of a five-degree-of-freedom robotic arm based on an improved dung beetle optimization algorithm. Background Technology
[0002] With the continuous improvement of industrial automation, robotic arms have been widely used in warehousing systems for tasks such as material handling, sorting, and loading / unloading. Solving inverse kinematics is crucial for achieving precise robotic arm operation; its goal is to calculate the corresponding joint degrees based on a given end effector pose. The accuracy and computational efficiency of inverse kinematics solutions directly affect the operational performance of the entire warehousing system. However, due to the complexity of the warehousing environment and the highly nonlinear nature of the robotic arm kinematic model, traditional geometric, iterative, or algebraic methods often face problems such as singularity, poor convergence, and sensitivity to initial conditions in practical applications.
[0003] In recent years, the application of intelligent algorithms in inverse kinematics solving has received widespread attention. Neural networks, with their nonlinear mapping capabilities, can map the end-effector pose to joint angles without explicit modeling, exhibiting good learning and generalization abilities, and have been applied to kinematic modeling of robotic arms. Takatani et al. established three neural network models, corresponding to forward kinematics, inverse kinematics solving, and evaluation functions, respectively, enabling computation independent of the evaluation function structure and calculating the inverse kinematics solution without consideration. Zhang et al. proposed a dual neural network (DNN) scheme based on compatible convex-nonconvex constrained quadratic programming (CCNC-QP) for solving the inverse kinematics of robotic arms, and proved that this method not only possesses the advantages of DNN such as parallel processing and real-time control, but also the advantages of CCNC-QP such as initial error zeroing and consideration of convex and nonconvex constraints. Gao et al. proposed an improved model based on backpropagation neural networks to solve the inverse kinematics problem of a 6-DOF robotic arm, and further achieved a reduction in position error.
[0004] Due to the complexity of warehousing environments and the highly nonlinear nature of robotic arm kinematics models, traditional geometric, iterative, or algebraic methods often face problems such as singularity, poor convergence, and sensitivity to initial conditions in practical applications. In real-world operating environments, relying solely on neural networks can easily lead to high positioning errors, especially after frequent task switching or long-term operation, which can cause error accumulation and affect system stability. Summary of the Invention
[0005] The purpose of this invention is to overcome the shortcomings of the prior art. In a first aspect, this invention provides a five-degree-of-freedom robotic arm inverse motion method based on an improved dung beetle optimization algorithm, comprising: Acquire the pose data of the robotic arm's end effector; The end-effector pose data is input into a trained genetic algorithm-optimized neural network model to obtain predicted joint angle values. An initial population is generated centered on the predicted joint angle, while a local search boundary is established that shrinks with iteration. Within the feasible region defined by the local search boundary, the fitness value of each individual in the initial population is calculated, and the current optimal individual is determined; Using the optimal individual as the guiding point, the population individuals are iteratively updated according to the improved whale optimization strategy. After each round of updates, the candidate solutions are sequentially processed by local search boundary trimming and joint limit projection feasibility processing until the iteration termination condition is met. The optimal joint angle is output as the inverse kinematic solution and used for trajectory point sequence solution and robotic arm trajectory tracking execution.
[0006] Furthermore, the predicted joint angle is ,by Generate the initial population around the center ,in Simultaneously, establish a local search boundary that shrinks with iteration. .
[0007] Furthermore, the formula for calculating the fitness of each individual is as follows: Determine the current optimal individual .
[0008] Furthermore, the specific steps for improving and optimizing the whale population are as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Scheduling ,structure , Update # When an individual is formed, the first step is to generate... :like Then perform a spiral refinement update; otherwise, when Perform a random search update, or a bounding update; to obtain candidate solutions. Then, perform shrinkage boundary trimming sequentially. Projection with joint limit and order .
[0009] Furthermore, to ensure that the iterative solution process balances global search capability with fine-tuning capability in later stages, a dynamic factor is introduced into the whale optimization iteration process. It is used as a convergence control parameter for scheduling whale optimization algorithms. Where t represents the current iteration number and T represents the maximum iteration number. This is the initial dynamic factor; The dynamic factor is set in an iteratively decreasing form:
[0010] And let the convergence control parameter decrease with each iteration:
[0011] With the above settings, in the initial iteration... Larger update steps and search range enhance global exploration and reduce sensitivity to initial values; in later iterations... By gradually reducing the search step size, the local refinement capability is improved and the stability of the final solution is enhanced.
[0012] 6. The five-DOF robotic arm inverse motion method based on the improved dung beetle optimization algorithm as described in claim 1, characterized in that it includes: to ensure that the candidate solution satisfies both the local search boundary centered on the neural network prediction value and shrinks with iteration, and the physical limits of the robotic arm joints, for... Perform two-stage feasibility testing to obtain the next round of individuals. ; Shrink boundary clipping, let the first... The contraction boundary of each joint dimension is Dimensionally pruning of candidate solutions:
[0013] Joint limiting projection, let the first The physical limits of each joint are Dimensionally project the clipped candidate solutions:
[0014] After completing the two-stage processing, let: ; The above processing ensures that each updated candidate solution is an executable joint corner solution, avoiding invalid searches due to out-of-bounds errors and improving convergence stability near the constraint boundary.
[0015] Furthermore, this includes: employing an adaptive allocation strategy for updating the operator trigger probability, so that the trigger probability of the spiral refinement operator increases with the number of iterations; let the spiral refinement trigger probability be... Its expression is: ; In the update When dealing with an individual, first generate random numbers. ):when Perform spiral refinement update when appropriate; otherwise, according to... Determine if it is in the exploration or development phase: If If a random search update is performed, a bounding update is performed; otherwise, a bounding update is performed. This scheduling mechanism enables global exploration to be the main focus in the early stages of iteration and local refinement to be the main focus in the later stages of iteration, thereby improving the accuracy and stability of the terminal solution.
[0016] Secondly, this invention provides a five-degree-of-freedom robotic arm inverse motion system based on an improved dung beetle optimization algorithm, comprising: The data acquisition module is used to acquire the pose data of the robotic arm's end effector. The joint angle prediction module inputs the end-effector pose data into a trained genetic algorithm-optimized neural network model to obtain predicted joint angle values. The population generation module generates an initial population centered on the predicted joint angle value, while simultaneously establishing a local search boundary that shrinks with iteration. The optimal individual determination module calculates the fitness of each individual based on the initial population and the local search boundary, and determines the current optimal individual; The optimal joint angle output module updates the population based on the optimal individual and the improved whale optimization. After iterating to the termination condition, it outputs the optimal joint angle as the inverse kinematics solution, which is used for trajectory point sequence solving and robotic arm trajectory tracking.
[0017] The beneficial effects of this invention include: 1. This invention addresses the inverse kinematics solution of a five-DOF robotic arm in a warehousing and logistics scenario. It proposes a method and system for the inverse kinematics of a five-DOF robotic arm based on an improved dung beetle optimization algorithm. First, a genetic algorithm is used to optimize the neural network structure, improving prediction accuracy and providing high-quality initial values for the subsequent improved DBO algorithm. Then, a hybrid model further optimizes the inverse kinematics solution by combining the efficient prediction of the neural network with the refined iteration of the improved DBO algorithm, achieving a balance between accuracy and computational efficiency.
[0018] 2. The hybrid model proposed in this invention outperforms individual neural networks and DBO algorithms in both positioning accuracy and inference efficiency. The total inference time is reduced by 20.7%, the average Euclidean distance is reduced by 16.4%, and the trajectory fitting error is less than 5mm, meeting the accuracy and stability requirements of warehouse handling. Comparative experiments also demonstrate the model's superiority. In summary, this method provides an efficient, accurate, and engineering-practical solution to the inverse kinematics problem of warehouse robotic arms. Attached Figure Description
[0019] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0020] Figure 1 This is a flowchart illustrating the inverse motion method of a five-degree-of-freedom robotic arm based on an improved dung beetle optimization algorithm in an embodiment of the present invention. Detailed Implementation
[0021] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.
[0022] like Figure 1 As shown, this invention discloses a five-degree-of-freedom robotic arm inverse motion method based on an improved dung beetle optimization algorithm, including: This paper takes a five-degree-of-freedom loading and unloading robot arm in the warehousing operation scenario as the research object, and proposes a neural network-assisted improved dung beetle optimization (DBO) algorithm
[52] to solve the problem of high precision and high efficiency in inverse kinematics. First, a neural network model based on genetic algorithm optimization is constructed to efficiently fit the nonlinear mapping relationship between the end pose of the robot arm and the joint angle, which realizes the improvement of the traditional manual parameter selection neural network and improves the model adaptability. Second, in view of the problems of limited accuracy of neural network and swarm intelligence algorithm, initial value dependence, easy to get trapped in local optimum and insufficient efficiency, a neural network-assisted evolutionary solution framework is proposed: DBO algorithm is introduced and its behavior mechanism and key parameters are designed and experimentally optimized in a targeted manner, and the neural network prediction results are used to provide high-quality initial values for DBO algorithm, so as to realize the effective integration of the fast prediction ability of neural network and the optimization ability of DBO algorithm. Finally, the superiority of the algorithm in this paper is proved by simulation experiment, the motion stability in trajectory planning is verified, and the feasibility and reliability of the algorithm in real work are verified.
[0023] This invention focuses on a five-DOF loading and unloading robotic arm in a warehousing operation scenario. Addressing the challenge of balancing accuracy and efficiency in inverse kinematics solving, it proposes a neural network-assisted swarm intelligence iterative solution. First, a neural network model optimized using a genetic algorithm is constructed to fit the nonlinear mapping between the robotic arm's end-effector pose and joint angles, outputting predicted joint angle values and improving the model's adaptability.
[0024] To obtain joint angle prediction values This embodiment constructs and trains a neural network model optimized by a genetic algorithm. The neural network is used to establish a nonlinear mapping relationship between the end-effector pose and joint angles, and its input is the target end-effector pose. (Position and attitude parameters), the output is the corresponding joint angle vector. .
[0025] Training data construction involves sampling joint angles within the robotic arm's workspace. (Saving joint constraint), the end-effector pose is obtained through forward kinematics calculation. Thus forming training sample pairs The training samples, after normalization, are divided into a training set and a validation set for network training and generalization evaluation.
[0026] Network structure and output definition: The neural network is a feedforward neural network or an equivalent multilayer perceptron structure. The number of nodes in its input layer corresponds to the end-effector pose dimension, and the number of nodes in its output layer corresponds to the robot arm's degrees of freedom. Network output. As the predicted joint angle value, it is denoted as .
[0027] To improve prediction accuracy and fitness, this embodiment employs a genetic algorithm to search and optimize key hyperparameters of the neural network. These hyperparameters include at least one or more of the following: number of hidden layers, number of neurons in each hidden layer, activation function type, learning rate, and number of training epochs. The genetic algorithm individual encoding represents a set of candidate hyperparameter configurations; the prediction error on the validation set is used as the fitness function, and fitness can be defined as:
[0028] in To verify the sample size, To predict joint angles for the network, The actual joint angles are used. The optimal or near-optimal network hyperparameter configuration is obtained through iterative updates via selection, crossover, and mutation.
[0029] Model training and output: Under the optimal hyperparameter configuration determined by the genetic algorithm, the neural network is trained using the training set and evaluated on the validation set. After training, the target end pose is input. This will output the predicted joint angle values. This serves as the initial basis for the subsequent "generating an initial population centered on prediction and establishing a search boundary that shrinks with iteration".
[0030] Secondly, addressing the issues of initial value sensitivity, susceptibility to local optima, and convergence instability under joint constraint constraints in swarm intelligence algorithms, an improved whale optimization solution strategy guided by a neural network is proposed. This strategy involves generating an initial population centered on the joint angles predicted by the neural network and constructing a search boundary that shrinks with each iteration. A dynamic factor λ(t) is introduced to weight the convergence factor and update step size, enabling adaptive switching between early global exploration and later local refinement. An adaptive allocation strategy based on the trigger probability of the update operator is employed to increase the proportion of spiral refinement operators, thereby improving end-effector positioning accuracy. Furthermore, after each update, constraint projection feasibility processing is performed on the joint angles to ensure that candidate solutions satisfy joint constraint constraints. Finally, simulations and trajectory tracking verify that the proposed method can improve the accuracy and stability of inverse kinematics solutions while maintaining motion stability.
[0031] Candidate joint angles:
[0032] Objective function (L2 norm of position + Euler angle error):
[0033] in The final pose (position + Euler angles) is obtained from positive kinematics. The target pose.
[0034] Joint limit projection:
[0035] (I) Neural Network Prediction and Initial Population Construction, assuming the neural network output Population size , No. Individual: And construct the "search boundary that shrinks with iteration": , , Improved WOA updates, dynamic factors To ensure that the iterative solution process balances global search capability and fine-tuning capability in later stages, this invention introduces a dynamic factor into the whale optimization iteration process. It is used as a convergence control parameter for scheduling whale optimization algorithms. Where t represents the current iteration number, and T represents the maximum iteration number. This is the initial dynamic factor.
[0036] The dynamic factor is set in an iteratively decreasing form:
[0037] And let the convergence control parameter decrease with each iteration:
[0038] With the above settings, in the initial iteration... Larger update steps and search range enhance global exploration and reduce sensitivity to initial values; in later iterations... By gradually decreasing the search step size, the local refinement capability is improved and the stability of the final solution is enhanced. To generate the random coefficients required for the update, this embodiment... Constructing vector coefficients in round iterations and ,in A uniform random vector of the same dimension as the joint angle vector (each component independently follows...) (By convergence control parameters) get: , ,in Used to randomly scale the position of the guided individual. Used to control the update pace and for judgment in subsequent exploration and development phases.
[0039] The definition and constraint feasibility processing of three types of update operators, in the first... In the round of iteration, let the individual with the best fitness in the population be... , No. Individuals Individuals randomly selected from the population are This invention generates candidate solutions based on three mechanisms: bounding update, random search, and spiral refinement. After the update, a two-level constraint feasibility process is performed to ensure that the candidate solution satisfies the constraints and improves convergence stability.
[0040] (a) Encirclement update, when the algorithm is in the development stage, with Update the bounding space around the center. First, calculate the distance vector:
[0041] Regenerate candidate solutions:
[0042] (b) Random search: When the algorithm is in the exploration phase, random selection is performed from the population to enhance its ability to escape local optima. As a search reference, first calculate the distance vector:
[0043] Regenerate candidate solutions:
[0044] (c) Spiral Refinement: To improve end-point positioning accuracy, this invention introduces spiral refinement updates, enabling individuals to perform a refined search around the current optimal solution. Let... , Let be the helical constant, and let:
[0045] The candidate solution is generated as follows:
[0046] (d) Two-level constraint feasibility processing: To ensure that the candidate solution satisfies both the local search boundary centered on the neural network prediction value and shrinks with iteration, and the physical constraints of the robotic arm joints, this invention... Perform two-stage feasibility testing to obtain the next round of individuals. .
[0047] Shrink boundary clipping, let the first... The contraction boundary of each joint dimension is Dimensionally pruning of candidate solutions:
[0048] Joint limiting projection, let the first The physical limits of each joint are Dimensionally project the clipped candidate solutions:
[0049] After completing the two-stage processing, let: .
[0050] The above processing ensures that each updated candidate solution is an executable joint corner solution, avoiding invalid searches due to out-of-bounds errors and improving convergence stability near the constraint boundary.
[0051] To achieve an update behavior that prioritizes early-stage exploration over later-stage refinement, this invention employs an adaptive allocation strategy for the trigger probability of update operators, increasing the trigger probability of the spiral refinement operator with each iteration. Let the spiral refinement trigger probability be... Its expression is: .
[0052] In the update When dealing with an individual, first generate random numbers. ):when Perform spiral refinement update when appropriate; otherwise, according to... Determine if it is in the exploration or development phase: If If a random search update is performed, then a bounding update is performed; otherwise, a bounding update is performed. This scheduling mechanism prioritizes global exploration in the early stages of iteration and local refinement in the later stages, thereby improving the accuracy and stability of the final solution.
[0053] Summary of steps: S1: Input target end-effector pose The predicted joint angles are obtained using a trained GA-optimized neural network. .
[0054] S2: with Generate the initial population around the center
[0055] ,in Simultaneously, establish a local search boundary that shrinks with iteration. .
[0056] S3: Calculate the fitness of each individual. Determine the current optimal individual .
[0057] S4: Update the population by improving whale optimization: by
[0058] Scheduling ,structure , Update # When an individual is formed, the first step is to generate... :like Then perform a spiral refinement update; otherwise, when Perform a random search update, or a bounding update; to obtain candidate solutions. Then, perform shrinkage boundary trimming sequentially. Projection with joint limit and order .
[0059] S5: Output the optimal joint angle after iterating to the termination condition. It serves as the inverse kinematics solution and is used for solving the trajectory point sequence and executing the robot arm trajectory tracking.
[0060] To solve the inverse kinematics of a five-DOF robotic arm in a warehousing and logistics scenario, a hybrid model based on neural networks and an improved DBO algorithm is proposed. First, a genetic algorithm is used to optimize the neural network structure, improving prediction accuracy and providing high-quality initial values for the subsequent improved DBO algorithm. Then, the hybrid model further optimizes the inverse kinematics solution by combining the efficient prediction of the neural network with the fine iteration of the improved DBO algorithm, achieving a balance between accuracy and computational efficiency. Experimental results show that the proposed hybrid model outperforms either the neural network or the DBO algorithm alone in terms of positioning accuracy and inference efficiency. The total inference time is reduced by 20.7%, the average Euclidean distance is reduced by 16.4%, and the trajectory fitting error is less than 5 mm, meeting the accuracy and stability requirements of warehousing and handling. Comparative experiments also demonstrate the superiority of the model. In summary, this method provides an efficient, accurate, and engineering-practical solution for the inverse kinematics problem of warehousing robotic arms.
[0061] Example 2 This embodiment provides a five-degree-of-freedom robotic arm inverse motion system based on an improved dung beetle optimization algorithm, including: The data acquisition module is used to acquire the pose data of the robotic arm's end effector. The joint angle prediction module inputs the end-effector pose data into a trained genetic algorithm-optimized neural network model to obtain predicted joint angle values. The population generation module generates an initial population centered on the predicted joint angle value, while simultaneously establishing a local search boundary that shrinks with iteration. The optimal individual determination module calculates the fitness of each individual based on the initial population and the local search boundary, and determines the current optimal individual; The optimal joint angle output module updates the population based on the optimal individual and the improved whale optimization. After iterating to the termination condition, it outputs the optimal joint angle as the inverse kinematics solution, which is used for trajectory point sequence solving and robotic arm trajectory tracking.
[0062] The data acquisition module, joint angle prediction module, population generation module, optimal individual determination module, and optimal joint angle output module have a one-to-one correspondence with the five-degree-of-freedom robotic arm inverse motion method based on the improved dung beetle optimization algorithm in this embodiment 1. The specific scheme will not be described in detail.
[0063] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.
Claims
1. A method for inverse motion of a five-DOF robotic arm based on an improved dung beetle optimization algorithm, characterized in that, include: Acquire the pose data of the robotic arm's end effector; The end-effector pose data is input into a trained genetic algorithm-optimized neural network model to obtain predicted joint angle values. An initial population is generated centered on the predicted joint angle, while a local search boundary is established that shrinks with iteration. Within the feasible region defined by the local search boundary, the fitness value of each individual in the initial population is calculated, and the current optimal individual is determined; Using the optimal individual as the guiding point, the population individuals are iteratively updated according to the improved whale optimization strategy. After each round of updates, the candidate solutions are sequentially processed by local search boundary trimming and joint limit projection feasibility processing until the iteration termination condition is met. The optimal joint angle is output as the inverse kinematic solution and used for trajectory point sequence solution and robotic arm trajectory tracking execution.
2. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, Predicted joint angle is ,by Generate the initial population around the center ,in Simultaneously, establish a local search boundary that shrinks with iteration. .
3. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, The formula for calculating the fitness of each individual is: Determine the current optimal individual .
4. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, The specific steps for improving and optimizing the whale population are as follows: Scheduling ,structure , Update # When an individual is formed, the first step is to generate... :like Then perform a spiral refinement update; otherwise, when Perform a random search update, or a bounding update; to obtain candidate solutions. Then, perform shrinkage boundary trimming sequentially. Projection with joint limit and order .
5. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, include: To ensure that the iterative solution process balances global search capability with fine-tuning capability in later stages, a dynamic factor is introduced into the whale optimization iteration process. It is used as a convergence control parameter for scheduling whale optimization algorithms. Where t represents the current iteration number and T represents the maximum iteration number. This is the initial dynamic factor; The dynamic factor is set in an iteratively decreasing form: And let the convergence control parameter decrease with each iteration: With the above settings, in the initial iteration... Larger update steps and search range enhance global exploration and reduce sensitivity to initial values; in later iterations... By gradually reducing the search step size, the local refinement capability is improved and the stability of the final solution is enhanced.
6. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, include: To ensure that the candidate solutions satisfy both the local search boundary centered on the neural network prediction value and shrinking with iteration, and the physical constraints of the robotic arm joints, the following measures are taken: Perform two-stage feasibility testing to obtain the next round of individuals. ; Shrink boundary clipping, let the first... The contraction boundary of each joint dimension is Dimensionally pruning of candidate solutions: Joint limiting projection, let the first The physical limits of each joint are Dimensionally project the clipped candidate solutions: After completing the two-stage processing, let: ; The above processing ensures that each updated candidate solution is an executable joint corner solution, avoiding invalid searches due to out-of-bounds errors and improving convergence stability near the constraint boundary.
7. The inverse motion method for a five-DOF robotic arm based on an improved dung beetle optimization algorithm as described in claim 1, characterized in that, include: An adaptive allocation strategy for updating operator trigger probabilities is adopted, so that the trigger probability of the spiral refinement operator increases with the number of iterations; let the spiral refinement trigger probability be... Its expression is: ； In the update When dealing with an individual, first generate random numbers. ):when Perform spiral refinement update when appropriate; otherwise, according to... Determine if it is in the exploration or development phase: If If a random search update is performed, a bounding update is performed; otherwise, a bounding update is performed. This scheduling mechanism enables global exploration to be the main focus in the early stages of iteration and local refinement to be the main focus in the later stages of iteration, thereby improving the accuracy and stability of the terminal solution.
8. A five-DOF robotic arm inverse motion system based on an improved dung beetle optimization algorithm, characterized in that, include: The data acquisition module is used to acquire the pose data of the robotic arm's end effector. The joint angle prediction module inputs the end-effector pose data into a trained genetic algorithm-optimized neural network model to obtain predicted joint angle values. The population generation module generates an initial population centered on the predicted joint angle value, while simultaneously establishing a local search boundary that shrinks with iteration. The optimal individual determination module calculates the fitness of each individual based on the initial population and the local search boundary, and determines the current optimal individual; The optimal joint angle output module updates the population based on the optimal individual and the improved whale optimization. After iterating to the termination condition, it outputs the optimal joint angle as the inverse kinematics solution, which is used for trajectory point sequence solving and robotic arm trajectory tracking.