US-12623342-B1 - Robot inverse kinematics solution prediction method based on POA-transformer-BiGRU-attention integrated optimization algorithm

Abstract

A robot inverse kinematics solution prediction method based on a POA-Transformer-BiGRU-Attention integrated optimization algorithm is disclosed. The method includes: initializing of a POA, positions evaluation and updating, training a Transformer to generate output features, processing a BiGRU and applying an Attention Mechanism, and global optimization. The evaluating and updating positions include: Evaluating P i using a fitness function, updating the individual positions, and acquiring renewed positions P i new . The BiGRU and Attention Mechanism includes: Feeding the output features into a BiGRU to obtain final hidden states, and then applying an attention mechanism to compute the weighted summation of these states. Subsequently, generating predicted inverse kinematics solution based on the weighted summation results and evaluating the accuracy of the predictions using an objective function, and determining a global optimal solution. The proposed algorithm demonstrated strong robustness and superior prediction accuracy under various working conditions and noise disturbances.

Inventors

• Guanglei LI
• Shuguang Li
• Jianbing Hu
• Jinglei Zhang
• CHAO SHEN

Assignees

• ZHEJIANG UNIVERSITY OF SCIENCE AND TECHNOLOGY

Dates

Publication Date

20260512

Application Date

20250516

Priority Date

20250224

Claims (6)

1. 1 . A robot inverse kinematics solution prediction method based on a POA-Transformer-BiGRU-Attention integrated optimization algorithm, wherein the method comprises: initializing a POA by randomly generating individual robot positions P i ; wherein the generating individual robot positions P i comprises: setting a number of the robot as N and a maximum iteration counts as T max ; initializing individual robot positions as: P i ={x i1 ,x i2 , . . . x id ,}(i=1,2, . . . , N), where x id represents a value of a i-th data point in a d-th feature dimension; evaluating and updating the individual robot positions P i using a fitness function to obtain updated positions P i new ; defining an input data X i = P i new , then training the X i through a Transformer model to generate output features Z′; processing the output features Z′ using a BiGRU to obtain final hidden states, and applying an attention mechanism to compute weighted summation results z; and generating predicted inverse kinematics solutions based on the weighted summation results z, evaluating an accuracy of the inverse kinematics solutions using an objective function, and determining a global optimal solution; wherein the evaluating an accuracy of the inverse kinematics solutions using an objective function comprises: calculating the objective function f(θ) as: f (θ)=ω 1 ·E position (θ)+ω 2 ·E orientation (θ)+ω 3 ·C (θ)+ω 4 ·E prediction (θ); where θ is a joint angle vector, ∫ 1 , ω 2 , ω 3 , ω 4 are weighting coefficients, E position is an position error; E orientation is an orientation error; E prediction is a prediction error, C(θ) is a joint limit constraint; wherein the position error is calculated as: E position (θ)=∥P desired −P actual (θ)∥ 2 ; where P desired is a desired end-effector position vector; P actual (θ) is an actual end-effector position vector; wherein the orientation error is calculated as: E orientation (θ)=∥R desired −R actual (θ)∥ F ; where R desired is a desired end-effector rotation matrix; R actual (θ) is an actual end-effector rotation matrix; wherein the joint limit constraint is calculated as: C ⁡ ( θ ) = ∑ i = 1 6 [ penalty · max ( 0 , θ i - θ i , m ⁢ a ⁢ x ) 2 + max ⁡ ( 0 , θ i , mi ⁢ n - θ i ) 2 ] ; where penalty is constraint coefficient, θ i is a i-th allowable rotation angle; θ i,max is a maximum allowable rotation angle for a i-th parameter; θ i,min is a minimum allowable rotation angle for a i-th parameter, wherein if θ i exceeds a defined robotic arm range θ i,limit , a penalty term is applied to enforce convergence to valid search space; minimizing a value of the objective function f(θ) via iterative parameter adjustment and POA optimization to ensure the accuracy of the inverse kinematics solutions and obtain the global optimum solution.
2. 2 . The method according to claim 1 , wherein the evaluating and updating the individual robot positions P i using a fitness function to obtain updated positions P i new comprises: evaluating the P i using the fitness function f(P i )=evaluate(P i ); updating the P i with a formula P i new = P i + r · ( P best - P i ) + ε , where P best denotes a current best position, r is a random number, and ε is a perturbation term to enhance search diversity.
3. 3 . The method according to claim 2 , wherein the defining an input data X i = P i new , then training the X i through a Transformer model to generate output features Z′ comprises: the Transformer model, processing an input sequence X=[x 1 ,x 2 , . . . , x i ] using a self-attention mechanism: Q=XW Q ; K=XW K ; V=XW V ; where Q is a query matrice, K is a key matrice, and V is a value matrice, and W Q is a query weight matrice, W K is a key weight matrice, W V is a value weight matrice, and x i represents an i-th element in the input sequence; computing an attention weight matrix via scaled dot-product: A = softmax ( QK T d k ) ; where A is the attention weight matrix and d k is a dimension of K; generating an output matrix Z=AV, and applying a ReLU activation to obtain the output features Z′=RELU(Z).
4. 4 . The method according to claim 3 , wherein the processing the output features Z′ using a BiGRU to obtain final hidden states comprises: the BiGRU, taking the Z′ as an input, wherein the BiGRU comprises two GRU layers, one is used for processing a forward sequence and the other is used for processing on is a backward sequence; for each time step t, updating a forward hidden state ĥ t and a backward hidden stateh t ; ĥ t =tan h ( W h ·x t +U h ·( r t ⊙h t−1 )), h t =(1− t )⊙ h t−1 +z t ⊙ĥ t ; z t =σ( W z ·x t +U z ·h t−1 ); r t =σ( W r ·x t +U r ·h t−1 ); where: x t is an output of Z′ at the timestep t; W h represents a weight matrix associated with candidate hidden states; W z represents a weight matrix associated with an update gate; W r represents a weight matrix associated with a reset gate; U h , U z , U r are weight matrices; r t is the reset gate; h t−1 represents the hidden state at the timestep t−1; z t is the update gate; σ represents a sigmoid function.
5. 5 . The method according to claim 4 , wherein the BiGRU processes sequences in two directions to respectively obtain a forward hidden state and a backward hidden state: h t forward = GRU forward ( x t ) ; h t backward = GRU backward ( x t ) ; where h t forward represents the forward hidden state and h t backward represents the backward hidden state; a final hidden state ĥ t is obtained based on the forward hidden state and the backward hidden state: h t ′ = [ h t forward ; h t backward ] .
6. 6 . The method according to claim 5 , wherein the applying an attention mechanism to compute weighted summation results z comprises: calculating energy scores: e t =score(ĥ t ,h context ); normalizing attention weights: α t = exp ⁡ ( e t ) ∑ j = 1 T ⁢ exp ⁡ ( e j ) ; computing the weighted summation results based on the α t and h t ⁢ z = ∑ t = 1 T ⁢ α t · h t ; where e t represents an energy value at a timestep t; h context represents a context vector; α t represents an attention weight at a timestep t; e j represents an energy value at a timestep j; T represents a total number of timesteps in a sequence.

Description

CROSS-REFERENCE TO RELATED APPLICATION This application claims the benefit and priority of Chinese Patent Application No. 202510200274.3, filed Feb. 24, 2025, the disclosures of which are incorporated by reference herein in their entirety. TECHNICAL FIELD The present invention relates to a field of robotics technology, particularly to a robot inverse kinematics solution prediction method based on the POA-Transformer-BiGRU-Attention integrated optimization algorithm, specifically designed to enhance motion control precision and robustness for multi-degree-of-freedom robots under complex working conditions. BACKGROUND TECHNOLOGY Multi-degree-of-freedom (DOF) robots are widely used in industrial manufacturing, medical applications, service robotics, and other fields, executing precision tasks such as welding, assembly, and surgery. However, the core challenge in motion control for multi-DOF robots lies in solving the inverse kinematics problem—determining the joint angles required to achieve a target end-effector position and orientation. Due to the complex geometric structures and multi-solution nature of multi-DOF robots, inverse kinematics exhibits highly nonlinear characteristics. Traditional analytical and numerical methods, while effective in simple applications, struggle to deliver precise, stable, and real-time solutions in complex scenarios and high-DOF systems. The complexity of inverse kinematics for multi-DOF robots stems from its strong nonlinearity and multiple-solution nature. The relationship between the end-effector position and joint angles often lacks a closed-form analytical expression, making the problem notoriously difficult to solve. Furthermore, robotic systems frequently yield multiple potential solutions, some of which may violate physical constraints or exceed joint motion limits. Conventional methods rely on intricate mathematical derivations or iterative algorithms, often trapping solutions in local optima and failing to guarantee global optimality. These limitations are exacerbated in high-dimensional nonlinear systems, where convergence speed and computational efficiency degrade significantly. Traditional inverse kinematics methods can be categorized into analytical methods and iterative methods. Analytical methods depend on mathematical models of robotic structures to derive closed-form solutions, but they are restricted to specific robot architectures and poorly suited for non-standard or complex systems. Iterative methods (e.g., the Newton-Raphson method) are more generalizable but require careful initialization to avoid local optima and suffer from slow convergence in high-dimensional nonlinear spaces, along with insufficient real-time performance for dynamic task execution. Furthermore, due to the non-unique nature of inverse kinematics solutions, conventional methods cannot optimize overall energy consumption during robotic arm trajectory planning nor prevent redundant motions and frequent start-stop cycles. These technical shortcomings collectively degrade system efficiency while accelerating hardware wear. Recent efforts integrating machine learning and deep learning approximate high-dimensional nonlinear mappings using large datasets. However, these approaches heavily depend on data distribution, exhibit limited generalization capabilities, and underperform in scenarios demanding high real-time responsiveness. Existing methods thus remain inadequate for solving inverse kinematics in complex multi-DOF robotic systems. SUMMARY To address limitations of traditional methods in achieving precise, stable, and real-time solutions for complex scenarios and high-DOF systems, the present invention provides a robot inverse kinematics solution prediction method based on the POA-Transformer-BiGRU-Attention integrated optimization algorithm. The method comprises the following steps: S1: initializing a Pelican Optimization Algorithm (POA) by randomly generating individual robot positions Pi;S2: evaluating and updating the individual robot positions Pi using a fitness function to obtain updated positions Pin⁢e⁢w;S3: defining an input data Xi=Pin⁢e⁢w, and processing the Xi through a Transformer-BiGRU-Attention algorithm to generate a target joint angle; S4: evaluating an accuracy of the target joint angle using an objective function constrained by physical joint limits, and adjust robotic joint angles to ensure precise end-effector positioning and orientation;S5: converting the target joint angles into servo motor control signals in a form of angular velocity, angular acceleration or displacement, then transmitting via bus or industrial Ethernet interface to robotic joint drive units for real-time speed regulation and precise position control. Optionally, the robot includes a sensor feedback module collecting real-time data from: actual end-effector position (via vision or laser measurement); current joint angles; or encoder readings and accelerometer or IMU (Inertial Measurement Unit) o