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A Hybrid Strategy for Forward Kinematics of the Stewart Platform Based on Dual Quaternion Neural Network and ARMA Time Series Prediction

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Udgivet i:Actuators vol. 14, no. 4 (2025), p. 159
Hovedforfatter: Tao Jie
Andre forfattere: Zhou Huicheng, Fan, Wei
Udgivet:
MDPI AG
Fag:
Kinematics
Accuracy
Artificial neural networks
Optimization
Back propagation networks
Newton-Raphson method
Jacobi matrix method
Numerical analysis
Autoregressive moving average
Algebra
Systems stability
Time series
Efficiency
Coordinate transformations
Neural networks
Sensors
Computational efficiency
Methods
Algorithms
Real time
Quaternions
Computing time
Jacobian matrix
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Resumen:The forward kinematics of the Stewart platform is crucial for precise control and reliable operation in six-degree-of-freedom motion. However, there are some shortcomings in practical applications, such as calculation precision, computational efficiency, the capacity to resolve singular Jacobian matrix and real-time predictive performance. To overcome those deficiencies, this work proposes a hybrid strategy for forward kinematics in the Stewart platform based on dual quaternion neural network and ARMA time series prediction. This method initially employs a dual-quaternion-based back-propagation neural network (DQ-BPNN). The DQ-BPNN is partitioned into real and dual parts, composed of parameters such as driving-rod lengths, maximum and minimum lengths, to extract more features. In DQ-BPNN, a residual network (ResNet) is employed, endowing DQ-BPNN with the capacity to capture deeper-level system characteristics and enabling DQ-BPNN to achieve a better fitting effect. Furthermore, the combined modified multi-step-size factor Newton downhill method and the Newton–Raphson method (C-MSFND-NR) are employed. This combination not only enhances computational efficiency and ensures global convergence, but also endows the method with the capability to resolve a singular matrix. Finally, a traversal method is adopted to determine the order of the autoregressive moving average (ARMA) model according to the Bayesian information criterion (BIC). This approach efficiently balances computational efficiency and fitting accuracy during real-time motion. The simulations and experiments demonstrate that, compared with BPNN, the R2 value in DQ-BPNN increases by 0.1%. Meanwhile, the MAE, MAPE, RMSE, and MSE values in DQ-BPNN decrease by 8.89%, 21.85%, 6.90%, and 3.3%, respectively. Compared with five Newtonian methods, the average computing time of C-MSFND-NR decreases by 59.82%, 83.81%, 15.09%, 79.82%, and 78.77%. Compared with the linear method, the prediction accuracy of the ARMA method increases by 14.63%, 14.63%, 14.63%, 14.46%, 16.67%, and 13.41%, respectively.
ISSN:2076-0825
DOI:10.3390/act14040159
Fuente:Advanced Technologies & Aerospace Database