Data-Driven Hybrid Kinematic Modeling of Stewart Platforms

This study presents a data-driven and highly accurate forward kinematic modeling approach for six-degree-of-freedom (DoF) Stewart platform mechanism. Traditional analytical and numerical methods have significant limitations due to high computational costs and multiple solution uncertainties. Furthermore, the gimbal lock singularity arising in orientation parameterizations based on Euler angles further reduces the reliability of these methods in practical applications. To overcome these issues, the proposed method represents the platform’s orientation directly via a 3x3 rotation matrix instead of Euler angles. To ensure the physical validity of the matrix, an orthogonal projection layer based on Singular Value Decomposition (SVD) is applied, strictly preserving the SO (3) constraints (RT R= I, det (R) = +1). To perform regression analysis for predicting the forward kinematics, a dataset consisting of 100, 000 workspace points was generated using random sampling in the MATLAB environment. A fully connected multi-layer perceptron (MLP) was employed as the regression model. Hyperparameters were systematically optimized using the Optuna Bayesian optimization framework, and model training was conducted in PyTorch with GPU acceleration. Experimental results show that the proposed model achieves sub-millimeter positional accuracy (MAE ≈ 0. 0042), angular error below 0. 02° and prediction performance at R²=0. 9998. Furthermore, the inference time of 0. 12 ms demonstrates that the method is directly applicable in high-frequency real-time control systems. In conclusion, SO (3) projection-based artificial neural network architecture eliminates singularities caused by gimbal lock, produces physically valid orientation estimates, and offers a powerful and generalizable alternative for solving the forward kinematics problem of Stewart platforms in a fast, stable, and highly accurate manner.