Forward geometric model prediction of a 6-RSU parallel manipulator using a modified NARX Bayesian neural network.

The precision and safety of robotic applications rely on accurate robot models. Bayesian Neural Networks (BNNs) offer the capability to acquire intricate models and provide insights into inherent uncertainties. While recent studies have successfully employed machine learning to predict the Forward Geometric Model (FGM) of a 6-DOF (degrees of freedom) parallel manipulator, traditional methods lack predictive uncertainty estimation. In this study, we propose a novel approach to enhance FGM prediction for a 6-RSU (Revolute-Spherical-Universal) parallel manipulator using a modified NARX-BNN (Nonlinear Autoregressive with Exogenous Inputs - Bayesian Neural Network). The proposed NARX-BNN model benefits from a synergistic combination of the BNN structure's powerful universal approximation feature and uncertainty estimation, and the nonlinear ARX model's strong predictive capability. The simulation and experiment results demonstrate the superiority of the proposed NARX-BNN model over traditional Bayesian shallow neural network employing the Variational inference method for this problem. At a 95 % confidence level, NARX-BNN reduces the RMSE of predicted values by up to 11 % and reduces the Average Width indicator of the prediction interval by approximately 12.7 % compared to traditional BNN. This study underscores the potential of NARX Bayesian Neural Networks in enhancing accuracy, reducing uncertainty, and bolstering the reliability of machine learning models for robotic applications, particularly in predicting the FGM of parallel manipulators. Moreover, these advancements hold promise for improving robotic control, planning, and overall system reliability.