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This paper offers a comprehensive investigation into the forward and inverse kinematics of a wrist rehabilitation robot, utilizing the Denavit-Hartenberg method for forward kinematics (FK) and a geometric approach, as well as artificial neural networks (ANN) and adaptive Neuro-Fuzzy inference systems (ANFIS) for inverse kinematics (IK) analysis. While the geometric method entails precise parameter measurements and faces uncertainties, ANN and ANFIS are explored as potential remedies to enhance accuracy and robustness. Evaluating 11 different training functions sourced from existing literature, our study conducts a thorough assessment of their performance within an ANN network. We aim to pinpoint the most suitable training function for achieving optimal IK solutions in the context of a wrist rehabilitation robotic. Additionally, the ANFIS model, trained using Fuzzy C-Means (FCM), sets itself apart from Grid Partitioning (GP) and Subtractive Clustering (SC). Among the ANN training functions, Bayesian regularization with 5 hidden layers emerges as the most effective, yielding low root mean square error (RMSE) values of 0.003, 0.004, and 0.007 degrees for pronation/supination (P/S), abduction/adduction (AB/AD), and flexion/extension (F/E), respectively. Conversely, ANFIS, trained with FCM, demonstrates satisfactory yet less precise results, with RMSE values of 0.191, 0.082, and 0.165 degrees for P/S, AB/AD, and F/E, respectively. Despite its adequacy, ANFIS trails behind ANN, showcasing RMSE reductions of 98.4%, 95.1%, and 95.7% for P/S, AB/AD, and F/E angles, respectively. This study contributes to leveraging ANN and ANFIS for IK analysis in wrist rehabilitation robotics, highlighting the efficacy of ANN, particularly when employing Bayesian regularization, to enhance accuracy.
Saeedi et al. (Wed,) studied this question.