EMG-Based Mathematical Modelling, Forward–Inverse Kinematics and Trajectory Planning for Intelligent Transradial Prosthetic Arm Systems

Abstract

Background: Intelligent transradial prosthetic arm systems have increasingly adopted electromyography (EMG), deep learning, and robotic kinematic modelling to improve motion recognition and prosthetic control. Although significant progress has been achieved in EMG-based gesture classification and robotic control, most existing studies address these components independently, with limited integration of EMG signal processing, deep learning, mathematical modelling, forward–inverse kinematics, and trajectory planning within a unified framework.
Objective: This study proposes an integrated EMG-driven intelligent prosthetic arm framework that combines multi-channel EMG signal processing, deep learning-based motion classification, mathematical modelling, forward and inverse kinematic analysis, trajectory planning, and MATLAB/Simulink validation for coordinated upper-limb movement.
Methods: EMG signals acquired from healthy individuals and transradial amputees performing representative functional activities were preprocessed and analysed using time-domain features including Root Mean Square (RMS), Mean Absolute Value (MAV), Zero Crossing (ZC), and Slope Sign Change (SSC). A hybrid Residual Convolutional Neural Network–Bidirectional Long Short-Term Memory–Multi-Head Attention (ResCNN–BiLSTM–MHA) architecture was employed to classify five upper-limb movement classes from eight-channel EMG recordings. The predicted movement classes were mapped to a 14-degree-of-freedom prosthetic arm mathematical model incorporating Denavit–Hartenberg-based forward and inverse kinematics, trajectory planning, and PID-controlled motion simulation within MATLAB/Simulink. Model performance was evaluated using classification metrics, kinematic accuracy, trajectory tracking, and simulation-based validation.
Results: The proposed ResCNN–BiLSTM–MHA framework achieved a classification accuracy of 94.2%, with a precision of 93.1%, recall of 92.3%, specificity of 97.1%, balanced accuracy of 93.6%, F1-score of 0.927, MCC of 0.91, Cohen's kappa of 0.90, and an ROC–AUC of 0.97. The model converged with 96.1% training accuracy and 93.4% validation accuracy, yielding final training and validation losses of 0.12 and 0.19, respectively. MATLAB/Simulink validation produced an RMSE of 0.041 rad, MAE of 0.028 rad, mean end-effector error of 3.62 mm, maximum error of 7.41 mm, and a trajectory tracking error of 3.62%, with an average inference time of 2.8 ms/sample. Conclusion: The proposed ResCNN–BiLSTM–MHA framework effectively integrates EMG-based motion classification with forward and inverse kinematic modelling and trajectory planning for transradial prosthetic arm control. The achieved 94.2% classification accuracy, low kinematic errors, and 2.8 ms/sample inference time demonstrate accurate, stable, and real-time prosthetic motion prediction, making the framework suitable for intelligent upper-limb prosthetic and rehabilitation applications.