Optimal Trajectory Generation of Various English Alphabets Using Deep Learning Model for 3-R Manipulator

Abstract

The modern era of medicine and industry extensively utilizes the manipulator's hand for a variety of vital automated activities. Handling a manipulator hand is a complex task. Due to the nonlinear characteristics of inverse kinematics (IK) mathematical model, inverse kinematics is a time-consuming and laborious procedure, making it difficult to provide a mathematical solution. This research employs a 3-R (revolute) robotic manipulator to achieve joint trajectories for drawing different alphabets and shapes. The IK problem has been solved using a hybrid model. The model is a hybrid of an artificial neural network (ANN) based model, the forward and backward reaching inverse kinematics (FABRIK) technique provides stability and the control barrier function (CBF) with the Lyapunov function. Using the proposed model, coordinates for different alphabets and shapes within the confined workspace were calculated. The ANN automatically obtains specific end-effector coordinates. This model combines the CBF with the Lyapunov function to ensure that a safe region is selected. The accuracy of the model exceeds 99.5%. We have calculated the mean square error (MSE) as 1.66, the root mean square error (RMSE) as 1.25, and the mean absolute error (MAE) as 0.96 for our model. The error between the model's predicted and actual coordinates also demonstrates letter coordinates and shapes drawn using a physical 3R manipulator model. As a result, this method can be applied to precisely estimate the angles in intricate 3DoF inverse kinematics models. © 2025 Wiley Periodicals LLC.