Path-based evaluation of deep learning models for solving inverse kinematics in a revolute-prismatic robot

This study investigates the generalization performance of deep learning (DL) models for solving the inverse kinematics (IK) problem in a 2-degrees of freedom (DOF) revolute-prismatic (RP) robotic manipulator. The goal is to evaluate how effectively different neural architectures predict joint configurations from end-effector positions across diverse workspace regions. Two training strategies were used: quadrant-based and full workspace training. To improve robustness, k-fold cross-validation (CV) was applied to the deep feedforward neural network (DFNN). The models evaluated include DFNN with k-fold CV using 2-input 1-output and 2-input 2-output formulations and without k-fold CV, long short-term memory (LSTM), and gated recurrent unit (GRU). Performance was tested on predefined Square and Circle paths within each quadrant and the full workspace. The DFNN with k-fold CV (2-input, 1-output) consistently achieved the lowest Cartesian deviation errors- for instance, 0.289 mm in Q1, 0.410 mm in Q2, 0.508 mm in Q3, and 0.715 mm in Q4 on Square path. Similar trends were observed on the Circle path, with errors of 0.312 mm, 0.366 mm, 0.438 mm and 0.662 mm in Q1 to Q4 respectively. In full workspace testing, it maintained strong performance with 1.594 mm (Square) and 2.084 mm (Circle) errors. In contrast, DFNN with k-fold CV (2-input, 2-output), without k-fold CV, LSTM and GRU exhibited significantly higher errors. These findings demonstrate that the k-fold CV-based DFNN with single-output formulation, achieves high accuracy and generalization and also capable of handling singularities and ambiguity in joint solutions.