Deep Neural Networks for Inverse Kinematics With Multi-Valued Solution Spaces: Limitations and Hybrid Learning––Optimization Approach
This paper investigates the use of deep neural networks (DNNs) for solving inverse kinematics problems exhibiting multiple valid joint-space solutions. A synthetic dataset is generated from the forward kinematics of the ABB IRB120 manipulator, with end-effector orientation represented using unit quaternions, and a DNN is trained to approximate the relationship between Cartesian pose and joint configuration under three scenarios: (i) full joint space, (ii) constrained joint space with fixed $q_{6}$ , and (iii) a hybrid approach combining neural inference with nonlinear optimization. The results show that, in the full joint space, the inverse kinematics mapping is inherently multi-valued, preventing the DNN from learning a consistent and physically realizable inverse mapping through deterministic regression and leading to large prediction errors. In contrast, constraining $q_{6}$ reduces the ambiguity present in the training dataset and improves learning stability at the cost of restricting the solution space. The hybrid formulation mitigates these limitations by using the DNN to provide an informed initial estimate for a nonlinear least-squares solver operating in the full joint space. The proposed Hybrid-DNN formulation achieves a mean position error of 1.406 mm, a mean orientation error of 0.900°, and a success rate of 94.2%, where success is defined as simultaneously achieving position and orientation errors below 5 mm and 2°, respectively. Although slightly less accurate than the Conventional-Multistart-10 baseline, it achieves near-equivalent solution quality while reducing the average number of function evaluations and execution time by approximately 95.1% and 82.5%, respectively. These results indicate that inverse kinematics problems characterized by one-to-many mappings cannot be effectively treated as deterministic regression tasks and demonstrate that informed neural initialization combined with numerical optimization constitutes an effective and computationally efficient solution strategy.