Inverse kinematics learning for robotic arms with fewer degrees of freedom by modular neural network systems

Artificial neural networks have been traditionally employed to learn and compute the inverse kinematics of a robotic arm. However, the inverse kinematics model of a typical robotic arm with joint limits is a multi-valued and discontinuous function. Because it is difficult for a multilayer neural network to approximate this type of function, an accurate inverse kinematics model cannot be obtained by using a single neural network. In order to overcome the difficulties of inverse kinematics learning, we propose a novel modular neural network system that consists of a number of expert modules, where each expert approximates a continuous part of the inverse kinematics function. The proposed system selects one appropriate expert whose output minimizes the expected position/orientation error of the end-effector of the arm. The system can learn a precise inverse kinematics model of a robotic arm with equal or more degrees of freedom than that of its end-effector. However, there are robotic arms with fewer degrees of freedom, where the system cannot learn their precise inverse kinematics model. We have adopted a modified Gauss-Newton method for finding the least-squares solution to address this issue. Through the modifications presented in this paper, the improved modular neural network system can obtain a precise inverse kinematics model of a general robotic arm.