Analytic Deep Neural Network-Based Robot Control

Neural networks have been extensively used in robot control for various applications because of their powerful capability in approximation of nonlinear functions. However, existing literature on feedback control of robots mainly focuses on shallow networks where the analysis is developed for the output weights only and the linearity in parameters is often a requirement. This is due to the fact that convergence analysis is difficult for deep networks. Since stability and convergence are critical in robot control, our main aim is to develop a theoretical framework for using deep networks in robotics in a safe and predictable manner. In this article, we use a deep network to approximate the Jacobian matrix of a robot with unknown kinematics. An analytic layer-wise deep learning framework is proposed where the deep network is progressively built and trained, and the convergence of the tracking error is guaranteed during the online learning process. The experimental results for tracking control tasks performed on an industrial robot are given to illustrate the effectiveness of the proposed method.