Neural Networks for the Dynamics of Multi-Link Systems

Abstract

This paper developed specialized artificial neural networks for dynamical systems. For single-degree-of-freedom systems, specialized networks were developed for a) first-order linear, b) second-order linear, complex, first-order, and c) second-order with sigmoid damping (a generalization of viscous damping and dry friction damping). Digitization errors were eliminated by a specialized sub-network that corrected amplitude and phase output. Next, a network was developed for normal-mode systems. Finally, networks were developed for multi-link systems. Trigonometric nonlinearities were handled by the activation functions and multiplicative nonlinearities were handled by a custom sub-network. The treatment of the trigonometric nonlinearities and the multiplicative nonlinearities are kernels that can be expanded into specialized networks for a broad class of multi-link systems. The paper closes with an illustrative example of a three-link system resembling an upper arm, forearm, and hand. The three-link system is optimized to throw a basketball in a hoop with minimum effort.