Real-time solution of the forward kinematics for a parallel haptic device using a numerical approach based on neural networks

This paper proposes a neural network (NN)-based approach to solve the forward kinematics of a 3-RRR spherical parallel mechanism designed for a haptic device. The proposed algorithm aims to remarkably speed up computation to meet the requirement of high frequency rendering for haptic display. To achieve high accuracy, the workspace of the haptic device is divided into smaller subspaces. The proposed algorithm contains NNs of two different precision levels: a rough estimation NN to identify the index of the subspace and several precise estimation networks with expected accuracy to calculate the forward kinematics. For continuous motion, the algorithm structure is further simplified to save internal memory and increase computing speed, which are critical for a haptic device control system running on an embedded platform. Compared with the mostly used Newton-Raphson method, the proposed algorithm and its simplified version greatly increase the calculation speed by about four times and 10 times, respectively, while achieving the same accuracy level. The proposed approach is of great significance for solving the forward kinematics of parallel mechanism used as haptic devices when high update frequency is needed but hardware resources are limited.