In this paper, we propose a graph neural network, DisGNet, for learning the graph distance matrix to address the forward kinematics problem of the Gough-Stewart platform. DisGNet employs the k-FWL algorithm for message-passing, providing high expressiveness with a small parameter count, making it suitable for practical deployment. Additionally, we introduce the GPU-friendly Newton-Raphson method, an efficient parallelized optimization method executed on the GPU to refine DisGNet's output poses, achieving ultra-high-precision pose. This novel two-stage approach delivers ultra-high precision output while meeting real-time requirements. Our results indicate that on our dataset, DisGNet can achieves error accuracys below 1mm and 1deg at 79.8\% and 98.2\%, respectively. As executed on a GPU, our two-stage method can ensure the requirement for real-time computation. Codes are released at https://github.com/FLAMEZZ5201/DisGNet.

翻译：本文提出图神经网络DisGNet，通过学习图距离矩阵解决Gough-Stewart平台的正运动学问题。DisGNet采用k-FWL算法进行消息传递，以较少参数实现高表达能力，适用于实际部署。此外，我们引入GPU友好的牛顿-拉夫森方法——一种在GPU上高效并行执行的优化算法，用于精化DisGNet的输出位姿，实现超高精度位姿。这一新型两阶段方法在满足实时性要求的同时，提供超高精度输出。结果表明，在我们的数据集上，DisGNet在79.8%和98.2%的情况下分别实现了低于1mm和1°的误差精度。由于在GPU上执行，我们的两阶段方法可确保实时计算要求。代码已发布在https://github.com/FLAMEZZ5201/DisGNet。