DisGNet: A Distance Graph Neural Network for Forward Kinematics Learning of Gough-Stewart Platform

TL;DR

The paper tackles forward kinematics for the 6-DOF Gough-Stewart platform by leveraging a distance-based graph representation as input and a highly expressive Distance Graph Neural Network, DisGNet, built with the $k$-FWL message-passing framework. It then couples this with a GPU-friendly Newton-Raphson refinement that efficiently approximates the Moore-Penrose inverse to deliver ultra-high precision poses in real time, enabling practical deployment. On a large synthetic dataset, the approach achieves sub-millimeter translation and sub-degree rotation accuracy, with a major portion of samples meeting these tight thresholds, and runs efficiently on modern GPUs. The work contributes a graph-based FK methodology, a high-expressivity neural architecture, a GPU-accelerated refinement stage, and a dataset with benchmarks to advance learning-based FK for parallel manipulators.

Abstract

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.

Figures (7)

• Figure 1: The pipeline of our proposed forward kinematics solver for the Gough-Stewart platform.
• Figure 2: Illustration of the 6-6 GSP structure. (a) Initial coordinate systems. (b) Perspective planar view.
• Figure 3: Our forward kinematics solver for the Gough-Stewart platform is based on a two-stage framework. DisGNet learns the geometric information from the distance representation of graph and outputs end-effector pose $\mathbf{T}$ with high precision in an end-to-end manner. Subsequently, with the estimated value $\mathbf{T}$ as the initial value, the Newton-Raphson method is utilized for optimization. It offers ultra-high precision for the end-effector pose and can optimize fast via GPU parallel processing.
• Figure 4: The backbone of our proposed DisGNet.
• Figure 5: The error accuracy of DisGNet on the test set during the training process. Left: Accuracy of translation errors (absolute error). Right: Accuracy of rotation errors (geodesic distance).