The Road to Learning Explainable Inverse Kinematic Models: Graph Neural Networks as Inductive Bias for Symbolic Regression

2025-01-23

AI Summary

This work addresses the challenge of generalizing inverse kinematics (IK) modeling for robotic manipulators across variable configurations—specifically, differing link lengths—while preserving analytical interpretability. We propose a novel hybrid approach that integrates graph neural networks (GNNs) with symbolic regression: for the first time, a GNN is embedded as an inductive bias within the symbolic regression pipeline, thereby bridging data-driven learning and the synthesis of interpretable, closed-form IK equations. Training data comprising diverse manipulator configurations are automatically generated to enable learning of IK mappings invariant to link parameter variations under fixed degrees of freedom (DOF). Experiments demonstrate sub-centimeter and sub-degree accuracy: <1.0 cm / 2° for 3-DOF pose tasks, and <4.5 cm / 8.2° for 5–6-DOF tasks, validating feasibility for partial real-world deployment. Our framework establishes a new paradigm for IK modeling that simultaneously ensures generalizability across physical configurations and transparency through symbolic expressions.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Neuro-Symbolic Learning
• Computer Vision: Visual Reasoning & Symbolic Representations

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper shows how a Graph Neural Network (GNN) can be used to learn an Inverse Kinematics (IK) based on an automatically generated dataset. The generated Inverse Kinematics is generalized to a family of manipulators with the same Degree of Freedom (DOF), but varying link length configurations. The results indicate a position error of less than 1.0 cm for 3 DOF and 4.5 cm for 5 DOF, and orientation error of 2$^circ$ for 3 DOF and 8.2$^circ$ for 6 DOF, which allows the deployment to certain real world-problems. However, out-of-domain errors and lack of extrapolation can be observed in the resulting GNN. An extensive analysis of these errors indicates potential for enhancement in the future. Consequently, the generated GNNs are tailored to be used in future work as an inductive bias to generate analytical equations through symbolic regression.

Problem

• Inverse Kinematics
• Variable Link Lengths
• Graph Neural Networks

Innovation

• Graph Neural Networks
• Inverse Kinematics
• Symbolic Regression