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

TL;DR

This paper demonstrates how Graph Neural Networks can learn inverse kinematic models that generalize across manipulators with different link lengths, paving the way for symbolic regression-based explainability.

Contribution

It introduces a GNN-based approach to learn inverse kinematics that generalizes to manipulators with varying link configurations, serving as an inductive bias for symbolic regression.

Findings

Position error less than 1.0 cm for 3 DOF

Orientation error of 2° for 3 DOF

Out-of-domain errors limit extrapolation

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.