Euclidean Equivariant Models for Generative Graphical Inverse Kinematics

Oliver Limoyo, Filip Maric, Matthew Giamou, Petra Alexson, Ivan Petrovic, Jonathan Kelly

Keywords: Inverse Kinematics, Generative Modelling, Equivariance, Graph Neural Networks

TL;DR: We present a learned generative graphical inverse kinematics solver that leverages Euclidean equivariance to learn solution sets across multiple manipulator structures.

Abstract: Quickly and reliably finding accurate inverse kinematics (IK) solutions remains a challenging problem for robotic manipulation. Existing numerical solvers typically only produce a single solution and rely on local search techniques to minimize highly nonconvex objective functions. Recently, learning-based approaches that approximate the entire feasible set of solutions have shown promise as a means to generate multiple fast and accurate IK results in parallel. However, existing learning-based techniques have a significant drawback: each robot of interest requires a specialized model that must be trained from scratch. To address this key shortcoming, we investigate a novel distance-geometric robot representation coupled with a graph structure that allows us to leverage the flexibility of graph neural networks (GNNs). We use this approach to train a generative graphical inverse kinematics (GGIK) solver that is able to produce a large number of diverse solutions in parallel while also generalizing well---a single learned model can be used to produce IK solutions for a variety of different robots. The graphical formulation elegantly exposes the symmetry and Euclidean equivariance of the IK problem, stemming from the spatial nature of robot manipulators. We exploit this symmetry by explicitly encoding it into the architecture of our learned model, yielding a flexible solver that is able to produce IK solution sets for multiple robots.