Inverse Kinematics as Low-Rank Euclidean Distance Matrix Completion

TL;DR

This paper introduces a novel approach to inverse kinematics by framing it as a low-rank Euclidean distance matrix completion problem, leveraging Riemannian optimization for efficient solutions across different robots.

Contribution

It presents a new geometric perspective on inverse kinematics, connecting it to low-rank matrix completion and developing an optimization-based solution applicable to various articulated robots.

Findings

Effective IK solutions for multiple robot types

Demonstrates the equivalence between IK and matrix completion

Uses Riemannian optimization for improved performance

Abstract

The majority of inverse kinematics (IK) algorithms search for solutions in a configuration space defined by joint angles. However, the kinematics of many robots can also be described in terms of distances between rigidly-attached points, which collectively form a Euclidean distance matrix. This alternative geometric description of the kinematics reveals an elegant equivalence between IK and the problem of low-rank matrix completion. We use this connection to implement a novel Riemannian optimization-based solution to IK for various articulated robots with symmetric joint angle constraints.