Comparison of Distal Teacher Learning with Numerical and Analytical Methods to Solve Inverse Kinematics for Rigid-Body Mechanisms

TL;DR

This paper compares distal teacher learning with analytical and numerical methods for inverse kinematics in rigid-body mechanisms, showing DT's advantages in solve rate and speed under certain conditions.

Contribution

It provides an extensive evaluation of distal teaching against traditional methods, demonstrating its practical effectiveness for rigid-body inverse kinematics.

Findings

DT has higher solve rate with enough data and relaxed precision.

DT is faster and unaffected by singularities compared to numerical methods.

Analytical solutions outperform other methods when available.

Abstract

Several publications are concerned with learning inverse kinematics, however, their evaluation is often limited and none of the proposed methods is of practical relevance for rigid-body kinematics with a known forward model. We argue that for rigid-body kinematics one of the first proposed machine learning (ML) solutions to inverse kinematics -- distal teaching (DT) -- is actually good enough when combined with differentiable programming libraries and we provide an extensive evaluation and comparison to analytical and numerical solutions. In particular, we analyze solve rate, accuracy, sample efficiency and scalability. Further, we study how DT handles joint limits, singularities, unreachable poses, trajectories and provide a comparison of execution times. The three approaches are evaluated on three different rigid body mechanisms with varying complexity. With enough training data and relaxed precision requirements, DT has a better solve rate and is faster than state-of-the-art numerical solvers for a 15-DoF mechanism. DT is not affected by singularities while numerical solutions are vulnerable to them. In all other cases numerical solutions are usually better. Analytical solutions outperform the other approaches by far if they are available.