Provably Safe Tolerance Estimation for Robot Arms via Sum-of-Squares Programming

TL;DR

This paper introduces an efficient sum-of-squares programming method to accurately estimate the maximum joint deviation in robot arms while ensuring safety constraints, providing tight bounds and practical implementation tools.

Contribution

It presents a novel algorithm that computes tight lower bounds for robot joint tolerance using sum-of-squares programming, with proven theoretical guarantees and practical efficiency.

Findings

The algorithm provides tight lower bounds for joint tolerance.

It is computationally efficient and near optimal.

The method is implemented in the open-source JTE toolbox.

Abstract

Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, \ie the maximal allowable deviation from a reference robot state such that safety constraints are still satisfied. This paper presented an efficient algorithm to estimate the joint tolerance using sum-of-squares programming. It is theoretically proved that the algorithm provides a tight lower bound of the joint tolerance. Extensive numerical studies demonstrate that the proposed method is computationally efficient and near optimal. The algorithm is implemented in the JTE toolbox and is available at \url{https://github.com/intelligent-control-lab/Sum-of-Square-Safety-Optimization}.