Provably Safe Tolerance Estimation for Robot Arms via Sum-of-Squares Programming
This addresses a challenging safety issue in robotics for engineers and researchers, though it appears incremental as it builds on existing sum-of-squares methods for tolerance estimation.
The paper tackles the problem of efficiently estimating joint tolerance for robot arms, which is the maximum allowable deviation from a reference state while satisfying safety constraints, by presenting an algorithm using sum-of-squares programming that is proven to provide a tight lower bound and shown to be computationally efficient and near optimal in numerical studies.
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}.