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

Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, i.e., the maximal allowable deviation from a reference robot state such that safety constraints are still satisfied. This letter presents an efficient algorithm to estimate the joint tolerance using sum-of-squares programming. It is theoretically proved that the algorithm provides a lower bound of the joint tolerance. Extensive numerical studies demonstrate that the proposed method is computationally efficient and near optimal.