Robust Hand-Eye Calibration via Iteratively Re-weighted Rank-Constrained Semi-Definite Programming

Abstract

This paper addresses the problem of estimating the Euclidean transformation relating two rigidly attached reference frames from motion measurements: a problem that is commonly referred to as the Hand-Eye calibration. The motion measurements are often affected by synchronization issues and hardware malfunctions. When using pose sensors, such as Electromagnetic or Inertial Measurement Units, the measurements are often less reliable than those obtained by a traditional robot-link and camera pair. Corrupt measurements, whether due to disturbances, large synchronization mismatches or malfunctions, are considered outliers that ought to be filtered out of the estimation process. While this may be achieved non-deterministically by using Random Sample Consensus, we propose a deterministic, robust and accurate method for solving the Hand-Eye calibration problem despite the presence of large amounts of outliers and high levels of measurement noise. The proposed method is based on a reformulation of this estimation problem as a rank-constrained semi-definite programming problem allowing for robustness to be enforced via an iteratively re-weighted optimization approach.