Research on New Mathematical Model A_ix=Yb_i for Hand-to-Eye Calibration and Application Scenery of This Model Based on iGPS

Hand-to-eye calibration is one of the most important steps to realize high flexibility and digitization of the industry. In this article, based on the research background of improving the degree of automation and flexibility in the field of aircraft fuselage inspection and detection, the hand-to-eye calibration under a large size of operating volume is first studied based on an indoor global positioning system (iGPS). A new calibration mathematical model <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\textbf {A}_{\textbf {i}} \textbf {x} = \textbf {Y} \textbf {b}_{\textbf {i}}$ </tex-math></inline-formula> is first proposed under this research background, and the solution of this model is given based on the orthogonal matrix property and multiobjective optimization algorithm includes the particle swarm algorithm (PSO) and differential evolutionary algorithm (DE). Verification experiments have shown that the method can achieve 3-D camera calibration with an average error of around 0.1021 mm in a large workspace. Thus, it is proved through experiments that this method can realize high-precision and high-robustness calibration of 3-D camera, tool center point (TCP) coordinate, and tool axis vector in a large-scale operating environment.