Kinematic Calibration of a 6-DoF Parallel Manipulator With Random and Less Measurements

Abstract

Parallel manipulator (PM) embraces more kinematic errors than serial mechanism. The substantial errors in PM usually demand more measurements, which leads to low efficiency and affects the accuracy of identification due to the ill-conditioning problem. Having realized this common problem in the kinematic calibration of PMs, we carried out a finite and instantaneous screw (FIS)-based kinematic calibration on a 6- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> UHU PM before application to fracture reduction. <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> , U, and H denote actuated revolute joint, universal joint, and helical joint, respectively. The error model is built by the error mapping of serial chains in the FIS framework. Instead of devoting to the measurement planning for more precise identification, the identifiability of kinematic errors is thoroughly analyzed. Redundant errors are categorized as the ones within limb and among limbs. A minimal identification model is thus defined and an error conversion method is proposed for compensation. Calibration experiments show that the FIS method has an improved accuracy of the 6- <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</u> UHU PM at least one magnitude higher than the precision demand, i.e., mean position and orientation errors 0.0574 mm and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.1197\,\,{\times }\,\, 10^{-4}$ </tex-math></inline-formula> rad after calibration. Compared with the conventional closed-loop vector (CLV) equation method, the accuracy improvement of FIS method is higher. In addition, comparisons with the commonly used configuration selection methods indicate that our method allows random and a smaller number of measurements and can reach satisfactory accuracy.