The misalignment error during assembly and/or manufacturing error of robot linkages maycompromise the accuracy of a serial manipulator, causing the actual forward kinematics model parameter to differ from the designed value. This demands the need for forward kinematics calibration.

To identify the actual model parameter, the calibration process involves recording datafrom a set of robot poses as input to a parameter identification algorithm. In order to save time on the data acquisition, optimal design of experiment is employed to use the least amount of data points. Also, to avoid unnecessary calculations and numerical issues during parameter identification, identifiability analysis is performed to determine and eliminate unidentifiable parameters. Lastly, this work proposes novel nested algorithm to improve computation efficiency and robustness for parameter identification. This approach exploits the fact that part of the model parameter can be obtained explicitly given the rest of the parameters. This effectively reduces the parameters to find during the iterative identification process and is shown to be more efficient and robust than the commonly used generic method in the literature.

The calibration method is applied to a common 6-DOF industrial robot and a customarilydesigned and fabricated 4-DOF surgical robot. For the industrial robot, the nested algorithm demonstrates better robustness, faster error convergence over iteration, and less calculation time than the commonly used generic algorithm. For the surgical robot, the results for optimally designed data points demonstrate a faster convergence of residual error over the number of data points compared to randomly designed data points.