Nonlinear estimation for kinematic calibration of 3PRR planar parallel kinematics manipulator

Abstract

Calibration is a common procedure to increase the accuracy of machine tools. Estimation as an important part of the calibration has been conducted by using various algorithms. This paper presents the implementation of nonlinear least squares (Gaussian least squares differential correction) algorithm to estimate the geometrical parameters of 3PRR planar parallel kinematics manipulator having nonlinear kinematics which can be used in a hybrid serial-parallel kinematics machine tool. The independent parameters are first estimated followed by the dependent parameters. The convergence to the true values with zero estimation error is guaranteed with any initial estimates provided that no measurement noise is introduced. Subsequently, the estimation by incorporating noise from all measurement devices is conducted which gives the estimates with certain estimation errors. While the estimation errors are affected by the noise level of the measurement devices, it is shown that larger size of measurement samples increases the estimation accuracy. Finally, the uncertainty of the estimates is evaluated by using Monte Carlo simulation.