Kinematic modeling and calibration of a flexure based hexapod nanopositioner

This paper covers the kinematic modeling of a flexure-based, hexapod nanopositioner and a new method of calibration for this type of nanopositioner. This six degrees of freedom tri-stage nanopositioner can generate small displacement, high-resolution motions with high accuracy by actuating three inexpensive, high quality planar stages. Each stage is equipped with linear actuators. In this paper, we discuss the calibration of the nanopositioner and methods to improve its accuracy. First, we derive the kinematic model of the nanopositioner that is a Stewart platform with spherical joints. Based on this kinematic model, we then calculate the actuation data for a set of commands for decoupled and coupled motions. We use an interferometer and an autocollimator to measure the actual displacement and rotation of the platform. Finally, we obtain the Jacobian matrix of the moving platform for the controller. Experiments showed that with the calibration-corrected parameters, the maximum error is approximately 0.002° in rotations and 3.3 μm in translation for a workspace of ± 0.2° and ±200 μm in x, y and z direction.

► This paper covers the kinematic modeling of a flexure, platform-based, hexapod nanopositioner.
► By means of interferometer and autocollimator, a new set up of calibration for this type of nanopositioner is built.
► Based on combining kinematic modeling and the new set up, a new calibration method of the Stewart platform type of nanopositioners is developed.
► The Jacobian matrix of the high-accuracy controller for the nanopositioner is finally obtained in the calibration.