Multi-DOF precision positioning methodology using two-axis Hall-effect sensors

A novel sensing methodology using two-axis Hall-effect sensors is proposed, where the absolute positioning of a device atop any magnet matrix is possible. This methodology has the capability of micrometer-order positioning resolution as well as unrestricted translational and rotational range in planar 3-DOF (degree-of-freedom) motions, with potential capability of measuring all 6-DOF motions. This research presents the methodology and preliminary experimental results of 3-DOF planar motion measurements atop a Halbach magnet matrix using two sets of two-axis Hall-effect sensors. Analysis of the Halbach magnet matrix is presented to understand the generated magnetic field. The algorithm uses the Gaussian least squares differential correction (GLSDC) algorithm to estimate the relative position and orientation from the Hall-effect sensor measurements. A recursive discrete-time Kalman filter (DKF) is used in combination with the GLSDC to obtain optimal estimates of position and orientation, as well as additional estimates of velocity and angular velocity, which we can use to design a multivariable controller. The sensor and its algorithm is implemented to a magnetic levitation (maglev) stage positioned atop a Halbach magnet matrix. Preliminary experimental results show its position resolution capability of less than 10 ??m and capable of sensing large rotations. Controllers were designed to close the control loop for the three planar degrees of freedom motion using the GLSDC outputs at a sampling frequency of 800 Hz on a Pentek 4284 digital signal processor (DSP). Calibration was done by comparing the laser interferometers?? and the GLSDC??s outputs to improve the positioning accuracy.