A 6-DOF Measurement Solution for Permanent Magnet Synchronous Planar Motors Based on Motion Continuity Principle

Exploiting motor-inherent magnetic field for displacement measurement has been paid much attention as it can greatly reduce setup complexity. In this paper, a successive solving iterative algorithm based on the magnetic field detection model and motion continuity is proposed for 6-DOF displacement measurement of the permanent magnet synchronous planar motor. A convergence theorem is given to ensure convergence of the algorithm. On the basis convergence conditions independent with the desired displacement are derived. Furthermore convergence (iteration) rate is given from an engineering point of view. Simulations are carried out to evaluate the feasibility and robustness to noise and parameter deviation of the algorithm. Translational comparison experiments with commercial displacement sensors are conducted on a self-developed experimental platform, and the experimental results verified the feasibility of the proposed method. The results of repeated measurement experiments on fixed positions show that compared with the commercial sensors, the mean of measurement deviation is 100- $\mu \text{m}$ scale in both the $x$ - and $y$ -directions, and the standard deviation is better than 4.5 and 3 $\mu \text{m}$ in the $x$ - and $y$ -directions, respectively. The implementation simplicity and the favorable measurement accuracy make the proposed method attractive for 6-DOF applications with large planar travel ranges, such as semiconductor manufacturing equipment and inspection equipment of printed circuit boards.