A probabilistic approach for on-line positioning in nano manipulations

Nanomanipulation and nanoassembly using atom force microscopy (AFM) is a potential and promising technology for nanomanufacturing. Precise position of the tip of AFM is important to increase the accuracy and efficiency on fabricate complex nanostructures. However at the nano-scale, it is difficult to acquire the tip position expressed by the coordinate in real time due to PZT nonlinearity and thermal drift through the general measure. In this paper, a probabilistic approach incorporating a Kalman filter based localization algorithm is introduced into the on-line estimation of the tip position expressed by probability distribution known as probability density function. A probabilistic motion model of AFM tip is introduced that consists of a PZT dynamic model based on the Prandtl-Ishlinskii (PI) model, and motion error distribution obtained from calibration experiments. An observation model by using a local scanning algorithm is proposed and the change of uncertainty distribution on scanning landmarks, e.g. nano-particles, near the target position is analyzed. Some experiment results are included for showing the motion error distribution and a simulation result is presented to illustrate the validity of the proposed method.