Pose estimation and calibration using nonlinear capacitance sensor models for micro/nano positioning

This paper presents a technique to perform pose estimation of planar three degrees of freedom (DOF) motions using two-plate capacitive sensors. These sensors are commonly utilised to measure linear motion, however their capacitance response becomes nonlinear and errors can be introduced with the introduction of angular motions. This paper focusses on the development of a methodology to invert a nonlinear model which maps the pose of the end effector of a planar positioner to the capacitances of each sensor, in effect providing pose estimates from capacitance measurements. Strategies for the calibration of model parameters, for cases where full reference or only yaw sensor measurements are available, are extensively explored. The points evaluated through the proposed method are shown to outperform the best affine transformation when trained with a full reference, and improved performance is also observed when the single reference is employed.