Modeling of two-plate capacitive position sensing systems for high precision planar three DOF measurement

This paper investigates the issues associated with the use of two-plate capacitive sensors for the measurement of coupled linear and angular motions, particularly those of three planar degrees of freedom (DOF) micro/nano positioners. Commonly, such sensors are employed for the measurement of linear motions, and angular motion could introduce non-linearities in the capacitance response. An analytic model of a general three sensor system is developed, together with its linearization, which transform the position and orientation (pose) of the end effector of a planar positioner to the capacitance of each sensor. The sensitivities of pose estimations to capacitance non-linearity and parameter variation are analyzed, which further leads to the identification of optimized sensor positioning strategies. The response of a single sensor to tilt is investigated, and experimentation is performed to determine the magnitude of non-linear effects, and its subsequent impact on the three DOF position estimation.