Calibration of multi-axis MEMS force sensors using the shape from motion method

Abstract

-This paper presents a new design of a two-axis MEMS (microelectromechanical systems) capacitive force sensor with strict linearity and a new sensor calibration method for micro-sensors. Precise calibration of multi-axis micro force sensors is difficult for several reasons, including the need to apply many known force vectors at precise orientations at the micro force scale, and the risk of damaging the small, fragile MEMS device. In this paper the shape from motion method is introduced for micro force sensors resulting in a rapid and effective calibration technique. Structural-electrostatic coupled field simulations are conducted in order to optimize the sensor design, which is calibrated with the shape from motion method as well as the least squares method for comparison purposes. Calibration results demonstrate that the shape from motion method is an effective, practical, and accurate method for calibrating multiaxis micro force sensors.

Investigation on calibration methods for multi-axis, linear and redundant force sensors

“…The device hyperplane characterization method guarantees an accuracy which is similar to that achievable using traditional least-squares methods and is time effective, requiring, like the shape from motion method, only a few precise force measurements. This method is inspired by the shape from motion method [3,5] and collaborative calibration [14] since it reduces the burden of data collection and considers sensor calibration as an output focused problem. Furthermore, according to the kind of sensor, it may require a simpler test bench with respect to shape from motion, given that there is no need for any geometrical bond for applied forces.…”

“…In the latter case, since the sensor is redundant, fractional changes in resistance vectors have a constraint because they ideally belong to a hyperplane of R 4 . Those two opposite points of view give the two linear relations (4) and (5), where B is a uniquely determined 4 × 3 matrix (the aim is to evaluate it, according to a certain optimum criterion), and A is a 3 × 4 one (A matrix can be chosen in various suitable ways, as explained in section 3.3.3):…”

“…Traditional least-squares calibration methods perform with high accuracy [1,2], but outputs recording require the precise application of a wide set of known forces carefully selected to adequately span the space of the sensor [3,4]. The shape from motion method [3,5] performs with accuracy comparable to traditional least-squares methods, but eliminates the need for explicit knowledge of all the applied load vectors, yielding fast and precise calibration results. In such a method [3], a constant-magnitude force (a mass in a gravity field [6]) is randomly moved through the sensing space of the sensor while raw data are continuously gathered.…”

Probing-error compensation using 5 degree of freedom force/moment sensor for coordinate measuring machine

“…Haitjema et al, Tibrewala et al and Dai et al developed MEMS-type piezoresistive probe [7][8][9]. And, some calibration methods have also been proposed for 3-DOF force sensor based CMM probes [10][11][12]. These probes used highly sensitive 3-DOF force sensors (or displacement sensors) for improving triggering sensitivity to minimize the pretravel and the anisotropic sensitivity errors.…”