Figure 9.1: The vibrating MEMS elements respond to Coriolis forces during rotation, which are converted into an electrical signal. (Figure by Fabio Pasolini.)

Recall from Section 2.1 (Figure 2.9) that IMUs have recently gone from large, heavy mechanical systems to cheap, microscopic MEMS circuits. This progression was a key enabler to high-quality orientation tracking. The gyroscope measures angular velocity along three orthogonal axes, to obtain $ \hat{\omega}_x$, $ \hat{\omega}_y$, and $ \hat{\omega}_z$. For each axis, the sensing elements lie in the perpendicular plane, much like the semicircular canals in the vestibular organ (Section 8.2). The sensing elements in each case are micromachined mechanical elements that vibrate and operate like a tuning fork. If the sensor rotates in its direction of sensitivity, then the elements experience Coriolis forces, which are converted into electrical signals. These signals are calibrated to produce an output in degrees or radians per second; see Figure 9.1.

Figure 9.2: (a) A MEMS element for sensing linear acceleration (from [325]). (b) Due to linear acceleration in one direction, the plates shift and cause a change in capacitance as measured between the outer plates. (Figure by David Askew, Mouser Electronics.)
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(a) & (b) \\

IMUs usually contain additional sensors that are useful for detecting drift errors. Most commonly, accelerometers measure linear acceleration along three axes to obtain $ \hat{a}_x$, $ \hat{a}_y$, and $ \hat{a}_z$. The principle of their operation is shown in Figure 9.2. MEMS magnetometers also appear on many modern IMUs, which measure magnetic field strength along the three perpendicular axis. This is often accomplished by the mechanical motion of a MEMS structure that is subject to Lorentz force as it conducts inside of a magnetic field.

Steven M LaValle 2020-01-06