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84 in a similar way to how capacitive accelerometers sense acceleration. The transducers vibrate the silicon ring at its resonant frequency, and detect any radial motion of the ring’s perimeter. When a planar rotation is applied to the gyroscope, transducers also account for the motion driven by the vibration, and for the Coriolis force and its effects. The Coriolis force causes each outward- moving point on the ring to ‘squeeze’ in one direction, while the inward-moving points bend the opposite way. As a result, the ‘centre of vibration’ rotates proportionally with angular velocity. Much like accelerometers, gyroscopes’ angular velocity measurement can be open loop, in which the amount of movement undergone by the points around the ring is detected, or closed loop, in which a rebalancing force drives the vibrating ring back to its null position (or the original locus of its vibrations). Closed-loop gyros are also more expensive, but are anticipated to become the standard. In a quartz dual tuning-fork gyro, the piezoelectric property of quartz is used to vibrate one set of tines in the fork structure. The Coriolis force generated when the fork rotates produces vibrations in the other set of tines. The electrical signal generated by the vibration of the second set of tines can then be used to measure the rotation. Other VSGs are also available, including vibrating beams, plates, cylinders or ‘wine glasses’. The last of these are used in hemispherical resonator gyroscopes, which are highly accurate but extremely complex to manufacture, so not many companies produce them. Tuning-fork structures are the most popular for unmanned vehicle gyros. However, while they can be easier and cheaper than rings to fabricate, rings can have greater sensitivity, and can provide greater resistance to external shock and vibration. Bias stability is often cited in degrees per hour (or per second) as a useful measure of reliability, in terms of the smallest mean change in consecutive gyroscope update measurements when analysed over periods of time. However, errors can come from other sources, meriting examination of other key error stats. Scale factor (or ‘sensitivity’) for example is the ratio between the measured output and the change in sensor input. This adds less error than bias overall, but it can be especially problematic for angle tracking during dynamic motion. Sensitivity error worsens under larger angular velocities: for example, a scale- factor error of 0.1% during a 90°/s angular velocity motion might output an error of 0.09°/s. These two error terms are particularly critical to UAV payload stabilisation, as are high bandwidths and low random walk, which should be above 100 Hz and below 15°/Hz respectively. Unmanned vehicle designers in general should pay attention to all of these, as well as vibration and shock tolerance, VRE and range. For commercial UGVs, UUVs and fixed-wing UAVs, a range of ±400°/s or wider is ideal, and for rotor-wing UAVs, ±900°/s might be more suitable. Optical gyroscopes Some closed-loop MEMS gyroscopes are said to be approaching the performance levels of fibre optic gyros and laser ring gyros (LRGs). That said, most FOGs still tend to exhibit one-tenth (or less) the angular random walk of typical MEMS gyros, as well as generally 20-70% higher bandwidth, and less than a third of MEMS gyroscope VRE. They are therefore expected to maintain a significant presence among unmanned vehicles for the foreseeable future. LRGs can offer even higher performance than FOGs, with some LRGs offering bias stability with less December/January 2019 | Unmanned Systems Technology Focus | IMUs, gyros and accelerometers Most MEMS gyroscopes use a vibrating structure to detect angular velocity through Coriolis forces acting on the structure as the vehicle rotates (Courtesy of Silicon Sensing) After manufacture, gyroscopes and accelerometers are thoroughly calibrated to optimise for stability and precision (Courtesy of Inertial Labs))