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of the plate, with respect to the environment, causes the oscillator frequency to change This change is sensed by the frequency detector, which sends a signal to a microcomputer or robot controller Substances that conduct electricity to some extent, such as metal, saltwater, and living tissue, are sensed more easily by capacitive transducers than are materials that do not conduct, such as dry wood, plastic, glass, or dry fabric
D31
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Photoelectric Proximity Sensor Reflected light can provide a way for a mobile robot to tell if it is approaching something A photoelectric proximity sensor uses a light-beam generator, a photodetector, a frequency-sensitive amplifier, and a microcomputer (Fig 30-10) The light beam reflects from the object and is picked up by the photodetector The light beam is modulated at a certain frequency, say 1000 Hz The amplifier responds only to light modulated at that frequency This prevents false imaging that can otherwise be caused by lamps or sunlight (Such light sources are unmodulated, and will not actuate a sensor designed to respond only to modulated light) If the robot is approaching an object, its controller senses that the reflected, modulated beam is getting stronger The robot can then steer clear of the object
(D19)
Letting b denote the unit quaternion that transforms vectors represented in frame a to representations in frame c, by eqn (D11) qz = b qr b the derivative of the quaternion qz is qz = b qr b + b qr b
proximity sensor Modulation of the light beam allows the device to distinguish between sensorgenerated light and background illumination
Using the facts that qr = b qz b and that b b is the identity quaternions, we have that qz = b b qz b b + b b q z b b = b b qz + qz b b (D20) (D21)
This method of proximity sensing does not work for objects that do not reflect light, or for windows or mirrors approached at a sharp angle In these scenarios, the light beam is not reflected back toward the photodetector, so the object is invisible
Using the fact that b is a unit vector, it can be shown that the scalar portion of both b b and b b is zero Therefore, as expected, the scalar portion of eqn (D21) is zero It can also be shown that the vector portions of these quaternions are equal in magnitude and opposite in sign Therefore, if we let b b = 0 + w, then b b = 0 w The vector portion of eqn (D21) is z = 2w z (D22)
(D23)
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