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Sonar Sonar is a medium-range method of proximity sensing The acronym derives from the words sonic navigation and ranging The basic principle is simple: Bounce acoustic waves off of objects, and measure the time it takes for the echoes to return An elementary sonar system consists of an ac pulse generator, an acoustic emitter, an acoustic pickup, a receiver, a delay timer, and an indicating device such as a numeric display, CRT, LCD, or pen recorder The transmitter sends out acoustic waves through the medium, usually water or air These waves are reflected by objects, and the echoes are picked up by the receiver The distance to an object is determined on the basis of the echo delay, provided the speed of the acoustic waves in the medium is known A simple sonar system is diagrammed in Fig 30-13A A computer map can be generated on the basis of sounds returned from various directions in two or three dimensions This can help a mobile robot or vessel navigate in its environment However, the system can be fooled if the echo delay is equal to or longer than the time interval between pulses, as shown at B To overcome this, a computer can instruct the generator to send pulses of various frequencies in a defined sequence The computer keeps track of which echo corresponds to which pulse Acoustic waves travel faster in water than in air The amount of salt in water makes a difference in the propagation speed when sonar is used on boats, for example, in depth finding The density of water can vary because of temperature differences as well If the true speed of the acoustic waves is not accurately known, false readings will result In freshwater, the speed of sound is about 1400 meters per second (m/s), or 4600 feet per second (ft/s) In saltwater, it is about 1500 m/s (4900 ft/s) In air, sound travels at approximately 335 m/s (1100 ft/s) In the atmosphere, sonar can make use of audible sound waves, but ultrasound is often used instead Ultrasound has a frequency too high to hear, ranging from about 20 kHz to more than 100 kHz One advantage of ultrasound is that the signals will not be heard by people working around machines equipped with sonar Another advantage is the fact that it is less likely to be fooled by people talking, machinery operating, and other noises At frequencies higher than the range of human hearing, acoustical disturbances do not normally occur as often, or with as much intensity, as they do within the hearing range In its most advanced forms, sonar can rival vision systems (also called machine vision) as a means of mapping the environment for a mobile robot or vessel Sonar has one significant limitation: all acoustic waves, including sound and ultrasound, require a gaseous or liquid medium in order to propagate Therefore, sonar is useless in outer space, which is practically a vacuum Signal Comparison A machine or vessel can find its geographical position by comparing the signals from two fixed stations whose positions are known, as shown in Fig 30-14A By adding 180 to the bearings of the sources X and Y, the machine or vessel (small square block) obtains its bearings as seen from the sources (round dots) The machine or vessel can determine its direction and speed by taking two readings separated by a certain amount of time In the old days, diagrams such as the one in Fig 30-14A were actually plotted on maps by the captains of oceangoing vessels and aircraft Nowadays, computers do that work, with more accurate results Figure 30-14B is a block diagram of an acoustic direction finder such as can be used by a mobile robot The receiver has a signal-strength indicator and a servo that turns a directional ultrasonic.

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Given the results derived above, the quaternion approach can be de ned by the following sequence of actions 1 At t = 0, the initial attitude is estimated and Rb (0) is computed n according to eqns (243) 2 The initial value of the quaternion b(0) is computed according to eqn (D15) 3 Given b (t), the quaternion b(t) for t 0 is computed using either bn eqn (D28) or (D30) 4 The rotation matrix Rb (t) is computed from b(t) using eqn (D13) n when required Alternatively, vectors can be transformed between the frames-of-reference directly by use of eqn (D11) 5 The attitude is computed according to eqns (D16-D18) at any time that it is needed

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transducer There are two signal sources at different frequencies When the transducer is rotated so the signal from one source is maximum, a bearing is obtained by comparing the orientation of the transducer with some known standard such as a magnetic compass The same is done for the other source A computer determines the precise location of the robot, based on this data

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