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33.8.2 INERTIAL NAVIGATION
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You can use the same physics that keeps a bicycle upright when its wheels are in motion to provide motion data to a robot. Consider a bicycle wheel spinning in front of you while you hold the axle between your hands. Turn sideways and the wheel tilts. This is the gyroscopic effect in action; the angle of the wheel is directly proportional to the amount and time you are turning. Put a gyroscope in an airplane or ship and you can record even imperceptible changes in movement, assuming you are using a precision gyroscope. Gyros are still used in airplanes today, even with radar, ground controllers, and radios to guide their way. While many modern aircraft have substituted mechanical gyros with completely electronic ones, the concept is the same. During flight, any changes in direction are
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33.8 EXPLORING OTHER POSITION-REFERENCING SYSTEMS
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recorded by the inertial guidance system in the plane (there are three gyros, for all three axes). At any time during the flight the course of the plane can be scrutinized by looking at the output of the gyroscopes. Inertial guidance systems for planes, ships, missiles, and other such devices are far, far too expensive for robots. However, there are some low-cost gyros that provide modest accuracies. One reasonably affordable model is the Max Products MX-9100 micro piezo gyro, often used in model helicopters. The MX-9100 uses a piezoelectric transducer to sense motion. This motion is converted into a digital signal whose duty cycle changes in proportion to the rate of change in the gyro. Laser- and fiber-optic-based gyroscopes offer another navigational possibility, though the price for ready-made systems is still out of the reach of most hobby robot enthusiasts. These devices use interferometry the subtle changes in the measured wavelength of a light source that travels in opposite directions around the circumference of the gyroscope. The light is recombined onto a photosensor or a photocell array such as a CCD camera. In the traditional laser-based gyroscopes (e.g., the Honeywell ring gyro), the two light beams create a bull s-eye pattern that is analyzed by a computer. In simpler fiber-optic systems, the light beams are mixed and received by a single phototransistor. The wave patterns of the laser light produce sum and difference signals (heterodyning). The difference signals are well within audio frequency ranges, and these can be interpreted using a simple frequency-tovoltage converter. From there, relative motion can be calculated. A low-cost method to experiment with inertial navigation is to use accelerometers (similar to those described in detail in 35, Experimenting with Tilt and Gravity Sensors ). The nature of accelerometers, particularly the less-expensive piezoelectric variety, can make them difficult to employ in an inertial system. Accelerometers are sensitive to the earth s gravity, and tilting on the part of the robot can introduce errors. By using multiple accelerometers one to measure movement of the robot and one to determine tilt it is generally possible to reduce (but perhaps not eliminate) these errors.
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33.8.3 MAP MATCHING
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Maps help us navigate strange towns and roads. By correlating what we see out the windshield with the street names on the map, we can readily determine where we are or just how lost we are! Likewise, given a map of its environment, a robot could use its various sensors to correlate its position with the information in a map. Map-based positioning, also known as map matching, uses a map you prepare for the robot or that the robot prepares for itself. During navigation, the robot uses whatever sensors it has at its disposal (infrared, ultrasonic, vision, etc.) to visualize its environment. It checks the results of its sensors against the map previously stored in its memory. From there, it can compute its actual position and orientation. One common technique, developed by robot pioneer Hans Moravec, uses a certainty grid that consists of squares drawn inside the mapped environment (think of graph paper used in school). Objects, including obstacles, are placed within the squares. The robot can use this grid map to determine its location by attempting to match what it sees through its sensors with the patterns on the map. Obviously, map matching requires that a map of the robot s environment be created first. Several consumer robots, like the Cyebot, are designed to do this mapping autonomously
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