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INS: Inertial Navigation Systems

INS: Inertial Navigation Systems. An overview of 4 sensors. What is an INS?. Position (dead reckoning) Orientation (roll, pitch, yaw) Velocities Accelerations. Sampling of INS Applications. Accelerometers. Accelerometers. F = ma (Newton’s 2 nd Law) F = kx (Hooke’s Law).

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INS: Inertial Navigation Systems

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  1. INS: Inertial Navigation Systems An overview of 4 sensors

  2. What is an INS? • Position (dead reckoning) • Orientation (roll, pitch, yaw) • Velocities • Accelerations

  3. Sampling of INS Applications

  4. Accelerometers

  5. Accelerometers • F = ma (Newton’s 2nd Law) • F = kx (Hooke’s Law)

  6. Accelerometers • C = ε0A/d (parallel-plate capacitor) • ε0 = permitivity constant • Q = CV Voltage  Capacitance  Surface Area and distance  Spring displacement  Force  Acceleration Integrate to get velocity and displacement

  7. Gyroscopes

  8. Gyroscopes How does it maintain angular orientation? Disk rotating Disk stationary Disk on an axis Red pen indicates applied force

  9. Gyroscopes – Precession As green force is applied to axis of rotation, red points will attempt to move in blue directions These points rotate and continue to want to move in the same direction causing precession Rotating around red axis, apply a moment around axis coming out of paper on red axis

  10. Gyroscopes – Gimbaled • Rotor Axle wants to keep pointing in the same direction • Mounting in a set of gimbals allows us to measure the rotation of the body

  11. Gyroscopes – MEMS • Coriolis effect – “fictitious force” that acts upon a freely moving object as observed from a rotating frame of reference

  12. Gyroscopes – MEMS • Comb drive fingers can be actuated by applying voltage • Coriolis effect induces motion based on rotation • Capacitive sensors (similar to accelerometers) detect the magnitude of this effect and therefore the rotation Vibrating Ring Gyroscope Tuning Fork Gyroscope

  13. Fiber Optic Gyroscope (FOG) DSP 4000 w= attitude rate, 1 = laser light source, 2 = beamsplitter, 3 = wound optical fiber, 4 = photosensor. turret, antenna, and optical stabilization systems

  14. GPS – Global Positioning System • Constellation 27 satellites in orbit • Originally developed by U.S. military • Accuracy ~ 10 m • 3D Trilateration

  15. GPS – 2D Trilateration A B 50 mi 75 mi C You are here 30 mi

  16. GPS – 3D Trilateration • Location of at least three satellites (typically 4 or more) • Distance between receiver and each of those satellites • Psudo-random code is sent via radio waves from satellite and receiver • Since speed of radio signal is known, the lag time determines distance

  17. GPS – Improvements • Some sources of error • Earth’s atmosphere slows down signal • Radio signal can bounce off large objects • Misreporting of satellite location • Differential GPS (DGPS) • Station with known location calculates receiver’s inaccuracy • Broadcasts signal correction information • Accuracy ~ 10 m

  18. GPS – Improvements • WAAS (Wide Area Augmentation System) • Similar to DGPS • Geosynchronous Earth Orbiting satellites instead of land based stations • Accuracy ~ 3 m

  19. Encoders

  20. Encoders – Incremental Photodetector Encoder disk LED Photoemitter

  21. Encoders - Incremental

  22. Encoders - Incremental • Quadrature (resolution enhancing)

  23. Encoders - Absolute • More expensive • Resolution = 360° / 2N where N is number of tracks 4 Bit Example

  24. Pros and Cons

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