1. EE 495 Modern Navigation Systems Inertial Sensors Wed, Feb 17 EE 495 Modern Navigation Systems Slide 1 of 18

2. Inertial Sensors Wed, Feb 17 EE 495 Modern Navigation Systems As the name implies, inertial sensors measure motion wrt an inertial frame  Advantages: Self-contained & non-reliant on external fields (e.g., EM radiation, Earth’s magnetic field, …)  Disadvantages: Typically rate measurements & expensive Accelerometers measure linear acceleration  Actually measure specific force, typically, in the body frame Gyroscopes measure angular velocity  Most gyroscopes measure angular speed, typically, in the body frame Slide 2 of 18

3. Inertial Sensors Accelerometers Wed, Feb 17 EE 495 Modern Navigation Systems Inertial Sensors Accelerometers Pendulous Mass Vibratory Closed loop Open loop Closed loop Open loop Gyroscopes Slide 3 of 18

4. Inertial Sensors Accelerometer: Pendulous Mass Wed, Feb 17 EE 495 Modern Navigation Systems Acceleration due to gravity Reaction force Mass (m) damper k spring b displacement (x) Sense axis Slide 4 of 18

5. Inertial Sensors Accelerometer: Pendulous Mass Wed, Feb 17 EE 495 Modern Navigation Systems Pendulous Accelerometer  Closed loop config. (generates a force to null the displacement) o Improved linearity and measurement range Figure: Clipp (2006) Sensitive axis Slide 5 of 18

6. Inertial Sensors Accelerometer: Vibratory Wed, Feb 17 EE 495 Modern Navigation Systems Vibratory accelerometers  Vibrating Beam Accelerometers (VBA)  Acceleration causes a change in resonance frequency Mass Sensitive axis Acceleration Slide 6 of 18

7. Inertial Sensors Accelerometer: Vibratory Wed, Feb 17 EE 495 Modern Navigation Systems MEMS Accelerometers www.ett.bme.hu/memsedu Slide 7 of 18

8. Inertial Sensors Accelerometer: Vibratory Wed, Feb 17 EE 495 Modern Navigation Systems MEMS Accelerometers  Spring and mass from silicon and add fingers make a variable differential capacitor  Change in displacement => change in capacitance CS1 < CS2 APPLIED ACCELERATION SENSOR ACCELERATING MASS SPRING SENSOR AT REST FIXED ANCHOR TO SUBSTRATE Slide 8 of 18

9. Inertial Sensors Gyroscopes Wed, Feb 17 EE 495 Modern Navigation Systems Inertial Sensors Gyroscopes Rotating Mass Sagnac Effect Coriolis Effect FloatedDTG Fluid Suspension Magnetic Suspension Mech Suspension ResonatorInterferometer Ring Laser Gyro Fiber Optic Gyro Hemispherical Resonator Gyro magnetohydrodynamic Conductive fluid based Microelectromechanical Accelerometers Slide 9 of 18

10. Inertial Sensors Gyroscopes: Rotating Mass Wed, Feb 17 EE 495 Modern Navigation Systems Slide 10 of 18

11. Inertial Sensors Gyroscopes: Rotating Mass x y z H(t+dt) H(t)  dt Wed, Feb 17 EE 495 Modern Navigation Systems H = Angular momentum Slide 11 of 18

12. Inertial Sensors Gyroscopes: Rotating Mass y z Wed, Feb 17 EE 495 Modern Navigation Systems H = Angular momentum Slide 12 of 18 x 

13. Inertial Sensors Gyroscopes: Sagnac Effect Gyros Wed, Feb 17 EE 495 Modern Navigation Systems Fiber Optical Gyro (FOG)  Basic idea is that light travels at a constant speed  If rotated (orthogonal to the plane) one path length becomes longer and the other shorter  This is known as the Sagnac effect  Measuring path length change (over a dt) allows  to be measured R  Detector Transmitter Slide 13 of 18

14. Inertial Sensors Gyroscopes: Sagnac Effect Gyros Fiber Optical Gyro (FOG)  Measure the time difference betw the CW and CCW paths  CW transit time = t CW  CCW transit time = t CCW  L CW = 2  R+R  t CW = ct CW  L CCW = 2  R-R  t CCW = ct CCW  t CW = 2  R/(c-R  )  t CCW = 2  R/(c+R  )  With N turns  Phase R  Splitter Transmitter Detector R  Splitter Transmitter Detector Wed, Feb 17 EE 495 Modern Navigation Systems Slide 14 of 18

15. Inertial Sensors Gyroscopes: Sagnac Effect Gyros Wed, Feb 17 EE 495 Modern Navigation Systems Ring Laser Gyro  A helium-neon laser produces two light beams, one traveling in the CW direction and the other in the CCW direction  When rotating o The wavelength in dir of rotation increases (decrease in freq) o The wavelength in opposite dir decreases (increase in freq) o Similarly, it can be shown that Slide 15 of 18

16. Inertial Sensors Gyroscopes: Coriolis Effect Vibratory Coriolis Angular Rate Sensor  Virtually all MEMS gyros are based on this effect Linear motion   Wed, Feb 17 EE 495 Modern Navigation Systems Slide 16 of 18

17. Inertial Sensors Gyroscopes: Coriolis Effect Basic Planar Vibratory Gyro Wed, Feb 17 EE 495 Modern Navigation Systems Slide 17 of 18

18. Inertial Sensors Gyroscopes: Coriolis Effect In plane sensing (left) Out of plane sensing (right) www.ett.bme.hu/memsedu Wed, Feb 17 EE 495 Modern Navigation Systems Slide 18 of 18

19. Inertial Sensors Summary Wed, Feb 17 EE 495 Modern Navigation Systems Accelerometers  Measure specific force of the body frame wrt the inertial frame in the body frame coordinates o Need to remove the acceleration due to gravity to obtain the motion induced quantity  In general, all points on a rigid body do NOT experience the same linear velocity Gyroscopes  Measure the inertial angular velocity o Essentially, the rate of change of orientation  All points on a rigid body experience the same angular velocity Slide 19 of 18