EE 495 Modern Navigation Systems Inertial Sensors Monday, Feb 09 EE 495 Modern Navigation Systems Slide 1 of 19

Inertial Sensors Monday, Feb 09 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 19

Inertial Sensors Accelerometers Monday, Feb 09 EE 495 Modern Navigation Systems Inertial Sensors Accelerometers Pendulous Mass Vibratory Closed loop Open loop Closed loop Open loop Gyroscopes Slide 3 of 19

Inertial Sensors Accelerometer: Pendulous Mass Monday, Feb 09 EE 495 Modern Navigation Systems Acceleration due to gravity Reaction force Mass (m) damper k spring b displacement (x) Sense axis Slide 4 of 19

Inertial Sensors Accelerometer: Pendulous Mass Monday, Feb 09 EE 495 Modern Navigation Systems Closed-loop version generates a force to null the displacement  Can improve linearity and measurement range Slide 5 of 19

Inertial Sensors Accelerometer: Pendulous Mass Monday, Feb 09 EE 495 Modern Navigation Systems Pendulous Accelerometer  Closed loop configuration o Improved linearity Figure: Clipp (2006) Sensitive axis Slide 6 of 19

Inertial Sensors Accelerometer: Vibratory Monday, Feb 09 EE 495 Modern Navigation Systems Vibratory accelerometers  Vibrating Beam Accelerometers (VBA)  Acceleration causes a change in resonance frequency Mass Sensitive axis Slide 7 of 19

Inertial Sensors Accelerometer: Vibratory Monday, Feb 09 EE 495 Modern Navigation Systems MEMS Accelerometers Slide 8 of 19

Inertial Sensors Accelerometer: Vibratory Monday, Feb 09 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 9 of 19

Inertial Sensors Gyroscopes Monday, Feb 09 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 10 of 19

Inertial Sensors Gyroscopes: Rotating Mass Monday, Feb 09 EE 495 Modern Navigation Systems Slide 11 of 19

Inertial Sensors Gyroscopes: Rotating Mass x y z Precession rate (  ) H(t+dt) H(t)  dt Monday, Feb 09 EE 495 Modern Navigation Systems Slide 12 of 19 H = Angular momentum

Inertial Sensors Gyroscopes: Sagnac Effect Gyros Monday, Feb 09 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 19

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 Monday, Feb 09 EE 495 Modern Navigation Systems Slide 14 of 19

Inertial Sensors Gyroscopes: Sagnac Effect Gyros Monday, Feb 09 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 19

Inertial Sensors Gyroscopes: Coriolis Effect Vibratory Coriolis Angular Rate Sensor  Virtually all MEMS gyros are based on this effect Linear motion   Monday, Feb 09 EE 495 Modern Navigation Systems Slide 16 of 19

Inertial Sensors Gyroscopes: Coriolis Effect Basic Planar Vibratory Gyro Monday, Feb 09 EE 495 Modern Navigation Systems Slide 17 of 19

Inertial Sensors Gyroscopes: Coriolis Effect In plane sensing (left) Out of plane sensing (right) Monday, Feb 09 EE 495 Modern Navigation Systems Slide 18 of 19

Inertial Sensors Summary Monday, Feb 09 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 19