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Inertial Measurement Units (IMUs) – Theory and Practice

Inertial Measurement Units (IMUs) – Theory and Practice. H.J. Sommer III, Ph.D. The Pennsylvania State University University Park, PA 16802 hjs1@psu.edu www.mne.psu.edu/sommer. Inertial Measurement Unit ?. Kinematic measurements using inertial references Attitude and magnetic heading

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Inertial Measurement Units (IMUs) – Theory and Practice

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  1. Inertial Measurement Units(IMUs) – Theory and Practice H.J. Sommer III, Ph.D. The Pennsylvania State University University Park, PA 16802 hjs1@psu.edu www.mne.psu.edu/sommer IMU Tutorial 10.05.12

  2. Inertial Measurement Unit ? • Kinematic measurements using inertial references • Attitude and magnetic heading • Angular velocity • Acceleration • Fuse data to provide more reliable results IMU Tutorial 10.05.12

  3. Inertial Measurement Unit ? 14x28 mm IMU Tutorial 10.05.12

  4. Inertial Measurement Unit ? IMU Tutorial 10.05.12

  5. qOP m, JP qOP qP rP qOP+qP h r rP s Inertial Measurement Unit ? IMU Tutorial 10.05.12

  6. Inertial Measurement Unit ? IMU Tutorial 10.05.12

  7. Inertial Measurement Unit ? IMU Tutorial 10.05.12

  8. Traditional KinematicMeasurements • Photogrammetry • Absolute location of point markers • Goniometry • Relative angles across body segments • Electromagnetic digitizers • 6DOF of discrete sensors IMU Tutorial 10.05.12

  9. Photogrammetry IMU Tutorial 10.05.12

  10. Photogrammetry Quiz(for Oldtimers) • Vanguard or RightGuard? • DLT or BLT? • Lo-Cam or Hi-Cam? IMU Tutorial 10.05.12

  11. Photogrammetry • Positive • Absolute location and attitude of body segments • Multiple IR cameras with ambient lighting • Automatic marker tracking • No cables to subject • > 100 Hz, high resolution • Markerless motion capture (MMC) IMU Tutorial 10.05.12

  12. Photogrammetry • Negative • Calibration relative to anatomy (joints and mass centers) • Requires finite differences for velocity and acceleration • Marker occlusion • Soft tissue artifact • Limited workspace in a gait lab IMU Tutorial 10.05.12

  13. Goniometry IMU Tutorial 10.05.12

  14. Goniometry • Positive • Direct measurement of joint motion • Easy to use • Negative • Does not measure absolute position/attitude • Physical attachment to subject IMU Tutorial 10.05.12

  15. Electromagnetic Digitizers IMU Tutorial 10.05.12

  16. Electromagnetic Digitizers • Positive • 6 DOF for each body segment • Negative • Limited workspace • Cables (new wireless) • Physical attachment to subject • Accuracy degraded by speed IMU Tutorial 10.05.12

  17. IMUs Integrated Kinematic Sensor (IKS) Wu and Ladin, 1993 IMU Tutorial 10.05.12

  18. IMUs • Attitude relative to gravity vector • Magnetic heading • Rotational velocity • Translational acceleration IMU Tutorial 10.05.12

  19. IMUs • Positive • Absolute attitude of body segments • Direct measurement of angular velocity • Direct measurement of acceleration • No marker occlusion • Large work space in unstructured environment IMU Tutorial 10.05.12

  20. IMUs • Negative • Does not provide absolute location, translational velocity or rotational acceleration • Calibration relative to anatomy • Soft tissue artifact • Data communication • < 100 Hz, medium resolution IMU Tutorial 10.05.12

  21. History of IMUs • Vehicle navigation • Intercontinental ballistic missiles (ICBM) • Nuclear submarines • Cruise missiles • MicroElectroMechanical Systems (MEMS) • Automotive • Consumer products IMU Tutorial 10.05.12

  22. MEMS IMUs - Automotive • Automotive • Accelerometers to deploy airbags • Vehicle roll handling IMU Tutorial 10.05.12

  23. MEMS IMUs – Consumer Products • Games (WiiMote) • PDA (iPhone) • Camera stabilization • Hard disks IMU Tutorial 10.05.12

  24. MEMS Fabrication IMU Tutorial 10.05.12

  25. MEMS Comb Sensor/Drive IMU Tutorial 10.05.12

  26. MEMS accelerometer(proof mass) gravity acceleration IMU Tutorial 10.05.12

  27. MEMS accelerometer IMU Tutorial 10.05.12

  28. MEMS gyro (tuning fork) IMU Tutorial 10.05.12

  29. MEMS magnetometer (magnetoresistive) IMU Tutorial 10.05.12

  30. MEMS IMU Outputs • Signal • Analog voltage (0 to 3V) • Fixed frequency, variable duty cycle • Digital (internal A/D converter) • Bandwidth • < 150 Hz IMU Tutorial 10.05.12

  31. Two-Dimensional (2D) IMU • Biaxial accelerometer • Uniaxial gyro IMU Tutorial 10.05.12

  32. az ay ax Three-Dimensional (3D) IMU • Triaxial accelerometer • Triaxial gyro • Triaxial magnetometer • Required to determine spin about gravity vector IMU Tutorial 10.05.12

  33. MEMS 9DOF IMU • Triaxial accelerometer • ±3g, 300 mV/g, 550 Hz • Triaxial gyro • ±300 deg/sec (dps), 3.3mV/dps, 140 Hz • Triaxial magnetometer • 50 Hz • On-board CPU, serial I/O IMU Tutorial 10.05.12

  34. Break Time Stand up Stretch Say hello to your neighbor IMU Tutorial 10.05.12

  35. Data Fusion • Sensor uncertainty • Geometric • Rigid body • Articulated model • State space • Kalman filter IMU Tutorial 10.05.12

  36. Sensor Uncertainty • s = measured signal • b = zero drift or bias (function of temp) • f = scale factor (function of temp) • w = Gaussian white noise • s2 = variance IMU Tutorial 10.05.12

  37. LSY530 gyro ±300 degps • Nonlinearity ±1% • b = 1.23 V, 0.05 degps/C° • f = 300 degps/V, 0.05 %/C° • s = 0.035 degps/sqrt(Hz) pink noise IMU Tutorial 10.05.12

  38. ayC axC C ayD axD r D Rigid Body Fusion • Multiple IMUs per body • Parallel axes • Rejects gravity effects IMU Tutorial 10.05.12

  39. P G ayD axD D Articulated Model - Pendulum IMU Tutorial 10.05.12

  40. Multiple Segment Model IMU Tutorial 10.05.12

  41. Kalman Filter • Uses state space model • Position • Velocity • Adaptive time domain filter • Combines states • Tracks variance-covariance • Rejects zero drift IMU Tutorial 10.05.12

  42. Kalman Filter - 2D IMU IMU Tutorial 10.05.12

  43. Kalman Filter - Simplified IMU Tutorial 10.05.12

  44. Kalman Filter – Prediction probability q latitude IMU Tutorial 10.05.12

  45. Kalman Filter - Measurement probability q latitude IMU Tutorial 10.05.12

  46. Kalman Filter - Correction probability q latitude IMU Tutorial 10.05.12

  47. Kalman Filter - Prediction probability constant speed fixed time q latitude IMU Tutorial 10.05.12

  48. Kalman Filter – 2D IMU probability q angle IMU Tutorial 10.05.12

  49. Kalman Filter - Extended • State space • Include acceleration • Nonlinear state relationships • ax-ay-qdot versus q-qdot • Include geometric multisegment model • Include states for multiple bodies IMU Tutorial 10.05.12

  50. Kalman Filter IMU Tutorial 10.05.12

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