Inertial Measurement Units IMUs Theory and Practice H

Inertial Measurement Units (IMUs) – Theory and Practice H. J. Sommer III, Ph. D. The Pennsylvania State University Park, PA 16802 hjs 1@psu. edu www. mne. psu. edu/sommer IMU Tutorial 10. 05. 12 1

Inertial Measurement Unit ? n Kinematic measurements using inertial references n n Attitude and magnetic heading Angular velocity Acceleration Fuse data to provide more reliable results IMU Tutorial 10. 05. 12 2

Inertial Measurement Unit ? 14 x 28 mm IMU Tutorial 10. 05. 12 3

Inertial Measurement Unit ? IMU Tutorial 10. 05. 12 4

Inertial Measurement Unit ? q. OP m, JP q. OP q. P h r. P q. OP+ q. P r s IMU Tutorial 10. 05. 12 5

Inertial Measurement Unit ? IMU Tutorial 10. 05. 12 6

Inertial Measurement Unit ? IMU Tutorial 10. 05. 12 7

Traditional Kinematic Measurements n Photogrammetry n n Goniometry n n Absolute location of point markers Relative angles across body segments Electromagnetic digitizers n 6 DOF of discrete sensors IMU Tutorial 10. 05. 12 8

Photogrammetry IMU Tutorial 10. 05. 12 9

Photogrammetry Quiz (for Oldtimers) n Vanguard or Right. Guard? n DLT or BLT? n Lo-Cam or Hi-Cam? IMU Tutorial 10. 05. 12 10

Photogrammetry n Positive n n n 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 11

Photogrammetry n Negative n n n 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 12

Goniometry IMU Tutorial 10. 05. 12 13

Goniometry n Positive n n n Direct measurement of joint motion Easy to use Negative n n Does not measure absolute position/attitude Physical attachment to subject IMU Tutorial 10. 05. 12 14

Electromagnetic Digitizers IMU Tutorial 10. 05. 12 15

Electromagnetic Digitizers n Positive n n 6 DOF for each body segment Negative n n Limited workspace Cables (new wireless) Physical attachment to subject Accuracy degraded by speed IMU Tutorial 10. 05. 12 16

IMUs Integrated Kinematic Sensor (IKS) Wu and Ladin, 1993 IMU Tutorial 10. 05. 12 17

IMUs n n Attitude relative to gravity vector Magnetic heading Rotational velocity Translational acceleration IMU Tutorial 10. 05. 12 18

IMUs n Positive n n n 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 19

IMUs n Negative n n n 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 20

History of IMUs n Vehicle navigation n n Intercontinental ballistic missiles (ICBM) Nuclear submarines Cruise missiles Micro. Electro. Mechanical Systems (MEMS) n n Automotive Consumer products IMU Tutorial 10. 05. 12 21

MEMS IMUs - Automotive n n Accelerometers to deploy airbags Vehicle roll handling IMU Tutorial 10. 05. 12 22

MEMS IMUs – Consumer Products n n Games (Wii. Mote) PDA (i. Phone) Camera stabilization Hard disks IMU Tutorial 10. 05. 12 23

MEMS Fabrication IMU Tutorial 10. 05. 12 24

MEMS Comb Sensor/Drive IMU Tutorial 10. 05. 12 25

MEMS accelerometer (proof mass) gravity acceleration IMU Tutorial 10. 05. 12 26

MEMS accelerometer IMU Tutorial 10. 05. 12 27

MEMS gyro (tuning fork) IMU Tutorial 10. 05. 12 28

MEMS magnetometer (magnetoresistive) IMU Tutorial 10. 05. 12 29

MEMS IMU Outputs n Signal n n Analog voltage (0 to 3 V) Fixed frequency, variable duty cycle Digital (internal A/D converter) Bandwidth n < 150 Hz IMU Tutorial 10. 05. 12 30

Two-Dimensional (2 D) IMU n n Biaxial accelerometer Uniaxial gyro IMU Tutorial 10. 05. 12 31

Three-Dimensional (3 D) IMU n n n Triaxial accelerometer Triaxial gyro Triaxial magnetometer n Required to determine spin about gravity vector az ay ax IMU Tutorial 10. 05. 12 32

MEMS 9 DOF IMU n Triaxial accelerometer n n Triaxial gyro n n ± 300 deg/sec (dps), 3. 3 m. V/dps, 140 Hz Triaxial magnetometer n n ± 3 g, 300 m. V/g, 550 Hz On-board CPU, serial I/O IMU Tutorial 10. 05. 12 33

Break Time Stand up Stretch Say hello to your neighbor IMU Tutorial 10. 05. 12 34

Data Fusion n n Sensor uncertainty Geometric n n n Rigid body Articulated model State space n Kalman filter IMU Tutorial 10. 05. 12 35

Sensor Uncertainty n n n s = measured signal b = zero drift or bias (function of temp) f = scale factor (function of temp) w = Gaussian white noise s 2 = variance IMU Tutorial 10. 05. 12 36

LSY 530 gyro ± 300 degps n n 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 37

Rigid Body Fusion n ay. C ax. C n n C r ay. D Multiple IMUs per body Parallel axes Rejects gravity effects ax. D D IMU Tutorial 10. 05. 12 38

Articulated Model - Pendulum P G ay. D ax. D D IMU Tutorial 10. 05. 12 39

Multiple Segment Model IMU Tutorial 10. 05. 12 40

Kalman Filter n Uses state space model n n n Position Velocity Adaptive time domain filter Combines states Tracks variance-covariance Rejects zero drift IMU Tutorial 10. 05. 12 41

Kalman Filter - 2 D IMU Tutorial 10. 05. 12 42

Kalman Filter - Simplified IMU Tutorial 10. 05. 12 43

Kalman Filter – Prediction probability q latitude IMU Tutorial 10. 05. 12 44

Kalman Filter - Measurement probability q latitude IMU Tutorial 10. 05. 12 45

Kalman Filter - Correction probability q latitude IMU Tutorial 10. 05. 12 46

Kalman Filter - Prediction probability constant speed fixed time q latitude IMU Tutorial 10. 05. 12 47

Kalman Filter – 2 D IMU probability q angle IMU Tutorial 10. 05. 12 48

Kalman Filter - Extended n State space n n Nonlinear state relationships n n Include acceleration ax-ay-qdot versus q-qdot Include geometric multisegment model n Include states for multiple bodies IMU Tutorial 10. 05. 12 49

Kalman Filter IMU Tutorial 10. 05. 12 50

Kalman Filter IMU Tutorial 10. 05. 12 51

Applications n n n Stationary Simple attitude Simple motion Coordinated movement Inverse dynamics IMU Tutorial 10. 05. 12 52

Stationary n n Minimal change in sensor orientation Hand/arm tremor n n n Extended arm, tracing spiral Triaxial accelerometer, >150 Hz Postural sway n n Supracranial accelerometer Lumbar accelerometer IMU Tutorial 10. 05. 12 53

Simple Attitude n Body position during sleep n n Treatment for sleep apnea Triaxial accelerometer, very low sample rate Not interested in spin about gravity vector Restless Leg Syndrome (RLS) n n n Monitor sudden movement High frequency sample rate Interested in event itself, not characterization IMU Tutorial 10. 05. 12 54

Simple Motion n Planar lifting or reaching n n n Simple articulated model 2 D IMU provides position, velocity, acceleration Passive manipulation or drop n n Assess spasticity Compute jerk from acceleration IMU Tutorial 10. 05. 12 55

Coordinated Movement n Basic assessment n n n Triaxial accelerometer, >100 Hz Number of strides, timing Asymmetry of motion n n Rehabilitation, prosthetic fitting Full body motion n n Thirteen 9 DOF IMUs Multiple segment model IMU Tutorial 10. 05. 12 56

Inverse Dynamics n 2 D n n Lower data throughput (3 ch versus 9 ch) Require sagittal and frontal IMUs Does not require magnetometers 3 D n n Lifting or reaching most promising Difficulty in assessing absolute location of feet IMU Tutorial 10. 05. 12 57

Practical Considerations n Motion variables n n Number of IMUs n n Consider alternate signals to describe motion May require two per segment Synchronization n In-shoe pressure transducers IMU Tutorial 10. 05. 12 58

Data Transfer n n Umbilical with local A/D Belt-pack data logger n n Belt-pack wireless n n SD card Bluetooth, longer battery life Network wireless n Dropouts, battery life IMU Tutorial 10. 05. 12 59

Commercial Systems n n n n Xsens MVN Biosyn FAB Nex. Gen Ergonomics Microstrain wireless MEMSense Sparkfun Wi. Tilt Nintendo Wii. Mote IMU Tutorial 10. 05. 12 60