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MARK LOONEY
MEMS IMUsfor GNC(Guidance Navigation Control)
24 June 2019 ©2019 Analog Devices, Inc. All rights reserved.1
What is an IMU (Inertial Measurement Unit)?
► Angular rate of rotation (spin rate) Delta-angle
► Linear acceleration Delta-velocity Orientation, with respect to gravity
(aka….tilt, incline angle)
► Triaxial measurements Mutually orthogonal
► Legacy IMUs also had magnetometers and barometers
► Primary use is in dynamic orientation tracking► Secondary use in short-term velocity and
position tracking
Analog Devices Confidential Information. ©2018 Analog Devices, Inc. All rights reserved.2
Y-AXIS
ωz
X-AXIS
Z-AXIS
ωxωy
1543
8-02
9
az
axay
Y-AXIS X-AXIS
Z-AXIS
1543
8-03
1
Let’s start with basic pointing and noise influences
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What are IMUs used for? Measure angles
► Accelerometers respond to their orientation, with respect to the earth’s gravitational field, according to a very simple trigonometric function
► Gyroscopes measure the angular rate of rotation, around their measurement axis, which enables an simple integration for estimating angle displacement
Analog Devices Confidential Information. ©2018 Analog Devices, Inc. All rights reserved.4
0709
6-00
8ay
θx
ax
θx
HORIZON
GRAVITY = 1g
∅ ·
x
yx a
aa tan
Sensor FusionReal-time
angle estimation
gaa x
x 1sin
Y-AXIS
ωz
X-AXIS
Z-AXIS
ωxωy
1543
8-02
9
What are IMUs used for? Measure angles
► Accelerometers also respond to linear vibration and changes in linear velocity (aka….linear acceleration)
► Gyroscope bias error translates into an angle error, which is proportional to time.
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0709
6-00
8
ay
θx
ax
θx
HORIZON
GRAVITY = 1g
∅ · Y-AXIS
ωz
X-AXIS
Z-AXIS
ωxωy
1543
8-02
9
sin 1
MobileRobots Seekur®Improvement opportunities
► Full implementation of IMU function Terrain compensation of GPS location
data
► Implementing next-generation devices, which represent advancing performance. ADIS16265, ADIS16135, ADIS16385
► Using in-system calibration options. For example, running the robot around a 360° circle while integrating the output, enables application-specific accuracy correction, using a very simple pattern.
Vehicle Platform
Actual locationGPS thinks it is right hereKnowing the tilt angle & height of the receiver to ground enables
this distance to be corrected using simple trigonometery
Gyroscopes: feedback sensing element
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Real-world example
► Optical inspection system► Problem: swinging motion
causes loss of resolution on theinspection surface
► Solution: mounting an IMU on the lens of the camera to track the orientation, sothat a servo motor can adjust the orientationof the lens in an equal but opposite manner
► The effectiveness of this type of system is directly dependent on howwell the IMU can track the orientationof the camera
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Conveyor belt
Video Camera
Swinging motion
ωSW(t)
D
dSW
±φSW
Ideal center of camera view
Basic Feedback Control
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ServoMotor
DigitalFiltering ADIS1647xIntegrator
-
ωG(t)
φE(t)
φCOR(t)
Mechanical Connection
CalibrationAlignment
φCMD(t)
ωF(t)
φP(t)
OPENING INPACKAGE LID
1543
6-04
6
Success!► Optical inspection system► Problem: swinging motion
causes loss of resolution on theinspection surface
► Solution: mounting an IMU on the lens of the camera to track the orientation, sothat a servo motor can adjust the orientationof the lens in an equal but opposite manner
► The effectiveness of this type of system is directly dependent on howwell the IMU can track the orientationof the camera.
► Primary limitation, in this case, isnoise, or Angle Random Walk
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Conveyor belt
Video Camera
Swinging motion
ωSW(t)
D
±φRE
dREIdeal center of
camera view
Why does noise performance matter?
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±φRE
-0.0006
-0.0004
-0.0002
0
0.0002
0.0004
0.0006
0 0.005 0.01 0.015 0.02 0.025
Inte
grat
ion
Erro
r ()
Integration Time (seconds)
ARW = 0.17°/√hour
What messes up your measurements?
► REFERENCES: http://www.analog.com/en/technical-articles/critical-noise-sources-mems-gyroscopes.html http://www.analog.com/en/analog-dialogue/articles/low-noise-feedback-control.html
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What nobody talks about……
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ie: Vehicle-mounted antenna, camera, other optics, etc.ie: Vehicle-mounted antenna, camera, other optics, etc.
Rough conditions cause angular vibration (±10°/sec) in the y-axis (pitch). High cross-axis sensitivity (GCAS) will cause angular jitter on the x-axis (roll).
ØROLL xθPITCH
PIN 1PIN 23
aY
mY
gY
Y-AXIS
gX
X-AXIS
aX
mX
Z-AXIS
aZ mZgZ
1027
7-01
7
Typical Device Spec: +/-2% ADI Spec: <0.087%
Cross-AxisSensitivity
PIN 1PIN 23
aY
mY
gY
Y-AXIS
gX
X-AXIS
aX
mX
Z-AXIS
aZ mZ
gZ
1027
7-01
7
Rough conditions cause up/downvibration (±2g‐rms) in the z-axisHigh Linear-g sensitivity (GL) will cause angular jitter on all three gyroscopes.
ØROLL x
Typical Device Spec: 0.1 o/s/g ADI Spec: 0.015 o/s/g
Linear-gResponse
14
Vibration/Cross-axis on top of noise
ConsequenceNoise/Jitter Increase
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What matters?
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Stability/Repeatability (long term drift; scale and bias)
Noise (angle random walk)
Vibration rectification
Hysteresis
Non-linearity
g-effect error (linear accel)
Offset / Bias
Scale / Gain Error
Tempco’s
Cross Axis Sensitivity
Correctable through test and calibration, to the limits of resolution and stability
Theoretically capable of being corrected through test and calibration, to limits of resolution and stability
Inherent to sensor performance (limited opportunity to calibrate)
ADI D
esigned-in Performance
at MEM
s Sensor LevelAD
I System-Level
Calibration Focus
o Architected to Reject Performance Limiting Errors
o Sensor Conditioning and Filtering Optimized for Reliable Precision at Application Level
o Packaging Minimizes Stress; avoids long-term drift (ie: from overmold/moisture)
o Sub-System Test & Calibration Ensures out-of-box best Precision, & Reliability
o Fully, Conservatively, Specified
Guidance Navigation Systems
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Ground Vehicle Example
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2
1
t
tH dt
Axis of rotation
rategyro K
Independent steering & drivecontrol for all4 wheels!
What are IMUs used for?
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TrajectoryPlanner
ServoControl
&Motor
ServoControl
&Motor
ServoControl
&Motor
ServoControl
&Motor
Forward Kinematics
Encoders Encoders Encoders Encoders
Inverse Kinematics
GyroIMU
GPSor
Laser
TrajectoryPlanner
Localization (position correction)GPS for outdoor systemsLaser range finding for indoor systems
► It is easy to get wrapped up in the entire system
► While remembering that we are looking to support accurate motion representation….
► Look for context with each system, environment, as we help customers understand their performance needs
► For those who seem to “start cheap,” the discussion is in how complex the other inertial observers need to be
► For those who are moving from more expensive technologies, it is about what they have to add/understand, to make ADI IMUs work
Example Robot System Steering control
The forward kinematics system employs Ackermann Steering on all four wheels to help minimize tire slip and improve efficiency.
Each tire will have a different steering angle.
The example shown is for a rack and pinion system, which employs the Ackermann relationship mechanically.
The Mobile Robots Seekur employs this individually on each wheel, using separate servo motors
MobileRobots Seekur®Kinematics Basics, Dead Reckoning via Odometry
D(Tire Diameter)
LLength/Displacement
NC = Number of encoder counts per rotationNE = Number of encoder counts read into Inverse Kinematics
C
EN
NDL
The basic idea is that each wheel uses an optical encoder to measure the wheel rotation, which can be translated into distance traveled, using the following relationships
MobileRobots Seekur®Odometry error sources
D(Tire Diameter)
LLength/Displacement
NC = Number of encoder counts per rotationNE = Number of encoder counts read into Inverse Kinematics
C
EN
NDL
Tire diameter is dependent on: Temperature, tread wear, air pressure
Gear backlash in the drive and steering system Vehicle geometry: relative tire positions Tire slip Non-uniform surface Flex in the structure of the robot BOTTOM LINE: With well-calibrated tires, the odometry-based dead reckoning
provides useful position data over short distances, up to 20 meters
MobileRobots Seekur®GPS: Outdoor position/velocity measurement & correction
GPS receiver receives coded messages from 3-10 satellites, out of a constellation of 24-32.
Flight times are used to measure distance to each satellite. Positions of each satellite are fixed Triangulation techniques lock in on the position Differential GPS uses fixed receiver to reference platform measurements Challenges: Requires line of sight, only provide fixed time position, 1-4SPS
MobileRobots Seekur®Laser: Indoor position measurement & correction
Seekur comes with the SICK LSM111 Laser Range Finder system.
270° scan angles 25-50Hz scan rates 20m range Some conditions requires a stop to
get stable measurements.
What are IMUs used for?
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Indoor: Gyroscope feedback
Indoor: Poor or no gyro feedback Massive improvement, expansion of robot capability
Outdoor:- Uncertain terrain- GPS obstruction
management
http://www.analog.com/en/analog-dialogue/articles/inertial-sensors-and-autonomous-operation-in-robots.html
MEMS GyroscopesTypical Block Diagram
Axis of rotation
rategyro K Gyroscopes are angular rate sensors They provide a simple relationship
between angular rate and the electrical output signal.
Assuming a single-axis (yaw/z), the heading estimate is calculated by integrating the angular rate.
2
1
t
tH dt
iSensor®
Understanding specifications – mathematical representation
Axis of rotation
rategyro K
MEMS Gyroscope ImplementationImportant performance parameters, scale accuracy
Sensitivity error directly translates to heading error when the gyroscope is rotating.
2
1
2
1
2
1
1t
t
t
t
t
tH dtKdtKdtK
Error term from sensitivity error
Correct HeadingSensitivity Error
MEMS Gyroscope ImplementationImportant performance parameters: bias accuracy
► Noise is dependent on bandwidth and will impact bias estimates.
► Alan Variance curves provide a relationship between bias accuracy and averaging time.
► For the Seekur system to get the best bias accuracy out of the ADIS16135, the Allan Variance shows that an average of 100 seconds will provide ~0.002 °/sec of bias accuracy.
► The Allan Variance curve also provides accuracy for lower average times, in case the application doesn’t have 100 seconds
► In-run bias stability is the minima on the curve. This time also sets the optimal integration time (t2-t1) for the heading calculation.
► In the case of the ADIS16135, t2-t1 = 100 seconds will provide the best accuracy.
0888
8-00
7
1 10 100 1k0.001
0.1
0.01
10k
(°/s
ec)
Tau (sec)
2
1
t
tH dt
Quick reference to typical cause/effect
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de Ψe
de
Ψe
Heading error = Ψe
Position error = de
Sensitivity error causes heading and position errors during a turn
Nonlinearity (2nd order) causes a heading error that can show up in patterns like an S-turn
Bias causes a drift in heading and position errors, even when there is zero turning.
de
Ψe
Proper path, heading position in blueError-burdened path in red ADIS16495:
+/-0.2% error over temperature0.05% end of life!
©2019 Analog Devices, Inc. All rights reserved.30 24 June 2019
Presented By:Mark Looney
Application Engineer
Analog Devices, Inc.One Technology WayNorwood, MA 02062PHONE [email protected]