Inertial Sensors Using Accelerometers

1
Inertial SensorsUsing Accelerometers
Gyrosfor FIRST Robotics

• Jan 6, 2007
• Chris Hyde
• (Also of Team 1073 TheForceTeam.com )

2
During the Game (particularly Autonomous)Things
you might like to know

• How far has the Robot traveled?
• Did it turn? How much?
• Where is it now?
• Where is it pointing (orientation)?
• Is it level or on an incline (or on its side)?
• Did it hit something?
• Things Inertial Measurements can Answer

3
Newtonian Mechanics
Coriolis Acceleration
MEMs
Data Acquisition
Filtering
Integration
zeptofarads
PID Algorithm
Inertial Navigation Odometry
4
I LOVE THE SMELL OF PHYSICS IN THE MORNING
(with regrets to Coopola)

• Newtons 1st Law
• Every body continues in its state of rest, or
  uniform motion in a straight line, unless it is
  compelled to change that state by forces
  impressed on it
• Newtons 2nd Law
• Acceleration is proportional to the resultant
  force and is in the same direction as this force
• Which translates to
• F ma mf mg
• Where f Acceleration from force F, other than
  gravitational acceleration (g)

5
Inertial Measurements

• What do you need to measure?
• Tilt (inclination) - Accelerometer
• Acceleration (speed distance via integration) -
  Accelerometer
• Shock - Accelerometer
• Vibration - Accelerometer
• Angular rate (rotational) - Gyroscope

6
Inertial Sensors 101
What Does an Accelerometer do?

• Measurement of static gravitational force
• e.g. Tilt and inclination
• Measurement of dynamic acceleration
• e.g. Vibration and shock measurement
• Inertial measurement of velocity and position
• Acceleration single integrated for velocity
• Acceleration double integrated for position

7
How Do Accelerometers Work?

• Acceleration can be measured using a simple
  mass/spring system.
• Force Mass Acceleration
• Force Displacement Spring Constant
• So Displacement Mass Acceleration / Spring
  Constant

Change in Displacement
Add Acceleration
MASS
MASS
8
So Whats all this MEMs Stuff ?

• Micro Electro-Mechanical Systems
• Silicon that Moves

9
How Do MEMs Accelerometers Work?

• We use Silicon to make the spring and mass, and
  add fingers to make a variable differential
  capacitor
• We measure change in displacement by measuring
  change in differential capacitance

10
Silicon that MovesSuspended Structures
11
MEMs Accelerometer
Source Great MEMS education sitewww.ett.bme.hu/m
emsedu/
12
C to V conversion
100KHz
CLOCK A
MOVABLE BEAM
ACCELERATION
AMP
UNIT CELL
CLOCK B
RECTIFIED VOLTAGE OUTPUT
SYNCHRONOUS DEMODULATOR
13
ADXL203 2D Accelerometer Die Photo
14
ADXL 2D Proof Mass Springs

• All anchors placed close to the beam center
• Stoppers at the outside of beam
• Self-test elements at the outside of beam

ADI Proprietary Information
15
Determining RotationCoriolis Effect and
Acceleration
Acor
v
w

• Acor 2 (w v)
• w applied angular rate
• v Velocity

Left Image Source Wikipedia http//en.wikipedia.o
rg/wiki/Coriolis_effect
16
Gyro
What Does a Gyro Do?

• Measures angular rate (how fast it is turning
  around its axis).
• Measures change of inclination or change of
  direction by integration of angular rate.

17
Gyro Principle of Operation

• How does it measure angular rate?
• By measuring the Coriolis force
• What is the Coriolis force?
• When an object is moving in a periodic fashion
  (either oscillating or rotating), rotating the
  object in an orthogonal plane to its periodic
  motion causes a translational force in the other
  orthogonal direction.

ROTATION
CORIOLIS FORCE
OSCILLATION
MASS
18
MEMs Gyro Operation
Coriolis acceleration
Coriolis Sense Fingers
Resonator tether
Resonator
Resonator Drive Fingers
Applied Rotation
Resonator motion
Accelerometer frame
Accelerometer tether
19
MEMs Comb Drive
Source www.ett.bme.hu/memsedu/
20
Gyro Animation
Source www.ett.bme.hu/memsedu/
21
ADXRS150 Gyro Family Beam Structure
Beam movements 16 femtometers (0.000116
Angstroms) Hydrogen 0.5 A Diameter
Resolve 12 x10-21 farads(ZeptoFarads)
22
iMEMs - Integrated IC with MEMs
23
Resonator Control Loop
Drive
? 90
Sense
Clipping Amplifier
Trans-resistance Amp
24
Coriolis Measurement Signal Chain
Moving Fingers _at_ 1.5V
Beam
Gain proportional to temperature
Trans-Capacitance Amp
Fixed Finger _at_ 12V
12V
25
Coriolis Measurement Signal Chain
How it really works
Beam 1
Trans-Capacitance Amp
Beam 2
Max Out 300uV
Large common mode signals (shock) are removed
before amplification, so huge dynamic range is
available
26
Applying Accelerometers and Gyros in the Robot

• Some things to do, dont do, etc.

27
Placement Mounting

• Q Does it matter where how they are mounted?
• A Yes and No.
• Best sensitivity when mounted in proper
  orientation
• Keep level for Navigation, Mount on side for tilt
• Avoid vibration places that flex - Makes
  measurements easier
• Doesnt need to be at center of rotation
• Keep them electrically close to the controller
• Wire parasitic resistance will reduce performance
• Keep wires short

28
Limits on Rotation Rate

• The kit gyro is an /- 80 degree/sec device
• Use in Autonomous mode is OK with slow turns
• Rotation gt 80 deg/s will not be shown at the
  output
• While there is a work around if you had access to
  the pins of the gyro, the FIRST board doesnt
  have that access.
• If you did you could put a 60.4K resistor in the
  feedback of the on chip output amplifier (pins 1B
  to 1C), shich would give 320 deg/s
• Buy ADXRS300EB or ADXRS150EB Evaluation boards
  from DigiKey and use them (300 or 150 deg/s)
• www.digikey.com

29
Getting the data into the controller

• Voltage outputs need to be sampled by the
  controller A/D converter.
• Must sample at gt 2 x the highest frequency
  (Bandwidth)
• Should sample more
• Use added samples to do some averaging to reduce
  noise, errors
• Can increase resolution by oversampling (gtgt 2X
  freq)
• Supported in EZ-C
• Good insight and details at Kevin Watsons
  wonderful site
• www.kevin.org/frc
• Also www.Chiefdelphi.com
• READ THE DATA SHEETS !!!

30
What to do with the data?

• To get distance traveled, integrate twice the
  accelerometer data.
• To get rotational change, integrate gyro once.
• Good white papers at www.chiefdelphi.com
• Use in PID control to guide your robot

31
PID Algorithm

• P - Proportional - The amount of correction
  (Gain) is based on (proportional to) the error
  between where we are and where we want to be
• I - Integral - The amount of correction (Gain) is
  based on the amount of time the error has gone
  uncorrected
• D - Differential - The amount of correction
  (Gain) is based on how fast the error is changing
  - Anticipate the future

32
What do the Gains do?

• The Gain terms define how important each of the
  PID terms are.
• Kp - Proportional Gain - Determines how fast your
  system reacts to error
• Ki - Integral Gain - Determines how hard your
  system will push to overcome error.
• Kd - Differential Gain - Limits the change in
  response to error. Helps to dampen or smooth the
  reactions.

33
How do I Tune my PID Control System ?

• Start by setting the Proportional gain (Kp)
  lowSet the Integral and Diferential gains (Ki,
  Kd) to zero
• Increase Kp until the system starts to react
  quickly enough. It will overshoot if you set it
  too high.
• Now increase Kd to compensate for overshoot. Now
  the system should react smoothly.

34
How do I Tune my PID Control System ?

• But you might notice that it never reaches the
  goal. That is because resistance in the system
  is holding it back and as you near the goal, the
  proportional term gets smaller and doesnt
  provide enough force to move the mass.
• Now it is time to increase Ki. Over time the
  error will build and the I term allows the system
  to overcome resistance.
• Youll probably need to go back and tune each of
  the terms to get the response you want in the
  time you have.

35
Thanks and Good Luck !

• Extra support material follows

36
Common Questions Accelerometer Gyro

• Why is there a maximum shock rating?
• Inertial sensors have moving parts inside. If you
  shock them hard enough, you can break them.
• What happens if I exceed the maximum shock rating
• Generally nothing. Most of our inertial sensors
  can handle very large shocks (tens of thousands
  of g) several times. But do it often enough and
  you may cause damage.
• What does the output do during high shock events?
• The output may rail for a short time (time
  constant determined by filter bandwidth)
• Occasionally output may be stuck at rail until
  power is cycled

37
Common Questions Accelerometer Gyro

• What is temperature hysteresis?
• All MEMS sensors (and most sensors in general)
  have some degree of temperature hysteresis.
• The zero point varies depending on whether the
  part goes from cold to hot, or hot to cold (see
  graph)
• The amount of hysteresis for a given part depends
  on the magnitude of the temperature excursion.

Temperature Hysteresis
38
Common Questions - Accelerometer

• Why is the output not Vdd/2 (or 50 for PWM
  outputs) at zero g?
• Initial zero g output varies from part-to-part,
  and also over temperature. Each part number has a
  specified initial zero g output on the data
  sheet.
• Why is the initial zero g output different on the
  X and Y axes?
• The 2 axes are independent. Both axes zero g
  output will comply with the spec sheet.
• Why does the zero g tempco, self test response,
  initial zero g output, you-name-it, vary from
  part-to-part?
• Because it does. Sorry, you have to live with it.
  We offer a broad array of parts with varying
  levels of accuracy. Choose one that has the
  performance you want.

39
Common Questions - Accelerometer

• I am only interested in tilt information. Why
  does acceleration information corrupt the output
  (or vice versa I want acceleration, but tilt
  disturbs me)?
• Tilt and acceleration are indistinguishable to
  the accelerometer. They are both acceleration.
  They only differ in frequency content. One can
  use a filter (high or low pass) to remove the
  undesirable frequency content, but no filter is
  perfect. It is very hard to pick out a few mg of
  tilt information from dozens of g of vibration,
  for example.

40
Common Questions Gyro

• Explain noise density, and how does that relate
  to random angle walk?
• Noise on our gyros is expressed in
  degrees/second/root Hz because the noise is
  Gaussian (equivalent noise energy at all
  frequencies). So the total output noise depends
  on the bandwidth chosen by the user.
• Random angle walk is expressed in
  degrees/second/second, so if we look at a 1
  second period, the random angle walk is
  equivalent to the noise density
• So can I reduce the bandwidth to almost zero and
  get virtually no noise?
• No. Reducing the bandwidth below the 1/f
  frequency (0.3Hz) of the output amplifier offers
  no further improvement.
• So how can I reduce the noise further?
• You can average the output if several gyros. For
  n gyros the noise will reduce by a factor of
  SQRT(n).

41
Common Questions - Gyro

• If I integrate the output over time the zero
  position drifts. Why is this, and how much drift
  can I expect?
• Integrating the gyro output over time allows
  errors to accumulate and grow.
• All gyros experience this effect. It is usually
  referred to as Null Stability, and expressed in
  degrees/hour.
• There are 2 sources of error that impact null
  stability over time
• Null stability over temperature
• Allen variance
• Null drift due to temperature is the dominant
  mechanism
• A 3 point temperature compensation scheme will
  give you about 300 degrees/hour null stability.
  More points will do better.
• Allen variance is an expression of the average
  over the sum of the squares of the differences
  between successive readings of the null output
  sampled over the sampling period.
• ADXRS150/300 Allen variance settles to about 75
  degrees/hour
• This is as good as youll get, even with perfect
  temperature compensation

42
Common Questions - Gyro

• Why is your gyro so noisy compared to
• Our gyro might appear noisy on the bench, but
• Our design is very resistant to external shock
  and vibration.
• Virtually all of our competitors are very
  sensitive to external shock and vibration. It
  adds a lot of noise to their output.
• As a result, in the real world our noise
  performance is usually better than our
  competitors. Often by a wide margin.