Transcript Micromachined Products Division

The World Leader in High Performance Signal Processing Solutions
Inertial Sensors
Using Accelerometers & Gyro’s
for FIRST Robotics
Jan 6, 2007
Chris Hyde
(Also of Team 1073 TheForceTeam.com )
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 it’s side)?
Did it hit something?
Things
Inertial Measurements can Answer
F  ma
v  2 x
a
 2
t t

“I LOVE THE SMELL OF PHYSICS IN THE MORNING”
(with regrets to Coopola)
 Newton’s
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”
 Newton’s
2nd Law
 “Acceleration
is proportional to the resultant force and is in the
same direction as this force”
 Which
F
translates to…
= ma = mf + mg
 Where f = Acceleration from force F, other than gravitational
acceleration (g)
Inertial Measurements
What
Tilt
do you need to measure?
(inclination) - Accelerometer
Acceleration (speed & distance via integration)
- Accelerometer
Shock - Accelerometer
Vibration - Accelerometer
Angular rate (rotational) - Gyroscope
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
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
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So What’s all this MEM’s Stuff ?
Micro Electro-Mechanical Systems
Silicon that Moves
How Do MEM’s 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
SPRING
APPLIED
ACCELERATION
MASS
FIXED
OUTER
PLATES
SENSOR AT REST
ANCHOR TO
SUBSTRATE
CS1 < CS2
RESPONDING TO AN APPLIED ACCELERATION
(MOVEMENT SHOWN IS GREATLY EXAGGERATED)
Silicon that Moves
Suspended Structures
MEM’s Accelerometer
Source: Great MEMS education site
www.ett.bme.hu/memsedu/
C to V conversion
~100KHz
ACCELERATION
CLOCK A
MOVABLE BEAM
AMP
UNIT CELL
CLOCK B
RECTIFIED VOLTAGE OUTPUT
SYNCHRONOUS DEMODULATOR
ADXL203 2D Accelerometer Die Photo
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
Determining Rotation
Coriolis Effect and Acceleration
Acor
v
w
Left Image Source: Wikipedia
http://en.wikipedia.org/wiki/Coriolis_effect
Acor = 2 * (w*v)
w = applied angular rate
v = Velocity
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.
Gyro Principle of Operation
How
 By
does it measure angular rate?
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
MEM’s Gyro Operation
Coriolis acceleration
Coriolis Sense Fingers
Resonator tether
Resonator
Resonator Drive Fingers
Applied Rotation
Accelerometer frame
Accelerometer tether
Resonator motion
MEM’s Comb Drive
Source:
www.ett.bme.hu/memsedu/
Gyro Animation
Source:
www.ett.bme.hu/memsedu/
ADXRS150 Gyro Family Beam Structure
Resolve 12 x10-21 farads
(ZeptoFarads)
Beam movements 16 femtometers
(0.000116 Angstroms)
Hydrogen 0.5 A Diameter
iMEMs - Integrated IC with MEM’s
Resonator Control Loop
Drive
 = +90°
Sense
Trans-resistance Amp
Clipping Amplifier
Coriolis Measurement Signal Chain
Moving Fingers @ ~+1.5V
Beam
Gain proportional
to temperature
Trans-Capacitance Amp
Fixed Finger @ +12V
+12V
Coriolis Measurement Signal Chain
Beam 1
…How it really works
Trans-Capacitance Amp
Beam 2
Max Out ~ 300uV
Large common mode signals (shock) are removed
before amplification, so huge dynamic range is available
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Applying Accelerometers and
Gyros in the Robot
Some things to do, don’t do, etc.
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
 Doesn’t need to be at center of rotation
 Keep them “electrically close” to the controller
 Wire parasitic resistance will reduce performance
 Keep wires short
Limits on Rotation Rate
 The
kit gyro is an +/- 80 degree/sec device
 Use
in Autonomous mode is OK with slow turns
 Rotation > 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 doesn’t 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
Getting the data into the controller
 Voltage
outputs need to be sampled by the controller A/D converter.
 Must sample at > 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 (>> 2X freq)

 Supported
in EZ-C
 Good
insight and details at Kevin Watson’s wonderful site
 www.kevin.org/frc
 Also
www.Chiefdelphi.com
 READ
THE DATA SHEETS !!!
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
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
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.


How do I Tune my PID Control System ?

Start by setting the Proportional gain (Kp) low
Set 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.
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 doesn’t 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.

You’ll probably need to go back and tune each of the
terms to get the response you want in the time you
have.
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Thanks and Good Luck !
Extra support material follows
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
 The
does the output do during high shock events?
output may rail for a short time (time constant determined by
filter bandwidth)
 Occasionally output may be stuck at rail until power is cycled
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.
Offset vs. Temperature
XL203 AB3902
Lot C05788W1
Temperature
Hysteresis
10
ZgB(mV) with respect to initial ZgB
5
0
X1
X2
X3
X4
X5
X6
X7
X8
-5
-10
-15
-20
-60°C
-40°C
-20°C
0°C
20°C
40°C
60°C
80°C
100°C
Temp C (part going hot first, then cold)
5 degrees per minute going down, 10 degrees per minute going up
120°C
140°C
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.
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.
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).
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 you’ll get, even with perfect temperature compensation

Common Questions - Gyro
 Why
 Our
is your gyro so noisy compared to ……
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.