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How could we use an accelerometer to find tilt angle?

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The artist exists because the world is not perfect. Art would be useless if the world were perfect, as man wouldn’t look for harmony but would simply live in it. Art is born out of an ill-designed world. Andrei Tarkovsky State Estimation: The search for harmony in an unideal world Mike Robinson.

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Presentation Transcript
slide1

The artist exists because the world is not perfect. Art would be useless if the world were perfect, as man wouldn’t look for harmony but would simply live in it. Art is born out of an ill-designed world. Andrei TarkovskyState Estimation: The search for harmony in an unideal worldMike Robinson

how could we use an accelerometer to find tilt angle
How could we use an accelerometer to find tilt angle?

Product images from Sparkfun electronics

how could we use an accelerometer to find tilt angle1
How could we use an accelerometer to find tilt angle?

Product images from Sparkfun electronics

how could we use a gyroscope to find tilt angle
How could we use a gyroscope to find tilt angle?

Product images from Sparkfun electronics

how could we use a gyroscope to find tilt angle1
How could we use a gyroscope to find tilt angle?

theta = theta + thetaDot*dt

Product images from Sparkfun electronics

slide10
The accelerometer is good long term and the gyroscope is good short term. How can we put them together?
a state estimator lets us combine these two measurements by using feedback
A state estimator lets us combine these two measurements by using feedback

Angle from accelerometer

Signal from gyroscope

Integrate

Multiply by gain

let s see if we can intuitively understand this feedback
Let’s see if we can intuitively understand this feedback

What would happen if the gyroscope signal was zero and our estimate was larger than the angle we measured with the accelerometer?

Angle from accelerometer

Integrate

Multiply by gain

let s see if we can intuitively understand this feedback1
Let’s see if we can intuitively understand this feedback

Angle from accelerometer

If is greater than , then we have a positive number here

Integrate

Multiply by gain

let s see if we can intuitively understand this feedback2
Let’s see if we can intuitively understand this feedback

Angle from accelerometer

If is greater than , then we have a positive number here

Integrate

Multiply by gain

Multiplied by a positive number

let s see if we can intuitively understand this feedback3
Let’s see if we can intuitively understand this feedback

Angle from accelerometer

And integrated, which reduces our estimate of

If is greater than , then we have a positive number here

Integrate

Then subtracted from zero

Multiply by gain

Multiplied by a positive number

the block diagram may look confusing but the code is easy
The block diagram may look confusing, but the code is easy

accelerometer angle = atan2(accel_y,accel_x)

angle error = estimated angle - accelerometer angle

estimated angle = estimated angle +

(gyroscope reading – angle error*gain)*dt

slide17
In general, high gains mean we trust the sensor (accelerometer), low gains mean we trust the model (integrated gyroscope)

Increasing gain

it s easy to see the improvement in performance over a low pass filter
It’s easy to see the improvement in performance over a low-pass filter

Estimated

Low-pass filtered

a kalman filter is an optimal way to find the estimator gain or gains
A Kalman filter is an optimal way to find the estimator gain (or gains)
  • In this example, if you know the statistics of the accelerometer and the gyroscope, you could use a Kalman filter to find the gain, which will be a function of time.
  • You can also estimate the bias in the gyroscope, which will improve the quality of your estimation.