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Gyrobota Two Wheel Balancing Robot

Larry Barello

http://www.barello.net/Robots/Gyrobot

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How Balancing Works

Easier to balance high GC object.

The Devil is in the details.

Balanced Tilted

Sense tilt and drive wheels to make robot erect.

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How Balancing Works

Restoring Torque = * K

= Angular rate (deg/sec)

K = some factor based upon robot mass & moment arm.

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How Balancing Works

Balance torque = M * g * sin(angle) M is moment arm (center of mass & distance from pivot).

g = acceleration of gravity

Angle is deviation from balance point

T = M * g * sin(0)

M

Motion

g

M

T = M * g * sin(90)

M

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Controlling Drive Torque As velocity increases, DC motors have less torque

(back-EMF)

Need to correct this so balance equation can work. Positive velocity feedback

Drive = drive + Kv * velocity

Kv = factor based upon motor specification.

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The robot tilts in the direction of movement.How to move

To move robot, need to adjust balance angle

By adding an error to the angle, the robot will drive alittle backwards, then forwards trying to maintain the

balance angle

Error can be simply a negative drive value.

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Tilt Sensor Gyroscope measures Rate Of Turn.

Integrate for angle

Gyroscopes drift

Drift changes withtemperature

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Tilt Sensor Accelerometers measure gravity.

Affected by movement.

Very accurate.

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Fusing Gyro and Tilt sensors Weighted Average Filter. Use fraction of error between tilt and gyro

Add to integrated Gyro output.

Results are fast & drift free The weighted average IIR filter technique can be

used to smooth out any noisy signal.

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Fusing Gyro and Tilt sensors Weighted Average Filter. Tiltgyro = Sum(Gyro Offset)

Tiltaccel = sin-1(x/g)

Tiltgyro = Tiltgyro + (Tiltaccel Tiltgyro) * K

Gyro

Accelerometer

+

+

+-

K

Tilt

Offset -

K = weighting factor (1%)

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Alternate to Tilt SensorF = g * sin(theta)F = A * m

A * M = g * sin(theta)

Theta = sin-1(A * m/g)

Presumably we can use the acceleration of therobot to infer the angle of tilt and correct forgyro drift. (Note: Moment arm not included, formulas must bewrong)

m = mass

A = Acceleration M/S2

g = Gravity

F = force

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Motion Sensor Encoders measure position and velocity of wheels.

Dead reckoning can be derived from encoders andthe robots position determined in X, Y and Theta.

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Current Status Motion control not implemented.

Navigation disabled.

Remote control (Radio link) not implemented.

Using acceleration to correct tilt not tried.

In short, it doesnt do anything interesting yet.

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Additional readingRobots & controls

www.barello.net/Papers/Motion_Control

Pendulum Joe http://leiwww.epfl.ch

Data sheetshttp://www.systron.com/prodinfo/AQRS.html

http://products.analog.com/products/info.asp?product=ADXL202