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Gyrobot a Two Wheel Balancing Robot Larry Barello http://www.barello.net/Robots/Gyrobot How Balancing Works Sense tilt and drive wheels to make robot erect. Easier to balance high GC object. The Devil is in the details. Balanced Tilted How Balancing Works Restoring Torque =  * K

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gyrobot a two wheel balancing robot

Gyrobota Two Wheel Balancing Robot

Larry Barello

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

how balancing works
How Balancing Works
  • Sense tilt and drive wheels to make robot erect.
  • Easier to balance high GC object.
  • The Devil is in the details.

Balanced

Tilted

how balancing works3
How Balancing Works
  • Restoring Torque =  * K
  •  = Angular rate (deg/sec)
  • K = some factor based upon robot mass & moment arm.
how balancing works4

M

M

g

Motion

M

T = M * g * sin(0)

T = M * g * sin(90)

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
controlling drive torque
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.
how to move
How to move
  • The robot tilts in the direction of movement.
  • To move robot, need to adjust “balance angle”
  • By adding an error to the angle, the robot will drive a little backwards, then forwards trying to maintain the “balance angle”
  • Error can be simply a negative drive value.
tilt sensor
Tilt Sensor
  • Gyroscope measures Rate Of Turn.
  • Integrate for angle
  • Gyroscopes drift
  • Drift changes withtemperature
tilt sensor8
Tilt Sensor
  • Accelerometers measure gravity.
  • Affected by movement.
  • Very accurate.
fusing gyro and tilt sensors
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.
fusing gyro and tilt sensors10
Fusing Gyro and Tilt sensors
  • Weighted Average Filter.
    • Tiltgyro = Sum(Gyro – Offset)
    • Tiltaccel = sin-1(x/g)
    • Tiltgyro = Tiltgyro + (Tiltaccel – Tiltgyro) * K

+

+

Gyro

Tilt

-

-

Offset

+

Accelerometer

K

K = weighting factor (1%)

alternate to tilt sensor
Alternate to Tilt Sensor
  • F = g * sin(theta)
  • F = A * m
  • A * M = g * sin(theta)
  • Theta = sin-1(A * m/g)
  • m = mass
  • A = Acceleration M/S2
  • g = Gravity
  • F = force

Presumably we can use the acceleration of the robot to infer the angle of tilt and correct for gyro drift. (Note: Moment arm not included, formulas must be wrong)

motion sensor
Motion Sensor
  • Encoders measure position and velocity of wheels.
  • Dead reckoning can be derived from encoders and the robots position determined in X, Y and Theta.
current status
Current Status
  • Motion control not implemented.
  • Navigation disabled.
  • Remote control (Radio link) not implemented.
  • Using acceleration to correct tilt not tried.

In short, it doesn’t do anything interesting yet.

additional reading
Additional reading

Robots & controls

www.barello.net/Papers/Motion_Control

Pendulum Joe http://leiwww.epfl.ch

Data sheets

http://www.systron.com/prodinfo/AQRS.html

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