Intelligent Steering Using PID controllers

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Intelligent Steering Using PID controllers

• Don DeLorenzo

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Euan Forrester Electronic Arts, Black Box

• Need For Speed Hot Pursuit 2
• Need For Speed Underground
• Semi-realistic driving physics on multiple
  surfaces

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What are PID controllers?

• Feedback-based algorithms used to minimize
  difference between measured output variable and a
  particular target
• First term proportional to current error
• Second term proportional to integral of current
  error
• Third term proportional to derivative of current
  error

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Background

• Engineering Algorithm
• In use for more than 50 years thermostats,
  cruise control, etc.
• Integral and Derivative terms are estimates

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Equations

• Difficulty lies in choosing coefficient weights

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Example

• Missile will have lift, drag, crosswinds, etc.
  that will affect its path
• Position in space missile is targeted towards is
  steer-to point

Velocity
Error
Desired Angle
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Example Continued

• Steer-to point must be sufficiently far from
  missile to avoid exaggerating error
• Direction of velocity is used rather than
  direction missile is facing

Velocity
Error
Desired Angle
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Proportional-Only Controller

• Asymptotic behavior
• If proportional coefficient is small, missile
  will follow lazy, asymptotic path back towards
  desired course
• Positive Feedback
• If proportional coefficient is large, missile
  will overshoot target and oscillate wildly
• Steady State Error
• If there is a crosswind, missiles course will be
  parallel to desired course but will never reach
  it

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Solutions

• Integral term
• Deals with steady state and asymptotic errors
  because sum of errors will continue to increase
  until missile is back on course
• Derivative term
• Deals with positive feedback, because as missile
  turns sharply towards target, derivative of error
  becomes negative, serving as a damper
• Derivative term also increases to kick start
  system if target moves

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Tuning PID Controller

• Proportional coefficient first
• Vary one coefficient at a time
• Real-time tuning
• No perfect solution, engineering tradeoffs

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Extensions to PID Algorithm

• Variable coefficients
• Missile may handle differently at high than low
  speeds
• Switching PID controllers based on object state
• Car on snow vs. mud vs. asphalt
• More complex P, I, D functions
• Capping functions to avoid spikes, or more
  complex functions
• Filtering input data
• Noisy input data will give jumpy D value
• Smoothes path at cost of responsiveness

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Other Applications

• Any problem expressible in terms of minimizing
  error of single variable, occurring over a length
  of time while corrective efforts are applied
• Steering
• Thrust
• Braking
• Temperature

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Need For Speed
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Conclusion

• PID Proportional, Integral, Derivative
  components
• Robust, easy to implement solution
• Can be used for any problem minimizing error in a
  single variable over time