1. Intelligent Steering Using PID controllers
Don DeLorenzo

2. Euan Forrester – Electronic Arts, Black Box
Need For Speed Hot Pursuit 2
Need For Speed Underground
Semi-realistic driving physics on multiple surfaces

3. 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

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

5. Equations
Difficulty lies in choosing coefficient weights

6. 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

7. 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

8. 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, missile’s course will be parallel to desired course but will never reach it

9. Solutions Integral term: Derivative 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

10. Tuning PID Controller Proportional coefficient first
Vary one coefficient at a time
Real-time tuning
No ‘perfect’ solution, engineering tradeoffs

11. 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

12. 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

13. Need For Speed

14. 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