Intelligent Steering Using PID controllers Don DeLorenzo

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

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

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

Equations Difficulty lies in choosing coefficient weights

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

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

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

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

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

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

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

Need For Speed

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