PDS Controller

A PDS (Proportional-Derivative-Static) controller is a type of feedback controller similar to a PID controller. It removes the integral (I) term from the PID controller, which is unnecessary for path following. Adding the static (S) term allows the controller to break through static friction, which is important for smooth robot movement. The PDS controller is used in Apex Pathing to control the robot’s movement along a path with high precision and accuracy.

Coefficients

Our controller contains four coefficients:

• Proportional: Multiplied by the current positional error in inches. This term is responsible for the majority of the robot’s movement.
• Derivative: Multiplied by the change in error since the last update. Helps to reduce oscillation.
• Static: A constant power added to the output that helps the robot to break through static friction.
• Static Deadzone: The minimum error required for the static term to be applied. This prevents the robot from oscillating when it is close to the target position.

How it works

First, the controller multiplies the current positional error by the proportional coefficient: double proportional = this.coeffs.kP * error;

The derivative term is calculated by multipling kD by the change in error since the last update divided by the time since the last update. If timeAnomalyDetected is true, the derivative term is set to 0.0 to prevent the controller from reacting to sudden changes in error due to deltaTime being too small/big: double derivative = this.coeffs.kD * (timeAnomalyDetected ? 0.0 : (error - lastError) / deltaTime);

Finally, the static term is calculated by multiplying kS by the sign of the error (+1 or -1). If the absolute value of the error is less than kSDeadzone, the static term is set to 0.0 to prevent oscillation: double minimum = this.coeffs.kS * Math.signum(error) * (Math.abs(error) > this.coeffs.kSDeadzone ? 1.0 : 0.0);

The terms are then summed together to produce the final output: return proportional + derivative + minimum;

Putting them all together into the computeOutput method, we have:

@Override
protected double computeOutput(double error, double lastError, double deltaTime) {
    double proportional = this.coeffs.kP * error;
    double derivative = this.coeffs.kD * (timeAnomalyDetected ? 0.0 :
            (error - lastError) / deltaTime);
    double minimum =
            this.coeffs.kS * Math.signum(error) * (Math.abs(error) > this.coeffs.kSDeadzone ?
                    1.0 : 0.0);
    return proportional + derivative + minimum;
}

See more about this controller on the GitHub page