How do I get my arduinobot to turn to the center of a moving object

Question

My objective: is to have a robot follow me. (I'm using an arduiono bot for this)

So I started off what some code that wasn't so dynamic. Essentially I had no issues with the robot following me (holding a cardboard because these robots need a good flat surface to see) when I was right in front of it, but when it turned it just simply scanned while turning to the right till it found presence of something and just followed it. As you might tell, this is very inefficient and doesn't accomplish a proper robot follow.

In order to make it more dynamic I was suggested to do this:

1. basically have the robot scan the right and left edges of the cardboard every n seconds, and the average the distance of the edges to get the center point of the cardboard and just have the sensor do a real time scan

My issue: I don't get how to get the robot to like, turn to the center distance. This is what I've written so far, and the pseudocode indicates my logic behind each of the steps

void loop() {
  //code for left side of cardboard
  myServo.write(initial); //servo facing straight ahead, initial set to 90
  leftDistance = getDistance();
  while (leftDistance < 30)){ //while the servo detects presence of cardboard
    myServo.write(initial); //increments of 5 to the left side of carboard
    leftDistance = getDistance(); //updates detected distance
    initial = initial - 5; 
    delay(100);
  }
  myServo.write(initial + 5); //the final distance before cardboard went undetected
  leftDistance = getDistance();
  delay(100);
//same code as above for right side
  myServo.write(initial); //servo facing straight ahead, initial set to 90
  rightDistance = getDistance();
  while (rightDistance < 30)){ //while the servo detects presence of cardboard
    myServo.write(initial); //increments of 5 to the right side of carboard
    rightDistance = getDistance(); //updates detected distance
    initial = initial + 5; 
    delay(100);
  }
  myServo.write(initial - 5); //the final distance before cardboard went undetected
  rightDistance = getDistance();
  delay(100);
avgDistance = (rightDistance + leftDistance)/2; //center point
  myServo.write();// HELP: basically i'm unsure how to get the robot to turn/acknowledge center of cardboard at this point 
  forward(); //it moves forward
  delay(200);
//loop begins again
}