This log starts with the so called circumplex model of affect. Re-drawn and simplified model:

You might notice, that this model implicates the use of the KNN algorithm immediately. More formally: let the sample space be a 2-dimensional Euclidean space IR², the center coordinates (0,0) and the radius r ∈ IR > 0, then our classes are located at:

and

A remark about Pleasure and Activation before we continue: Activation could be seen as a kind of entropy of the robot in a physical sense, depending for instance on the ambient light level and temperature. Pleasure could be seen as a success rate of a given task the robot has to fulfill or to learn.

The distance between two points in a 2-dimensional Euclidean space is given by

which follows directly from the Pythagorean theorem.

With the defined boundaries we get a maximum distance between a class point and a new sample point of:

Here is a little sketch I wrote to demonstrate how the emotional agent works:

const float r = 5.0; 

void setup() {
  Serial.begin(9600);
  Emotional_agent(5, 0);
}

void loop() { 
}

void Emotional_agent(float x_P, float y_A) {
  if(x_P < - r) x_P = - r; // limit the range of x_P and y_A
  else if(x_P > r) x_P = r;
  if(y_A < - r) y_A = - r;
  else if(y_A > r) y_A = r;
  float emotion_coordinates[2][9] = {
    {0.0,  0.0, r, - r, 0.0, r/sqrt(2.0), - r/sqrt(2.0), r/sqrt(2.0), - r/sqrt(2.0)}, // x-coordinate of training samples
    {0.0,  r, 0.0, 0.0, -r, r/sqrt(2.0), r/sqrt(2.0), - r/sqrt(2.0), -r/sqrt(2.0)} // y- coordinate of training samples
  };
  char *emotions[] = {"neutral", "vigilant", "happy", "sad", "bored", "excited", "angry", "relaxed", "depressed"};
  byte i_emotion; 
  byte closestEmotion;
  float MaxDiff;
  float MinDiff = sqrt(2.0) * r + r; //set MinDiff initially to maximum distance that can occure
  for (i_emotion = 0; i_emotion < 9; i_emotion ++) { 
    // compute Euclidean distances
    float Euclidian_distance = sqrt(pow((emotion_coordinates[0][i_emotion] - x_P),2.0) + pow((emotion_coordinates[1][i_emotion] - y_A),2.0));
    MaxDiff = Euclidian_distance;
    // find minimum distance 
    if (MaxDiff < MinDiff) {
      MinDiff = MaxDiff;
      closestEmotion = i_emotion;
    }
  }
  Serial.println(emotions[closestEmotion]);
  Serial.println("");
}