Arduino robot to move spirally

Question

I am planning to build robot like irobot Roomba. So cleaning in a spiral pattern is required like the image shown starting from the center:

This code is part of my full code which doesn't give me spiral pattern:

void spiralling() {
  for(int i=0;i<=2;i++) {
    digitalWrite(motor1,HIGH);
    digitalWrite(motor2,LOW);
    digitalWrite(motor3,HIGH);
    digitalWrite(motor4,LOW);
    analogWrite(pwm1,180);
    analogWrite(pwm2,80);
    delay(300);
    p=1;
  }
  analogWrite(pwm2,250); 
  delay(150); 
}

So my question is how can I make my bot trace spiral pattern (algorithm?,Logic? to use), as the only way to change the direction is with two wheels on sides.

Is there any code which constantly increases the radius of bot movement from center to radially outwards?

My robot has arduino uno ,l293d motordriver,two geared motors on either sides as shown in image and castor wheel in front:

Answer 1

the code should be like this:

int tourtime=1000; // circle tourtime. it is about intersection areas between each spiral. it should be less than circle time
int increasetime=10; // time for next tour, larger spiral needs more time
int numberofspiral=10; // number of circle
int minspeed=50; // initial speed for spiral. 
int maxspeed=200;// max speed 
void spiralling() {
  digitalWrite(motor1,HIGH);
  digitalWrite(motor2,LOW);
  digitalWrite(motor3,HIGH);
  digitalWrite(motor4,LOW);

  for(int i=0;i<=numberofspiral;i++) {
    analogWrite(pwm1,maxspeed);
    analogWrite(pwm2,minspeed);
    minspeed=minspeed+1;// increase the speed to increase radius
    delay(tourtime);
    tourtime=tourtime+increasetime;// increase the time for scan optimum area
  }
  analogWrite(pwm2,250); 
  delay(150); 
}