Random movement of game Object staying in a circle

Question

I want to write a script which makes several objects move in a random direction but within a range around another game object. If the parent object moves then that range should also be changed accordingly.

How can I achieve such behavior?

Here is a video which demonstrates the behavior I am looking for.

It looks approximately like this:

---

   void Update () 
   {    
        time += Time.deltaTime;

        if (time > 1.0f) 
        {
            CalculateRandomRotation ();
            time = 0f;
        }

        FindSpiritsBound ();

    }

    void CalculateRandomRotation()
    {
        x       = Random.Range(-velocityMax, velocityMax);
        z       = Random.Range(-velocityMax, velocityMax);
        angulo  = Mathf.Atan2(x, z) * (180 / 3.141592f);
        time    = 0.0f;
        transform.localRotation = Quaternion.Euler(0, angulo, 0);
    }

    void FindSpiritsBound()
    {
        if (Vector3.Distance (parentObj.transform.position, gameObject.transform.position) < 3f)
        {
            gameObject.transform.localPosition += gameObject.transform.forward * 4f * Time.deltaTime;
        }
       else
        {
         transform.position = Vector3.MoveTowards(transform.position, parentObj.transform.position, 2.0f);
        }
    }

Here is my script which doesn't seem to work properly as on moving the main character, spirits are going wayward.

Answer 1

In the script of the random movement of the sprites check the distance by using the command Vector3.Distance(object a, object b). If the sprite is not in range than move/change direction of the movement.