2D Top-Down shooter - collision not working

So, I am doing this little project in Unity 2D and I have an issue with my Player movement script. I want the character to face the mouse position, and move left, right, up and down. The code works perfectly, but the character is not detecting collision with walls (well, anything in general). I tried putting the RigidBody2D component onto the walls, but that just doesn't work. I think there is a problem in the code, but I can't tell what it is. I someone could tell me, or even post fixed version of the code, that would be well appreciated.

Here is the code for reference.

 Vector3 _position;
 Transform _transform;

 public float speed = 5f;
  Rigidbody2D rb2d;
  BoxCollider2D boxCollider2d;

 

 void Awake ()
 {
     _position = transform.position;
     _transform = transform;
     rb2d = GetComponent<Rigidbody2D>();
     boxCollider2d = GetComponent<BoxCollider2D>(); 

}

 void FixedUpdate ()
 {
     var mousePosition = Camera.main.ScreenToWorldPoint(Input.mousePosition);
     Quaternion rot = Quaternion.LookRotation(transform.position - mousePosition, Vector3.forward);

     
     
     transform.rotation = rot;
     transform.eulerAngles = new Vector3(0, 0, transform.eulerAngles.z);


     if (Input.GetKey(KeyCode.W) && _transform.position == _position)
     {
         _position += Vector3.down;
     }
     if (Input.GetKey(KeyCode.S) && _transform.position == _position)
     {
         _position += Vector3.down;
     }
     if (Input.GetKey(KeyCode.A) && _transform.position == _position)
     {
         _position += Vector3.left;
     }
     if (Input.GetKey(KeyCode.D) && _transform.position == _position)
     {
         _position += Vector3.right;
     }
     transform.position = Vector2.MoveTowards(transform.position, _position, Time.deltaTime * speed);

     
 }

}