Ideas to move across tile centers only?

Hi there,

My code will be posted below. Overall what I'm trying to achieve is a smooth movement of the player, that doesn't move into "out-of-bounds" tiles, and keeps the player at .5 of the y-axis when move left or right and .5 of the x-axis moving up and down. I've been able to achieve 2/3 of what I'm wanting. It's keeping my player centered is the problem. Basically, I want it to move on a tightrope for the neatness and because of the graphic I have on the tiles. Please take a look at my code and let me know what suggestions you may have.

Thank you!

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 using UnityEngine.Tilemaps;
 
 public class PlayerController : MonoBehaviour
 {
     public Rigidbody2D playerRB;
     public float moveSpeed = 1f;
     public GameObject player;
     public Tilemap outOfBounds;
 
     //used for camera controll limits
     private Vector3 bottomLeftLimit;
     private Vector3 topRightLimit;
 
 
     public static PlayerController instance;
 
 
 
 
 
     
     // Start is called before the first frame update
     void Start()
     {
         if (instance == null)
         {
             instance = this;
         }
         else
         {
             if (instance != this)
                 Destroy(gameObject);
         }
 
         DontDestroyOnLoad(gameObject);
     }
 
     // Update is called once per frame
     void Update()
     {
         //Debug.Log("movement running");
 
         float xPos = transform.position.x;
         float yPos = transform.position.y;
 
         Vector2 newPosition;
 
         
 
         //move right
         if(Input.GetButton("Horizontal") && Input.GetAxisRaw("Horizontal") > 0)
         {
             newPosition = new Vector2(xPos + .52f, yPos);
             if (TileTest(outOfBounds, newPosition) == null)
             {
                 this.transform.position = Vector2.MoveTowards(this.transform.position, newPosition, moveSpeed * Time.deltaTime);            
                 
             }        
        
         }
         //move left
         if (Input.GetButton("Horizontal") && Input.GetAxisRaw("Horizontal") < 0)
         {
             newPosition = new Vector2(xPos - .52f, yPos);
 
             if (TileTest(outOfBounds, newPosition) == null)
             {
                 this.transform.position = Vector2.MoveTowards(this.transform.position, newPosition, moveSpeed * Time.deltaTime);
             }
         }
         //move up
         if (Input.GetButton("Vertical") && Input.GetAxisRaw("Vertical") > 0)
         {
             newPosition = new Vector2(xPos, yPos + .52f);
 
 
             if (TileTest(outOfBounds, newPosition) == null)
             {
                 this.transform.position = Vector2.MoveTowards(this.transform.position, newPosition, moveSpeed * Time.deltaTime);
             }
             
         }
         //move down
         if (Input.GetButton("Vertical") && Input.GetAxisRaw("Vertical") < 0)
         {
             newPosition = new Vector2(xPos, yPos - .52f);
 
             if (TileTest(outOfBounds, newPosition) == null)
             {
                 this.transform.position = Vector2.MoveTowards(this.transform.position, newPosition, moveSpeed * Time.deltaTime);
             }
         }
 
     }
 
     public TileBase TileTest(Tilemap tilemap, Vector2 cellWorldPos)
     {
         return tilemap.GetTile(tilemap.WorldToCell(cellWorldPos));
     }
 
     public void SetBounds(Vector3 bottomLeft, Vector3 topRight)
     {
         bottomLeftLimit = bottomLeft + new Vector3(0.5f, 1f, 0f);
         topRightLimit = topRight + new Vector3(-1f, -1f, 0f);
     }
 
 }