Moving one square at the time with velocity

Hello

Third script. I'm using rigidbody2d and velocity instead of moving the transform, I didn't know physics didnøt work with the previous methods. Now however I don't know to to stop my character again so it only moves one square at the time.

I'm working on a topdown 2d game and want to use boxcast to check for collisions with the environment, instead of the overlapcircle I'm using right now. I have up, down, left, and right movement on a grid each 32px squares so 0.32 of a Unity unit I believe.

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class GridMovementTest : MonoBehaviour
 {
     [SerializeField] private float moveSpeed = 4f;
     //[SerializeField] private Transform movePoint;
 
     //[SerializeField] private Animator anim;
 
     [SerializeField] private LayerMask cannotMoveTo;
 
     private BoxCollider2D boxCollider2D;
     private Rigidbody2D _rigidbody2D;
 
     private RaycastHit2D hitdown, hitup, hitleft, hitright;
 
     private Vector2 movement;
 
     void Start()
     {
         //movePoint.parent = null;
         boxCollider2D = this.GetComponent<BoxCollider2D>();
         _rigidbody2D = this.GetComponent<Rigidbody2D>();
     }
 
     /*void OnDrawGizmos()
     {
         Gizmos.color = new Color(1, 0, 1, .5f);
         Gizmos.DrawCube(movePoint.position, new Vector2(.32f, .32f));
     }*/
 
     void FixedUpdate()
     {
         RaycastHit2D hitdown = Physics2D.BoxCast(boxCollider2D.bounds.center, boxCollider2D.bounds.size, 0f, Vector2.down, .32f, cannotMoveTo);
 
         RaycastHit2D hitup = Physics2D.BoxCast(boxCollider2D.bounds.center, boxCollider2D.bounds.size, 0f, Vector2.up, .32f, cannotMoveTo);
 
         RaycastHit2D hitleft = Physics2D.BoxCast(boxCollider2D.bounds.center, boxCollider2D.bounds.size, 0f, Vector2.left, .32f, cannotMoveTo);
 
         RaycastHit2D hitright = Physics2D.BoxCast(boxCollider2D.bounds.center, boxCollider2D.bounds.size, 0f, Vector2.right, .32f, cannotMoveTo);
 
         moveCharacter(movement);
     }
 
     private void Update()
     {
         if ((hitleft.collider == null) && Input.GetAxisRaw("Horizontal") < 0)
         {
             movement = Vector2.left * .32f;
         }
         if ((hitright.collider == null) && Input.GetAxisRaw("Horizontal") > 0)
         {
             movement = Vector2.right * .32f;
         }
         if ((hitdown.collider == null) && Input.GetAxisRaw("Vertical") < 0)
         {
             movement = Vector2.down * .32f;
         }
         if ((hitup.collider == null) && Input.GetAxisRaw("Vertical") > 0)
         {
             movement = Vector2.up * .32f;
         }
     }
         void moveCharacter(Vector2 direction)
         {
             _rigidbody2D.velocity = direction * moveSpeed;
         }
 }