Grid base movement - classic snake

Hi I want to make good feeling automatic grid mabe movement like in classic snake.

I have something but i think i could do this better.

Im retreiving nextDirection in update function and storing it in variable. Than in Start function i have Invoke(“Move”,0.5f), and in Move() function im tweening object (parent), at the end of the function Move() i have Invoke(“Move”,0.5). On child object i have little jump animation.

Everything is working, but i think it should be working better. I’m not satisfied with smoothness of the movement.
What do you think, how can I improve my movement script?
Im working on my first project.

I used this for mine, the movement reminds me of the original I played as a kid. I had a body segment prefab (just a coloured sphere)

using UnityEngine;
using System.Collections;
using System.Collections.Generic;
using UnityEngine.UI;

public class Manager : MonoBehaviour
static public Manager instance;

	// create list of body segments
	public List<InstantiateBody>bodySegments = new List<InstantiateBody> ();
	public GameObject bodyPrefab;
	// # of body segments, 2 is the minimum as 1 destroys & instantiates to quick to be seen.
	public int bodyNum = 5;
	// speed of snake & timer between destroy/instaniate for movement
	float speed = 2	;
	float moveTimer = 0.5f;
	// direction of movement for instantiation, player starts moving up the screen
	public static Vector3 direction;
	// player start position
	private GameObject startspot;
	// set exit gameobject
	public GameObject exit;

	// Use this for initialization
	void Start ()
			instance = this;
			// get position of starting place		
			startspot = GameObject.Find ("Start");
			// set player initial direction
			direction = Vector3.forward;

	// Update is called once per frame
	void Update ()

			// set player move direction by arrow keys

			if (Input.GetKey (KeyCode.UpArrow))
					direction = Vector3.forward;
			if (Input.GetKey (KeyCode.DownArrow))
					direction = Vector3.back;
			if (Input.GetKey (KeyCode.LeftArrow))
					direction = Vector3.left;
			if (Input.GetKey (KeyCode.RightArrow))
					direction = Vector3.right;

			//decrement timer of action to replicate speed.
			moveTimer -= speed * Time.deltaTime;
			if (moveTimer <= 0) {
					// replicate movement along 90 degree paths by destroying the body segment & removing it from the list
					// at the end of the snake & instantiating one at the beginning 1 unit in the direction of movement
					// from the segment at the start of the snake.  Insert this new piece into position 0 of the list.
					//remove last body segment in the list which will be the end of the snake
					if (InstantiateBody.bodySegments.Count >= bodyNum) {
							Destroy (InstantiateBody.bodySegments [InstantiateBody.bodySegments.Count - 1].gameObject);
							InstantiateBody.bodySegments.RemoveAt (InstantiateBody.bodySegments.Count - 1);
					// instantiate the body segments.  If it's a new game first piece is at the start position
					if (InstantiateBody.bodySegments.Count == 0) {
							Instantiate (bodyPrefab, startspot.transform.position, bodyPrefab.transform.rotation);
							// keep adding segments to the front of the snake
					} else if (InstantiateBody.bodySegments.Count < bodyNum)
							Instantiate (bodyPrefab, InstantiateBody.bodySegments [0].transform.position + direction, InstantiateBody.bodySegments [0].transform.rotation);
					//reset move timer
					moveTimer = 0.5f;

			// set isTrigger for other segments, not the head, to enable collision detection if the
			// snake hits itself.
			for (int i = 0; i<InstantiateBody.bodySegments.Count-1; i++) {
					if (i != 0) {
							InstantiateBody.bodySegments *.GetComponent<Collider> ().isTrigger = true;*
  •   				}*
  •   		}*
  •   }*