Controlling animation with IsTouchingLayers doesn't work on moving platform.

In my 2d platformer game I used IsTouchingLayers to check if the Player is on the ground. I made it according to a video tutorial series on youtube and it works like a wonder. It is always running when on ground, and after jumping, it loops the middle of jumping animation until it reaches the "Ground" layer again. It is perfectly fine, but on a moving platform it doesn't work. I trigger an invisible object to move that platform and the platform moves with the Player. (The Player is running at a constant speed to the right). The weird thing is that it triggers the grounded status on and off every half second while on the moving platform. So I can still jump, but the animation is bouncing between running and jumping really fast. I know I might have done it ineffectively but I just don't have the experience to fully understand what should I change. I tried various methods but things just got worse or simply didn't work.

Here's the PlayerController script on my Player:

using UnityEngine; using System.Collections;

public class PlayerController : MonoBehaviour {

 public float moveSpeed;
 public float jumpForce;
 private Rigidbody2D myRigidbody;
 public bool grounded;
 public LayerMask whatIsGround;
 private Collider2D myCollider;
 private Animator myAnimator;
 private bool canDoubleJump;
 public AudioClip deathSound;
 public AudioClip jumpSound;
 public int Health;
 public SoundManager SM;

 void Start () {
     Health = PlayerPrefs.GetInt("Health");
     myRigidbody = GetComponent<Rigidbody2D>();
     myCollider = GetComponent<Collider2D>();
     myAnimator = GetComponent<Animator>();
 }    
 void Update () {
     //if we touch the "Ground" Layer,grounded is true
     grounded = Physics2D.IsTouchingLayers(myCollider,whatIsGround);

    
     if (grounded)
     {
         canDoubleJump = true;
     }

     //running
     myRigidbody.velocity = new Vector2(moveSpeed, myRigidbody.velocity.y);
     //die if Player falls too low
     if (transform.position.y < -20)
     {
         if (Health > 1)
         {
             Health--;
             PlayerPrefs.SetInt("Health", Health);
             Application.LoadLevel(Application.loadedLevel);
         }
         else
         {
             Application.LoadLevel(0);
         }
     }
    //if grounded is true in Animator it is automatically playing the running animation
     myAnimator.SetBool("Grounded", grounded);
 }
 public void jump()
 {
     if (grounded)
     {
         myRigidbody.velocity = new Vector2(myRigidbody.velocity.x, jumpForce);
         SM.PlaySingle(jumpSound);
     }

     if (!grounded && canDoubleJump)
     {
         myRigidbody.velocity = new Vector2(myRigidbody.velocity.x, jumpForce);
         canDoubleJump = false;
         SM.PlaySingle(jumpSound);
     }
 }

 void OnCollisionEnter2D(Collision2D other)
 {
    //die when touching a trap
     if(other.gameObject.tag == "trap")
     {
         StartCoroutine(Die());
     }
 }

 IEnumerator Die()
 {
     myAnimator.SetBool("Dead", true);
     SM.PlaySingle(deathSound);
     yield return new WaitForSeconds(0.35f);
     if (Health > 1)
     {
         Health--;
         PlayerPrefs.SetInt("Health", Health);
         Application.LoadLevel(Application.loadedLevel);
     }
     else
     {
         Application.LoadLevel(0);
     }
 }

}