Make the player go into the direction I am looking at

Hi, I am having trouble with my animated FPS character.

I made this script and attached it to the camera. And yes the player rotates with the camera but when I move I am still moving towards the standard directions and the animation is playing towards the standard direction. Sorry for my bad English btw.

 Vector2 mouseLook;
 Vector2 smoothV;
 public float sensitivity = 5.0f;
 public float smoothing = 2.0f;   

 GameObject character;
  
 // Use this for initialization
 void Start ()
 {
     character = this.transform.parent.gameObject;
 }
 
 // Update is called once per frame
 void Update ()
 {
     var md = new Vector2(Input.GetAxisRaw("Mouse X"), Input.GetAxisRaw("Mouse Y"));

     md = Vector2.Scale(md, new Vector2(sensitivity * smoothing, sensitivity * smoothing));
     smoothV.x = Mathf.Lerp(smoothV.x, md.x, 1f / smoothing);
     smoothV.y = Mathf.Lerp(smoothV.y, md.y, 1f / smoothing);
     mouseLook += smoothV;

     transform.localRotation = Quaternion.AngleAxis(-mouseLook.y, Vector3.right);
     character.transform.localRotation = Quaternion.AngleAxis(mouseLook.x, character.transform.up);
 }

This is my player script:

 public Animator anim;
 public Rigidbody Rbody;
 public float Gravity;
 public float JumpHeight;
 private float currentrunspeed = 80;
 private bool run;
 //public GameObject Camera;
 public GameObject us;      

 private float inputH;
 private float inputV;
 private float inputJump;

 // Use this for initialization
 void Start ()
 {
     anim = GetComponent<Animator>();
     Rbody = GetComponent<Rigidbody>();
     run = false;
     Cursor.lockState = CursorLockMode.Locked;
 }
 
 // Update is called once per frame
 void Update ()
 {
     transform.localEulerAngles = new Vector3(transform.localEulerAngles.x, Camera.main.transform.localEulerAngles.y, transform.localEulerAngles.z);
     Physics.gravity = new Vector3(0f, -Gravity * Time.fixedDeltaTime, 0f);
     

     if (Input.GetKeyDown("1"))
     {
         anim.Play("Run", -1,0f);
     }

     if (Input.GetKey(KeyCode.LeftShift)&& inputV > 0.1)
     {
         currentrunspeed = 150f;
         run = true;                        
     }
     else
     {
         run = false;
         currentrunspeed = 80f;      
     }

     inputH = Input.GetAxis("Horizontal");
     inputV = Input.GetAxis("Vertical");

     anim.SetFloat("InputH", inputH);
     anim.SetFloat("InputV", inputV);
     anim.SetBool("Run",run);

    float moveX = inputH * 50f * Time.deltaTime;
    float moveZ = inputV * currentrunspeed * Time.deltaTime;
     
 Rbody.velocity = new Vector3(moveX,Rbody.velocity.y, moveZ);

    if (Input.GetKeyDown("space") && IsGrounded)
    {
         Rbody.AddForce(Vector3.up * JumpHeight * Time.deltaTime);
         anim.SetBool("Jump", true);            
    }
    else
     {
         anim.SetBool("Jump", false);
     }
 }
 public bool IsGrounded;

 void OnCollisionStay(Collision collisionInfo)
 {
     IsGrounded = true;
 }

 void OnCollisionExit(Collision collisionInfo)
 {
     IsGrounded = false;
 }

If someone knows any solutions I'd really appreciate it XD.