Defined player hight above the ground

Unzip and simply attach MovementLogic script to the ghost gameobject. It almost contains all movement aspects. Feel free to modify fields in the inspector. Good Lock :)

link text

 using UnityEngine;
 
 // A character controller component should be attached to player Gameobject...
 [RequireComponent(typeof(CharacterController))]
 public class MovementLogic : MonoBehaviour
 {
     // Fields to store input from player...
     private float horizontalInput;
     private float verticalInput;
 
     // Vectors to store player Horizontal and Vertical movement...
     private Vector3 horizontalMovement;
     private Vector3 verticalMovement;
 
     // Final movement vector...
     private Vector3 movementDirection;
     private Vector3 movement;
 
     // Player movement speed. Modify in the inspector...
     [Header("Movement Speed")]
     [SerializeField] private float speed = 5.0f;
 
     // How high can player jump? Modify in the inspector...
     [Header("Jump Height")]
     [SerializeField] private float jumpHeight = 0.2f;
 
 
 
     // Gravity Scale. Modify in the inspector...
     [Header("Gravity Scale")]
     [SerializeField] private float gravity = 3.0f;
 
     // How high should the player be of the ground? Modify in the inspector...
     [Header("Character's floating height")]
     [SerializeField] private float floatingHeight = 5.0f;
 
     [Header("Smooth factor")]
     // How smooth should we adjust the character's position above the ground? Modify in the inspector...
     [SerializeField] private float smoothingStep = 0.2f;
 
     // Floating position vector of player. Filled in Awake...
     private Vector3 floatingPosition;
 
     // Control jump status to prevent double jump...
     private bool hasJumped = false;
 
     // Stores jumping vector...
     private Vector3 jumpMovement;
 
     // Has the ray touched ground? This is used instead of isGrounded...
     private bool rayTouchedGround = false;
 
     // Reference to character controller component...
     private CharacterController characterController;
 
     // This method calculates all character movements inside fixed update...
     private void CharacterMovement()
     {
         // Fill in movement vectors with player input...
         horizontalMovement = horizontalInput * transform.right;
         verticalMovement = verticalInput * transform.forward;
 
         // Store movement direction of character...
         movementDirection = horizontalMovement + verticalMovement;
 
         // Clamp movement direction's magnitude to 1 so that diagonal speed does not exceed it...
         movementDirection = Vector3.ClampMagnitude(movementDirection, 1.0f);
 
         // Finally fill in movement vector with direction and speed...
         movement = movementDirection * speed * Time.fixedDeltaTime;
 
         // Move character Horizontally and Vertically...
         characterController.Move(movement);
 
         // Check if player has jumped...
         if (hasJumped)
         {
             // Fill jump movement vector to allow the player go upward...
             jumpMovement.y = jumpHeight;
 
             // Avoid jumping while in air...
             hasJumped = false;
         }
 
         // Apply gravity to player and pull him downwards...
         jumpMovement.y -= gravity * Time.fixedDeltaTime;
 
         // Move character Upwards with jump movement...
         characterController.Move(jumpMovement);
 
         // !!!IMPORTANT: AFTER ALL MOVEMENTS!!!, Make player float above the ground...
         AdjustHeight();
 
         // Not important, just avoid jumpMovement.y from going to low, BUT should be after AdjustHeight call...
         if (rayTouchedGround)
         {
             jumpMovement.y = 0.0f;
         }
     }
 
     private void AdjustHeight()
     {
         // Declare a RaycastHit...
         RaycastHit hit;
 
         // Declare a ray from player's position downwards...
         Ray ray = new Ray(transform.position, Vector3.down);
 
         // Check if the ray has collided with something bellow in amount of 5 or less(i.e. floatHeight)...
         if (Physics.Raycast(ray, out hit, floatingHeight))
         {
             // Smoothly move the character above any platform. Character's position should be in amount of floatingPosition above the ray's hit point...
             transform.position = Vector3.MoveTowards(transform.position, hit.point + floatingPosition, smoothingStep);
 
             // Allow character to jump because he is low enough...
             rayTouchedGround = true;
         }
         else
         {
             // Player is high, dont let him jump...
             rayTouchedGround = false;
         }
     }
 
     private void Awake()
     {
         // Fill in the character controller reference...
         characterController = GetComponent<CharacterController>();
 
         // Initialize floating position vector...
         floatingPosition = new Vector3(0, floatingHeight, 0);
     }
 
     private void FixedUpdate()
     {
         // Call CharacterMovement every fixedUpdate...
         CharacterMovement();
     }
 
     private void Update()
     {
         // Allow character to move and jump only if the player is floatingHeight above the ground. Same as isGrounded...
         if (rayTouchedGround)
         {
             // Get movement input from player...
             horizontalInput = Input.GetAxis("Horizontal");
             verticalInput = Input.GetAxis("Vertical");
 
             // Allow character to jump if the spacebar pressed...
             if (Input.GetButtonDown("Jump"))
             {
                 hasJumped = true;
             }
         }
     }
 }

Thank you for the reply! How can I add raycasts and how do I assign the components to my scene?