array(
  array(
    'post_type' => 'page',
    'post_name' => 'Home',
    'children' => array()
  ),
  array(
    'post_type' => 'page',
    'post_name' => 'About Us',
    'children' => array(
      array(
        'post_type' => 'page',
        'post_name' => 'Our History',
        'children' => array()
      )
    )
  )
)

function wpse170033_nav_menu_object_tree( $nav_menu_items_array ) {
    foreach ( $nav_menu_items_array as $key => $value ) {
        $value->children = array();
        $nav_menu_items_array[ $key ] = $value;
    }

    $nav_menu_levels = array();
    $index = 0;
    if ( ! empty( $nav_menu_items_array ) ) do {
        if ( $index == 0 ) {
            foreach ( $nav_menu_items_array as $key => $obj ) {
                if ( $obj->menu_item_parent == 0 ) {
                    $nav_menu_levels[ $index ][] = $obj;
                    unset( $nav_menu_items_array[ $key ] );
                }
            }
        } else {
            foreach ( $nav_menu_items_array as $key => $obj ) {
                if ( in_array( $obj->menu_item_parent, $last_level_ids ) ) {
                    $nav_menu_levels[ $index ][] = $obj;
                    unset( $nav_menu_items_array[ $key ] );
                }
            }
        }
        $last_level_ids = wp_list_pluck( $nav_menu_levels[ $index ], 'db_id' );
        $index++;
    } while ( ! empty( $nav_menu_items_array ) );

    $nav_menu_levels_reverse = array_reverse( $nav_menu_levels );

    $nav_menu_tree_build = array();
    $index = 0;
    if ( ! empty( $nav_menu_levels_reverse ) ) do {
        if ( count( $nav_menu_levels_reverse ) == 1 ) {
            $nav_menu_tree_build = $nav_menu_levels_reverse;
        }
        $current_level = array_shift( $nav_menu_levels_reverse );
        if ( isset( $nav_menu_levels_reverse[ $index ] ) ) {
            $next_level = $nav_menu_levels_reverse[ $index ];
            foreach ( $next_level as $nkey => $nval ) {
                foreach ( $current_level as $ckey => $cval ) {
                    if ( $nval->db_id == $cval->menu_item_parent ) {
                        $nval->children[] = $cval;
                    }
                }
            }
        }
    } while ( ! empty( $nav_menu_levels_reverse ) );

    $nav_menu_object_tree = $nav_menu_tree_build[ 0 ];
    return $nav_menu_object_tree;
}

$nav_menu_items = wp_get_nav_menu_items( 'main-menu' );
wpse170033_nav_menu_object_tree( $nav_menu_items );

Array
(
 [0] => WP_Post Object
  (
   [ID] => 51
   [post_author] => 1
   [post_date] => 2015-06-26 21:13:23
   [post_date_gmt] => 2015-06-26 19:13:23
   [post_content] =>
   [post_title] =>
   [post_excerpt] =>
   [post_status] => publish
   [comment_status] => open
   [ping_status] => open
   [post_password] =>
   [post_name] => 51
   [to_ping] =>
   [pinged] =>
   [post_modified] => 2015-07-29 20:55:10
   [post_modified_gmt] => 2015-07-29 18:55:10
   [post_content_filtered] =>
   [post_parent] => 0
   [guid] => http://example.com/?p=51
   [menu_order] => 1
   [post_type] => nav_menu_item
   [post_mime_type] =>
   [comment_count] => 0
   [filter] => raw
   [db_id] => 51
   [menu_item_parent] => 0
   [object_id] => 2
   [object] => page
   [type] => post_type
   [type_label] => Page
   [url] => http://example.com/example-page/
   [title] => Example-Page-1
   [target] =>
   [attr_title] =>
   [description] =>
   [classes] => Array
    (
     [0] =>
    )
   [xfn] =>
   [children] => Array
    (
     [0] => WP_Post Object
      (
       [ID] => 80
       [post_author] => 1
       [post_date] => 2015-06-27 14:03:31
       [post_date_gmt] => 2015-06-27 12:03:31
       [post_content] =>
       [post_title] =>
       [post_excerpt] =>
       [post_status] => publish
       [comment_status] => open
       [ping_status] => open
       [post_password] =>
       [post_name] => 80
       [to_ping] =>
       [pinged] =>
       [post_modified] => 2015-07-29 20:55:10
       [post_modified_gmt] => 2015-07-29 18:55:10
       [post_content_filtered] =>
       [post_parent] => 2
       [guid] => http://example.com/?p=80
       [menu_order] => 2
       [post_type] => nav_menu_item
       [post_mime_type] =>
       [comment_count] => 0
       [filter] => raw
       [db_id] => 80
       [menu_item_parent] => 51
       [object_id] => 69
       [object] => page
       [type] => post_type
       [type_label] => Page
       [url] => http://example.com/example-page/subpage-1/
       [title] => Subpage-1
       [target] =>
       [attr_title] =>
       [description] =>
       [classes] => Array
        (
         [0] =>
        )
       [xfn] =>
       [children] => Array
        (
        )
      )
    )
  )
 [1] => WP_Post Object
  (
   [ID] => 49
   [post_author] => 1
   [post_date] => 2015-06-26 21:13:23
   [post_date_gmt] => 2015-06-26 19:13:23
   [post_content] =>
   [post_title] =>
   [post_excerpt] =>
   [post_status] => publish
   [comment_status] => open
   [ping_status] => open
   [post_password] =>
   [post_name] => 49
   [to_ping] =>
   [pinged] =>
   [post_modified] => 2015-07-29 20:55:10
   [post_modified_gmt] => 2015-07-29 18:55:10
   [post_content_filtered] =>
   [post_parent] => 0
   [guid] => http://example.com/?p=49
   [menu_order] => 3
   [post_type] => nav_menu_item
   [post_mime_type] =>
   [comment_count] => 0
   [filter] => raw
   [db_id] => 49
   [menu_item_parent] => 0
   [object_id] => 41
   [object] => page
   [type] => post_type
   [type_label] => Page
   [url] => http://example.com/example-page-2/
   [title] => Example-Page-2
   [target] =>
   [attr_title] =>
   [description] =>
   [classes] => Array
    (
     [0] =>
    )
   [xfn] =>
   [children] => Array
    (
    )
  )
 [2] => WP_Post Object
  (
   [ID] => 48
   [post_author] => 1
   [post_date] => 2015-06-26 21:13:23
   [post_date_gmt] => 2015-06-26 19:13:23
   [post_content] =>
   [post_title] =>
   [post_excerpt] =>
   [post_status] => publish
   [comment_status] => open
   [ping_status] => open
   [post_password] =>
   [post_name] => 48
   [to_ping] =>
   [pinged] =>
   [post_modified] => 2015-07-29 20:55:10
   [post_modified_gmt] => 2015-07-29 18:55:10
   [post_content_filtered] =>
   [post_parent] => 0
   [guid] => http://example.com/?p=48
   [menu_order] => 4
   [post_type] => nav_menu_item
   [post_mime_type] =>
   [comment_count] => 0
   [filter] => raw
   [db_id] => 48
   [menu_item_parent] => 0
   [object_id] => 42
   [object] => page
   [type] => post_type
   [type_label] => Page
   [url] => http://example.com/example-page-3/
   [title] => Example-Page-3
   [target] =>
   [attr_title] =>
   [description] =>
   [classes] => Array
    (
     [0] =>
    )
   [xfn] =>
   [children] => Array
    (
     [0] => WP_Post Object
      (
       [ID] => 79
       [post_author] => 1
       [post_date] => 2015-06-27 14:03:31
       [post_date_gmt] => 2015-06-27 12:03:31
       [post_content] =>
       [post_title] =>
       [post_excerpt] =>
       [post_status] => publish
       [comment_status] => open
       [ping_status] => open
       [post_password] =>
       [post_name] => 79
       [to_ping] =>
       [pinged] =>
       [post_modified] => 2015-07-29 20:55:10
       [post_modified_gmt] => 2015-07-29 18:55:10
       [post_content_filtered] =>
       [post_parent] => 42
       [guid] => http://example.com/?p=79
       [menu_order] => 5
       [post_type] => nav_menu_item
       [post_mime_type] =>
       [comment_count] => 0
       [filter] => raw
       [db_id] => 79
       [menu_item_parent] => 48
       [object_id] => 70
       [object] => page
       [type] => post_type
       [type_label] => Page
       [url] => http://example.com/example-page-3/subpage-2/
       [title] => Subpage-2
       [target] =>
       [attr_title] =>
       [description] =>
       [classes] => Array
        (
         [0] =>
        )
       [xfn] =>
       [children] => Array
        (
         [0] => WP_Post Object
          (
           [ID] => 78
           [post_author] => 1
           [post_date] => 2015-06-27 14:03:31
           [post_date_gmt] => 2015-06-27 12:03:31
           [post_content] =>
           [post_title] =>
           [post_excerpt] =>
           [post_status] => publish
           [comment_status] => open
           [ping_status] => open
           [post_password] =>
           [post_name] => 78
           [to_ping] =>
           [pinged] =>
           [post_modified] => 2015-07-29 20:55:10
           [post_modified_gmt] => 2015-07-29 18:55:10
           [post_content_filtered] =>
           [post_parent] => 70
           [guid] => http://example.com/?p=78
           [menu_order] => 6
           [post_type] => nav_menu_item
           [post_mime_type] =>
           [comment_count] => 0
           [filter] => raw
           [db_id] => 78
           [menu_item_parent] => 79
           [object_id] => 76
           [object] => page
           [type] => post_type
           [type_label] => Page
           [url] => http://example.com/example-page-3/subpage-2/subpage-3/
           [title] => Subpage-3
           [target] =>
           [attr_title] =>
           [description] =>
           [classes] => Array
            (
             [0] =>
            )
           [xfn] =>
           [children] => Array
            (
             [0] => WP_Post Object
              (
               [ID] => 87
               [post_author] => 1
               [post_date] => 2015-06-27 15:27:08
               [post_date_gmt] => 2015-06-27 13:27:08
               [post_content] =>
               [post_title] =>
               [post_excerpt] =>
               [post_status] => publish
               [comment_status] => open
               [ping_status] => open
               [post_password] =>
               [post_name] => 87
               [to_ping] =>
               [pinged] =>
               [post_modified] => 2015-07-29 20:55:10
               [post_modified_gmt] => 2015-07-29 18:55:10
               [post_content_filtered] =>
               [post_parent] => 76
               [guid] => http://example.com/?p=87
               [menu_order] => 7
               [post_type] => nav_menu_item
               [post_mime_type] =>
               [comment_count] => 0
               [filter] => raw
               [db_id] => 87
               [menu_item_parent] => 78
               [object_id] => 85
               [object] => page
               [type] => post_type
               [type_label] => Page
               [url] => http://example.com/example-page-3/subpage-2/subpage-3/subpage-4/
               [title] => Subpage-4
               [target] =>
               [attr_title] =>
               [description] =>
               [classes] => Array
                (
                 [0] =>
                )
               [xfn] =>
               [children] => Array
                (
                 [0] => WP_Post Object
                  (
                   [ID] => 366
                   [post_author] => 1
                   [post_date] => 2015-07-29 20:52:46
                   [post_date_gmt] => 2015-07-29 18:52:46
                   [post_content] =>
                   [post_title] =>
                   [post_excerpt] =>
                   [post_status] => publish
                   [comment_status] => open
                   [ping_status] => open
                   [post_password] =>
                   [post_name] => 366
                   [to_ping] =>
                   [pinged] =>
                   [post_modified] => 2015-07-29 20:55:10
                   [post_modified_gmt] => 2015-07-29 18:55:10
                   [post_content_filtered] =>
                   [post_parent] => 85
                   [guid] => http://example.com/?p=366
                   [menu_order] => 8
                   [post_type] => nav_menu_item
                   [post_mime_type] =>
                   [comment_count] => 0
                   [filter] => raw
                   [db_id] => 366
                   [menu_item_parent] => 87
                   [object_id] => 112
                   [object] => page
                   [type] => post_type
                   [type_label] => Page
                   [url] => http://example.com/example-page-3/subpage-2/subpage-3/subpage-4/subpage-5/
                   [title] => Subpage-5
                   [target] =>
                   [attr_title] =>
                   [description] =>
                   [classes] => Array
                    (
                     [0] =>
                    )
                   [xfn] =>
                   [children] => Array
                    (
                    )
                  )
                )
              )
            )
          )
        )
      )
    )
  )
)

/**
 * Modification of "Build a tree from a flat array in PHP"
 *
 * Authors: @DSkinner, @ImmortalFirefly and @SteveEdson
 *
 * @link http://stackoverflow.com/a/28429487/2078474
 */
function buildTree( array &$elements, $parentId = 0 )
{
    $branch = array();
    foreach ( $elements as &$element )
    {
        if ( $element->menu_item_parent == $parentId )
        {
            $children = buildTree( $elements, $element->ID );
            if ( $children )
                $element->wpse_children = $children;

            $branch[$element->ID] = $element;
            unset( $element );
        }
    }
    return $branch;
}

/**
 * Transform a navigational menu to it's tree structure
 *
 * @uses  buildTree()
 * @uses  wp_get_nav_menu_items()
 *
 * @param  String     $menud_id
 * @return Array|null $tree
 */
function wpse_nav_menu_2_tree( $menu_id )
{
    $items = wp_get_nav_menu_items( $menu_id );
    return  $items ? buildTree( $items, 0 ) : null;
}

$tree = wpse_nav_menu_2_tree( 'my_menu' );  // <-- Modify this to your needs!
print_r( $tree );

$json = json_encode( $tree );

$w = new WPSE_Nav_Menu_Tree;
$args = (object) [ 'items_wrap' => '', 'depth' => 0, 'walker' => $w ];
$items = wp_get_nav_menu_items( 'my_menu' );
walk_nav_menu_tree( $items, $args->depth, $args );
print_r( $w->branch );

class WPSE_Nav_Menu_Tree extends Walker_Nav_Menu
{
   public $branch = [];

   public function display_element($element, &$children, $max_depth, $depth = 0, $args, &$output )
   {
      if( 0 == $depth )
         $this->branch[$element->ID] = $element;

      if ( isset($children[$element->ID] ) )
         $element->wpse_children = $children[$element->ID];

      parent::display_element($element, $children, $max_depth, $depth, $args, $output);
   }
}

wp_nav_menu(array(
    'menu' => 6, // your menu id, name, or slug
    'echo' => true, // set this to false if you want a string back instead
    'walker' => new Your_Walker(),
));