Add Page ID class to nav menu items

I would like to add classes containing the page id numbers to the <li> items in my nav menu. Similar classes are generated by wp_page_menu() but for some reason they’re not generated by wp_nav_menu().

I thought perhaps I could use the “walker” functionality (which I’m only now discovering) to add a custom class to the <li> tags, and use get_post_meta( $item->ID, '_menu_item_object_id', true ); to get the ID numbers, but I’m having a hell of a time figuring out how to do it. Everyone on the various forums seems to have questions about using the walker class for sub-menus and so forth and I’ve tried various codes from my searches but nothing is working. I just need a custom class with the page ID in each <li> tag.

My current menu code is the basic:

function abdmenu_nav()
{
wp_nav_menu(
array(
    'theme_location'  => 'header-menu',
    'menu'            => '',
    'container'       => 'div',
    'container_class' => 'menu-{menu slug}-container',
    'container_id'    => '',
    'menu_class'      => 'menu',
    'menu_id'         => '',
    'echo'            => true,
    'fallback_cb'     => 'wp_page_menu',
    'before'          => '',
    'after'           => '',
    'link_before'     => '',
    'link_after'      => '',
    'items_wrap'      => '<ul>%3$s</ul>',
    'depth'           => 0,
    'walker'          => ''
    )
);
}

I’m sure this is simpler than I’m making it but I’ve never dealt with the walker class before. I can’t even find anything about whether it’s even necessary for what I’m trying to do. If it is, how would I set it up?

We can add custom nav menu classes through the nav_menu_css_class filter.

Example:

The following should add the CSS class wpse-object-id-{object_id} to the <li> tags:

// Add filter
add_filter( 'nav_menu_css_class', 'wpse_menu_item_id_class', 10, 2 ); 

// Your navigational menu
wp_nav_menu( $args );

// Remove filter
remove_filter( 'nav_menu_css_class', 'wpse_menu_item_id_class', 10, 2 );

where we define the filter callback as:

/**
 * Custom Nav Menu Class For Page ID
 */
function wpse_menu_item_id_class( $classes, $item )
{
    if( isset( $item->object_id ) )
        $classes[] = sprintf( 'wpse-object-id-%d', $item->object_id );

    return $classes;
}

Here the object_id attribute should give us the corresponding page/post ID.

We can see that this attribute originates from the wp_setup_nav_menu_item() core function:

$menu_item->object_id = ! isset( $menu_item->object_id ) 
    ? get_post_meta( $menu_item->ID, '_menu_item_object_id', true ) 
    : $menu_item->object_id;