これは、現在のメニュー項目の子のみを表示するために使用したウォーカーです。または、独自の子がない場合はメニュー項目の兄弟。
クラス全体に各セクションを説明するコメントがあります
<?php
class SH_Child_Only_Walker extends Walker_Nav_Menu {
private $ID;
private $depth;
private $classes = array();
private $child_count = 0;
private $have_current = false;
// Don't start the top level
function start_lvl(&$output, $depth=0, $args=array()) {
    if( 0 == $depth || $this->depth != $depth )
        return;
    parent::start_lvl($output, $depth,$args);
}
// Don't end the top level
function end_lvl(&$output, $depth=0, $args=array()) {
    if( 0 == $depth || $this->depth != $depth )
        return;
    parent::end_lvl($output, $depth,$args);
}
// Don't print top-level elements
function start_el(&$output, $item, $depth=0, $args=array()) {
    $is_current = in_array('current-menu-item', $this->classes);
    if( 0 == $depth || ! $is_current )
        return;
    parent::start_el($output, $item, $depth, $args);
}
function end_el(&$output, $item, $depth=0, $args=array()) {
    if( 0 == $depth )
        return;
    parent::end_el($output, $item, $depth, $args);
}
// Only follow down one branch
function display_element( $element, &$children_elements, $max_depth, $depth=0, $args, &$output ) {
    // Check if element is in the current tree to display
    $current_element_markers = array( 'current-menu-item', 'current-menu-parent', 'current-menu-ancestor' );
    $this->classes = array_intersect( $current_element_markers, $element->classes );
    // If element has a 'current' class, it is an ancestor of the current element
    $ancestor_of_current = !empty($this->classes);
    // check if the element is the actual page element we are on.
    $is_current = in_array('current-menu-item', $this->classes);
    // if it is the current element
    if($is_current) {
        // set the count / ID / and depth to use in the other functions.
        $this->child_count = ( isset($children_elements[$element->ID]) ) ? count($children_elements[$element->ID]) : 0;
        $this->ID = $element->ID;
        $this->depth = $depth;
        $this->have_current = true;
        if($this->child_count > 0) {
            // if there are children loop through them and display the kids.
            foreach( $children_elements[$element->ID] as $child ) {
                parent::display_element( $child, $children_elements, $max_depth, $depth, $args, $output );
            }
        } else {
            // no children so loop through kids of parent item.
            foreach( $children_elements[$element->menu_item_parent] as $child ) {
                parent::display_element( $child, $children_elements, $max_depth, $depth, $args, $output );
            }
        }
    }
    // if depth is zero and not in current tree go to the next element
    if ( 0 == $depth && !$ancestor_of_current)
        return;
    // if we aren't on the current element proceed as normal
    if(! $this->have_current )
        parent::display_element( $element, $children_elements, $max_depth, $depth, $args, $output );
}
}
wp_nav_menuで他のカスタムウォーカーと同じように添付します
<?php
wp_nav_menu( array(
    'menu' => 'primary-menu'
    ,'container' => 'nav'
    ,'container_class' => 'subpages'
    ,'depth' => 0
    ,'walker' => new SH_Child_Only_Walker()
 ));
?>