Updated:
$('.slide').on('click', function(event) {
var el = $(this);
$('html, body').stop().animate({
scrollTop: $(el.attr('target')).offset().top
}, 1500);
event.preventDefault();
});
HTML
<ul class="nav">
<li class="slide" target="#slide-1">Slide 1</li>
<li class="slide" target="#slide-2">Slide 2</li>
<li class="slide" target="#slide-3">Slide 3</li>
</ul>
<div class="content" id="slide-1">Slide 1 content</div>
<div class="content" id="slide-2">Slide 2 content</div>
<div class="content" id="slide-3">Slide 3 content</div>
As royalSlider is removing html code and and adding slides, above will not work
*Updated Code for royalSlider
HTML
<div class="royalSlider rsDefault">
<img src="http://dimsemenov.com/plugins/royal-slider/img/previews/home/visible-nearby.jpg">
<img src="http://dimsemenov.com/plugins/royal-slider/img/previews/home/animated-blocks.jpg">
<img src="http://dimsemenov.com/plugins/royal-slider/img/previews/home/fullwidth.jpg">
</div>
<div class="content" id="slide-1">Slide 1 content</div>
<div class="content" id="slide-2">Slide 2 content</div>
<div class="content" id="slide-3">Slide 3 content</div>
JS
$(".royalSlider").royalSlider({});
var slider = $(".royalSlider").data('royalSlider');
slider.ev.on('rsSlideClick', function() {
$('html, body').stop().animate({
scrollTop: $('#slide-' + slider.currSlideId).offset().top
}, 1500);
});