NullPointerException

Olá. Estou com o erro de NullPointerException mesmo tratando um cookie null.

Erro:

HTTP Status 500 -

type Exception report

message

description The server encountered an internal error that prevented it from fulfilling this request.

exception

java.lang.NullPointerException
    br.com.alura.gerenciador.Filtro.doFilter(Filtro.java:31)
note The full stack trace of the root cause is available in the Apache Tomcat/7.0.79 logs.

Apache Tomcat/7.0.79

Minha classe:

package br.com.alura.gerenciador;

import java.io.IOException;

import javax.servlet.Filter;
import javax.servlet.FilterChain;
import javax.servlet.FilterConfig;
import javax.servlet.ServletException;
import javax.servlet.ServletRequest;
import javax.servlet.ServletResponse;
import javax.servlet.annotation.WebFilter;
import javax.servlet.http.Cookie;
import javax.servlet.http.HttpServletRequest;

@WebFilter(urlPatterns="/*")
public class Filtro implements Filter{

    @Override
    public void destroy() {
        // TODO Auto-generated method stub

    }

    @Override
    public void doFilter(ServletRequest req, ServletResponse resp, FilterChain chain)
            throws IOException, ServletException {

        HttpServletRequest request = (HttpServletRequest) req;
        Cookie cookie = getUsuario(request);
        System.out.println("Usuário acessando a página: " + request.getRequestURI());
        System.out.println("Cookie:" + cookie.getName());
        chain.doFilter(req, resp);
    }

    @Override
    public void init(FilterConfig arg0) throws ServletException {
        // TODO Auto-generated method stub

    }

    public Cookie getUsuario(HttpServletRequest req){
        Cookie[] cookies = req.getCookies();
        if (cookies == null){
            return null;
        }

        for (Cookie cookie : cookies) {
            if (cookie.getName().equals("usuario.logado")) {
                return cookie;
            }
        }        
        return null;
    }

}