this code work will on linux, it can just combine the path, if you want more, constructor of URI could be helpful.
URL baseUrl = new URL("http://example.com/first");
URL targetUrl = new URL(baseUrl, Paths.get(baseUrl.getPath(), "second", "/third", "//fourth//", "fifth").toString());
if you path contain something need to escape, use URLEncoder.encode to escape it at first.
URL baseUrl = new URL("http://example.com/first");
URL targetUrl = new URL(baseUrl, Paths.get(baseUrl.getPath(), URLEncoder.encode(relativePath, StandardCharsets.UTF_8), URLEncoder.encode(filename, StandardCharsets.UTF_8)).toString());
example:
import java.net.MalformedURLException;
import java.net.URL;
import java.nio.file.Path;
import java.nio.file.Paths;
public class Main {
    public static void main(String[] args) {
        try {
            URL baseUrl = new URL("http://example.com/first");
            Path relativePath = Paths.get(baseUrl.getPath(), "second", "/third", "//fourth//", "fifth");
            URL targetUrl = new URL(baseUrl, relativePath.toString());
            System.out.println(targetUrl.toString());
        } catch (MalformedURLException e) {
            e.printStackTrace();
        }
    }
}
output
http://example.com/first/second/third/fourth/fifth
baseUrl.getPath() are very important, don't forget it.
a wrong example:
import java.net.MalformedURLException;
import java.net.URL;
import java.nio.file.Path;
import java.nio.file.Paths;
public class Main {
    public static void main(String[] args) {
        try {
            URL baseUrl = new URL("http://example.com/first");
            Path relativePath = Paths.get("second", "/third", "//fourth//", "fifth");
            URL targetUrl = new URL(baseUrl, relativePath.toString());
            System.out.println(targetUrl.toString());
        } catch (MalformedURLException e) {
            e.printStackTrace();
        }
    }
}
output
http://example.com/second/third/fourth/fifth
we have lost our /first in baseurl.