I've never used Selenium but I guess it's for simulating user interaction in all browsers.
That's like integration tests.
But how do you test your js libraries/frameworks (unit testing) on all the browsers in an automated way?
For unit-testing you can try http://code.google.com/p/js-test-driver/
JsTestDriver consist of a single JAR file which contains everything you need to get started. For in depth discussion of command line option see GettingStarted.
Here is an overview of how JsTestDriver works at runtime...