I am sure there are other ways to analyse language, but the way I look at clauses and sentences is very similar to yours. In my definition of a sentence, no object is necessary, though. A sentence can consist of just one clause, a main clause, which need not have an object: The sun rose at six o'clock today.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.