Two options that I know of but there will certainly be more.
FileZilla is free but the problem is you really only want to publish what has changed and I don't believe FileZilla can do that.
I use SyncBack which is essentially a backup tool. It looks at what is in the source (the folder you have generated to) and looks at the target (where you last published) and identifies the differences. Then you let it update the target. RoboHelp's own publish does not delete unused files, SyncBack can. Depends on how you figure it.
The key thing is a tool that can be set up to only upload what has changed.