under one's own steam

Now the tug no longer moved under her own steam, nor had it been since coming alongside the wall of the central pier. For all vessels must be towed through the lock basins, and towed not by other craft, but by electric locomotives that run alongside, on top of the concrete walls.

"People come at their own risk, at their own expense, under their own steam," said Mhairi McKenzie-Robinson, chief administrator of the Fringe [Edinburgh Fringe Festival].

I'd been wanting her to go for a long, long time, hoping she'd get up the gumption to do it under her own steam so I wouldn't have to make a scene about it.