They all started 'on' an equal 'footing' (with one another). = They all started 'on' the same 'footing'. [=none of them had an advantage when they started]
a nation that is 'on' a friendly 'footing' with its neighbors [=a nation that has friendly relations with its neighbors]
The loose stones made it difficult for me to maintain/keep my 'footing'. [=to avoid slipping or falling]
(..) and now it's easier to target an individual. In the chaos a calf is separated from its mother. The calf is young, but it can outrun the wolf if only it manages to keep its footing. At this stage the odds are even - either the caribou will make a mistake or after a mile the wolf will give up. (..)2006 TvShow: Planet Earth Title: From Pole to Pole Season: 1 Episode 1