  We investigate a systematic approach to include curvature corrections to the
isometry algebra of flat space-time order-by-order in the curvature scale. The
Poincar\'e algebra is extended to a free Lie algebra, with generalised boosts
and translations that no longer commute. The additional generators satisfy a
level-ordering and encode the curvature corrections at that order. This
eventually results in an infinite-dimensional algebra that we refer to as
Poincar\'e${}_\infty$, and we show that it contains among others an (A)dS
quotient. We discuss a non-linear realisation of this infinite-dimensional
algebra, and construct a particle action based on it. The latter yields a
geodesic equation that includes (A)dS curvature corrections at every order.
