  We examine properties of generic automorphisms of the random poset, with the
goal of explicitly characterizing them. We associate to each automorphism an
auxiliary first-order structure, consisting of the random poset equipped with
an infinite sequence of binary relations which encode the action of the
automorphism. We then explicitly characterize generic automorphisms in terms of
properties of this structure. Two notable such properties are ultrahomogeneity,
and universality for a certain class of finite structures in this language. As
this auxiliary structure seems to be new, we also address some model-theoretic
questions. In particular, this structure fails to be saturated, and its theory
neither is $\omega$-categorical nor admits quantifier-elimination, in contrast
to many known ultrahomogeneous structures in finite languages. We also examine
orbitals -- order-convex hulls of orbits -- and their use in describing
automorphisms. In particular, we introduce and use new orders on the space of
orbitals.
