  Lead-free antiferroelectric perovskite $\rm AgNbO_3$ is nowadays attracting
extensive research interests due to its promising applications in energy
storage. Although great progress has been made in optimizing the material
performance, fundamental questions remain regarding the mechanism stabilizing
the antiferroelectric $Pbcm$ phase. Here, combining structural symmetry
analysis and first-principles calculations, we identified crucial anharmonic
couplings of oxygen octahedra rotations and cation antipolar motions which
contribute significantly to lowering the energy of the $Pbcm$ phase. The
stabilization of this phase shows close similarities with the stabilization of
the $Pbam$ phase in $\rm PbZrO_3$ except that in $\rm AgNbO_3$ the octahedra
rotations are the primary distortions while the antipolar cation motions appear
to be secondary. The appearance and significant amplitude of the latter are
explained from the combination of hybrid-improper and triggered mechanisms.
