  We study the existence and stability of $\pi$-solitons on a ring of
periodically oscillating waveguides. The array is arranged into
Su-Schrieffer-Heeger structure placed on a ring, with additional spacing
between two ends of the array. Due to longitudinal oscillations of waveguides,
this Floquet structure spends half of the longitudinal period in topological
phase, while on the other half it is nontopological. Nevertheless, waveguide
oscillations lead to the emergence of anomalous topological $\pi$-modes at both
ends of the structure that strongly couple in our ring geometry, leading to the
formation of previously unexplored in-phase and out-of-phase $\pi$-modes. We
study topological solitons bifurcating from such linear $\pi$-modes and
demonstrate how their properties and stability depend on the size of the ring
and on spacing between two ends of the array.
