Periodically driven quantum systems, known as Floquet systems, provide a versatile platform for engineering novel topological phases absent in static settings. However, dynamically characterizing these nonequilibrium topological invariants remains a challenge. Here, we develop a Floquet perturbation theory in the extended Hilbert space to analytically describe the center-of-mass (c.m.) dynamics of a wave packet. When applied to the driven Su-Schrieffer-Heeger model, our theory reveals that the c.m. exhibits multifrequency Zitterbewegung oscillations whose spectral composition and phase are directly tied to the system's Floquet band structure. Crucially, we find that band inversions at topological phase transitions imprint distinct signatures on the c.m. dynamics, including the emergence of low-frequency modes and phase shifts of the oscillatory trajectory. These dynamical signatures offer a practical protocol for detecting Floquet topological invariants, which we demonstrate for both high-frequency and strongly driven regimes. Our work establishes c.m. dynamics as a simple and experimentally accessible probe for exploring topological phase transitions in Floquet systems.

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• Topological phase transition
• Topological phases of matter
• Floquet systems