Floquet theory describes the linearization of an oscillator around its orbit. We convert this familiar classical result to an empirical form, allowing Floquet models to be constructed directly from experimentally obtained trajectories of periodic gaits. The Floquet model can be used to derive dimensionally reduced "templates" that predict responses to transient stimuli and be used as maneuvers through transient destabilization. The ability to express maneuvers in these reduced models holds promise for robot design and tuning, and for biomechanical research. We report on ongoing work applying our methods to human and cockroach data, and illustrate their use on some gaits of the Clock-Torqued Spring Loaded Inverted Pendulum (CT-SLIP) model.