When a volatile droplet, such as acetone, is deposited on a floating swellable polydimethylsiloxane (PDMS) sheet, it becomes asymmetric, lobed, and mobile. I will describe this phenomenon that involves nonequilibrium swelling, evaporation and motion, working together to realize a self-excitable spatially extended oscillator. Solvent penetration causes the film to swell locally and eventually buckle, changing its shape and the drop responds by moving. Simultaneously, solvent evaporation from the swollen film causes it to regain its shape once the droplet has moved away. The process repeats and leads to complex pulsatile spinning and/or sliding movements. I will present experiments and a minimal model to describe the excitable droplet system, and highlight potential applications of this new paradigm of autonomous droplet motion.