  Oscillations of flagella and cilia play an important role in biology, which
motivates the idea of functional mimicry as part of bio-inspired applications.
Nevertheless, it still remains challenging to drive their artificial
counterparts to oscillate via a steady, homogeneous stimulus. Combining theory
and simulations, we demonstrate a strategy to achieve this goal by using an
elasto-electro-hydrodynamic instability. In particular, we show that applying a
uniform DC electric field can produce self-oscillatory motion of a microrobot
composed of a dielectric particle and an elastic filament. Upon tuning the
electric field and filament elasticity, the microrobot exhibits three distinct
behaviors: a stationary state, undulatory swimming and steady spinning, where
the swimming behavior stems from an instability emerging through a Hopf
bifurcation. Our results imply the feasibility of engineering self-oscillations
by leveraging the elasto-viscous response to control the type of bifurcation
and the form of instability. We anticipate that our strategy will be useful in
a broad range of applications imitating self-oscillatory natural phenomena and
biological processes.
