  Ciliated microswimmers and flagellated bacteria alter their swimming
trajectories to follow the direction of an applied electric field exhibiting
electrotaxis. Both for matters of application and physical modelling, it is
instructive to study such behaviour in synthetic swimmers. We show here that
under an external electric field, self-propelling active droplets autonomously
modify their swimming trajectories in microchannels, even undergoing `U-turns',
to exhibit robust electrotaxis. Depending on the relative initial orientations
of the microswimmer and the external electric field, the active droplet can
also navigate upstream of an external flow following a centre-line motion,
instead of the oscillatory upstream trajectory observed in absence of electric
field. Using a hydrodynamic theory model, we show that the electrically induced
angular velocity and electrophoretic effects, along with the microswimmer
motility and its hydrodynamic interactions with the microchannel walls, play
crucial roles in dictating the electrotactic trajectories and dynamics.
Specifically, the transformation in the trajectories during upstream swimming
against an external flow under an electric field can be understood as a reverse
Hopf bifurcation for a dynamical system. Our study provides a simple
methodology and a systematic understanding of manoeuvring active droplets in
microconfinements for micro-robotic applications especially in biotechnology.
