  Liquid shells (e.g. double emulsions, vesicles etc.) are susceptible to
interfacial instability and rupturing when driven out of mechanical
equilibrium. This poses a significant challenge for the design of liquid shell
based micro-machines, where the goal is to maintain stability and dynamical
control in combination with motility. Here we present our solution to this
problem with controllable self-propelling liquid shells, which we have
stabilized using the soft topological constraints imposed by a nematogen oil.
We demonstrate, through experiments and simulations, that anisotropic
elasticity can counterbalance the destabilizing effect of viscous drag induced
by shell motility, and inhibit rupturing. We analyze their propulsion dynamics,
and identify a peculiar meandering behavior driven by a combination of
topological and chemical spontaneously broken symmetries. Based on our
understanding of these symmetry breaking mechanisms, we provide routes to
control shell motion via topology, chemical signaling and hydrodynamic
interactions.
