We present a novel computational fabrication method for the production of Functionally Graded Structures (FGS) via robotic control of Viscous Thread Instability (VTI). Of interest in several fields and at different scales of application, the fabrication of FGS is often relying on offline fabrication workflows and on stable material conditions. By introducing partial control in the process of spatial deposition of an extruded clay thread in a state of instability, our method extends the design and fabrication possibilities of VTI to the production of FGS. Traditionally exploited for the industrial production of not-graded two-dimensional nonwoven textiles or for surface treatments in design-related 3d printing applications, we frame VTI as the main design and fabrication driver for the computational fabrication of functionally graded clay volumetric structures. Without relying on predictive physical simulation models, our method relies on feedback information provided by sensing equipment in combination with an industrial 6 axis robotic manipulator integrated with a numerically controlled clay extruder. The sensed information is used to retroactively update the inputs of a computational model programmed to guide the robotic additive fabrication of user-defined functional volumetric gradients. We illustrate the main design- and fabrication-related parameters and a set of material experiments designed to validate the accuracy of our model. We present a set of fabricated outputs to illustrate the flexibility of the model to accommodate a variety of design intentions and, finally, we discuss its potential for further research involving cross-scalar and trans-disciplinary applications.