Construction throughout history typically assumes that its blueprints and building blocks are pre-determined. However, recent work suggests that alternative approaches can enable new paradigms for structure formation. Aleatory architectures, or those which rely on the properties of their granular building blocks rather than pre-planned design or computation, have thus far relied on human intervention for their creation. We imagine that robotic swarms could be valuable to create such aleatory structures by manipulating and forming structures from entangled granular materials. To discover principles by which robotic systems can effectively manipulate soft matter, we develop a robophysical model for interaction with geometrically cohesive granular media composed of u-shape particles. This robotic platform uses environmental signals to autonomously coordinate excavation, transport, and deposition of material. We test the effect of substrate initial conditions by characterizing robot performance in two different material compaction states and observe as much as a 75% change in transported mass depending on initial substrate compressive loading. These discrepancies suggest the functional role that material properties such as packing and cohesion/entanglement play in excavation and construction. To better understand these material properties, we develop an apparatus for tensile testing of the geometrically cohesive substrates, which reveals how entangled material strength responds strongly to initial compressive loading. These results explain the variation observed in robotic performance and point to future directions for better understanding robotic interaction mechanics with entangled materials.