This paper presents a combined origami-tensegrity modular system for the design of flat-foldable robots. Pre-tensioned cables integrated in the origami-inspired structure control both the deployed shape and the structural stiffness. The variable shape and stiffness allow for adaptation to uncertain environments, which can be challenging for conventional “stiff” robots. The modular design system is based on Miura-ori tubes and allows for robot designs tailored to specific missions. A particular example robot concept is presented, which demonstrates shape authority and stiffness modulation. We describe an analytical model for structural stiffness for such robot concepts.