Designing insect-scale robots with high mobility is becoming an essential challenge in the field of robotics research. Among the methods for fabricating the transmission mechanism of the insect-scale robot, the smart composite microstructure (SCM) method is getting more and more attention. This method can construct compact and functional miniature origami mechanisms through planarized fabrication and folding assembly processes. Our previous work has proposed an untethered robot S$^{\text{2}}$worm equipped with a novel 2-DoF origami transmission mechanism. The S$^{\text{2}}$worm is fabricated through SCM and holds a top speed of 27.4 cm/s. In this work, we propose a novel strategy for designing the insect-scale robot with high mobility, that is, applying Grassmann–Cayley Algebra (GCA) to avoid the singularity of the transmission mechanism. The experimental results prove that the singularity of the previous work has been solved. The new robot prototype S$^{\text{2}}$worm-G weighs 4.71 g, scales 4.0 cm, achieves a top speed of 75.0 cm/s and a relative speed of 18.8 bodylength/s. To the best of our knowledge, the 2-DoF origami transmission mechanism is the first parallel mechanism designed for the insect-scale robot and the singularity of the mechanism is found and solved here. The experimental results prove that the refined S$^{\text{2}}$worm-G robot is one of the best insect-scale robots for its size, mass, and mobility.