This much at least is clear from your question itself that you know about CRAM being a robot and that this has something to do with cockroach or the insect world.
In principle, CRAM is inspired by the ability of insects to fit in small spaces to ensure long survival. CRAM is an acronym for “compressible robot with articulated mechanisms”. The full form of CRAM is enough to suggest that this robot has bendable joints; and like insects, it can move through or get into very tiny spaces.
One more interesting fact about CRAM is that the insect world is not the only inspiration for its design. Inspiration also came from the Japanese art of paper-folding which is known as Origami. According to the co-creator of CRAM, Kaushik Jayaram, the making of this robo-roach incorporated the combination of Math and Physics. Kaushik Jayaram works in Cambridge, Mass., at Harvard University’s Wyss Institute for Biologically Inspired Engineering.
The technology of computers was used to overcome the limiting forces like Gravitational and Frictional Force. And the computation of the energy and force needed by CRAM was done through Algebra. And as the Origami is also incorporated, the designing uses the math of shapes, i.e., geometry as well. The combination of Physics, Algebra, and Geometry, gives CRAM immense amount of flexibility which can be developed for the use of mankind in the coming years.
How can it help mankind, you would ask. The answer is very simple and clear. CRAM’s ability to get into tiny spaces like debris and cracks formed in the aftermath of a disaster will be used to rescue the victims of such disasters which is difficult to do with the help of a human.