This paper discusses the concept and parameter design of a Robust Stair Climbing Compliant Modular Robot, capable of tackling stairs with overhangs. Modifying the geometry of the periphery of the wheels of our robot helps in tackling overhangs. Along with establishing a concept design, robust design parameters are set to minimize performance variation. The Grey-based Taguchi Method is adopted for providing an optimal setting for the design parameters of the robot. The robot prototype is shown to have successfully scaled stairs of varying dimensions, with overhang, thus corroborating the analysis performed.