SUMMARY This paper discusses the concept and parameter design of a robust stair-climbing compliant modular robot, capable of tackling stairs with overhangs. Geometry modifications of the periphery of the wheels of our robot helped in tackling overhangs. Along with establishing a concept design, the robust design parameters are set to minimize performance variations. The Grey-based Taguchi method is applied to provide 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. © Cambridge University Press 2018.