In this paper we elaborate a study on self-stabilizing humanoid robot that achieves run-time self-stabilization and energy optimized walking gait pattern parameters on different kinds of flat surfaces. The algorithmic approach named SelSta uses biologically inspired notions that introduce robustness into the self-stabilizing functionality of the humanoid robot. The approach has been practically tested on our S2-HuRo humanoid robot and the results from the tests demonstrate that it can be successfully used on humanoid robots to achieve autonomic optimized stabilization of their walking on different kinds of flat surfaces.