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The focus of this survey is the modeling and control of bipedal locomotion systems. More specifically, we seek to review the developments in the field within the framework of stability and control of systems subject to unilateral constraints. We place particular emphasis on three main issues that, in our view, form the underlying theory in the study of bipedal locomotion systems. Impact of the lower limbs with the walking surface and its effect on the walking dynamics was considered first. The key issue of multiple impacts is reviewed in detail. Next, we consider the dynamic stability of bipedal gait. We review the use of discrete maps in studying the stability of the closed orbits that represent the dynamics of a biped, which can be characterized as a hybrid system. Last, we consider the control schemes that have been used in regulating the motion of bipedal systems. We present an overview of the existing work and seek to …