I. Introduction
Safe walking has been studied from different perspectives, e.g., collision avoidance [1], [2], [3] and balance maintenance [4], [5], [6]. Recently, the concept of passive safety which was first exploited in mobile robots navigation [7] has attracted much attention [8], [9], [10]. In addition to preserving balance, passive safety also requires a robot to come to a stop after a finite number of steps or even zero step [9], which can be ensured by obeying - or zero-step capturability constraints [11].