This paper discusses a criterion judging whether a walking plan will be completely done or not, considering dynamics. A conventional“Zero Moment Point”is a useful criterion, but it is available for only a walk on a flat even terrain, and not available for that on a general rough terrain. So, we propose a new criterion named“Tumble Stability, ”in which considering a direction that a machine would be tumbling, if all the contact points except two were disappeared. The tumbling motion will be protected in practice, if some imaginarily disappeared contact points can produce a supporting force to avoid tumbling. In a case that no contact points can produce a force against tumbling, the machine will tumble indeed. By using this criterion, we can judge a plan of walking on any terrain, including walls and ceilings. We also propose a value indicating a stability named“Tumble Stability Margin, ”which equals to the conventional“Stability margin”in case of walking on a flat even terrain, and is useful for any other general terrain.
