广泛使用的稳定性参数,零力矩点(ZMP),通常在地面上定义,被重新定义,在本文中,以两种不同的方式获得更通用的形式,允许其应用于不仅在地面上支持的系统,因此,它们的支撑多边形不仅在地板上延伸。这样,它可以确定在任意高度与环境交互的人形机器人和其他基于漂浮的机器人的稳定性。在第一次重新定义中,ZMP表示为包含所有可能的ZMP的线,称为零力矩线(ZML),而在第二次重新定义中,ZMP表示为ZMP角度,即,ZML和垂直线之间的角度,通过被研究系统的质心(COM)。第一个重新定义在已知外力及其作用位置的情况下很有用,而第二个重新定义可以应用于已知所研究系统的COM并且可以跟踪的情况。ZMP的第一次重新定义也适用于使用两个测力板执行的两个不同的测量。两个力传感器,和Optitrack系统。在第一次测量中,一个受试者从长凳上站起来,坐下来,同时被他的手拉着,在第二次测量中,两个主体站着不动,抓住两个双把手,向后倾斜。在这两种情况下,研究和讨论了参与测量的受试者的稳定性。
The widely used stability parameter, the zero moment point (ZMP), which is usually defined on the ground, is redefined, in this paper, in two different ways to acquire a more general form that allows its application to systems that are not supported only on the ground, and therefore, their support polygon does not extend only on the floor. This way it allows to determine the stability of humanoid and other floating-based robots that are interacting with the environment at arbitrary heights. In the first redefinition, the ZMP is represented as a line containing all possible ZMPs, called the zero moment line (ZML), while in the second redefinition, the ZMP is represented as the ZMP angle, i.e., the angle between the ZML and the vertical line, passing through the center of mass (COM) of the investigated system. The first redefinition is useful in situations when the external forces and their acting locations are known, while the second redefinition can be applied in situations when the COM of the system under study is known and can be tracked. The first redefinition of the ZMP is also applied to two different measurements performed with two force plates, two force sensors, and the Optitrack system. In the first measurement, a subject stands up from a bench and sits down while being pulled by its hands, while in the second measurement, two subjects stand still, hold on to two double handles, and lean backward. In both cases, the stability of the subjects involved in the measurements is investigated and discussed.