Ground Reference Points in Legged Locomotion: Definitions, Biological Trajectories and Control Implications

The zero moment point (ZMP), foot rotation indicator (FRI) and centroidal moment pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. In this paper, we study these reference points for normal human walking, and discuss their applicability in legged machine control. Since the FRI was proposed as an indicator of foot rotation, we hypothesize that the FRI will closely track the ZMP in early single support when the foot remains flat on the ground, but will then significantly diverge from the ZMP in late single support as the foot rolls during heel-off. Additionally, since spin angular momentum has been shown to remain small throughout the walking cycle, we hypothesize that the CMP will never leave the ground support base throughout the entire gait cycle, closely tracking the ZMP. We test these hypotheses using a morphologically realistic human model and kinetic and kinematic gait data measured from ten human subjects walking at self-selected speeds. We find that the mean separation distance between the FRI and ZMP during heel-off is within the accuracy of their measurement (0.1% of foot length). Thus, the FRI point is determined not to be an adequate measure of foot rotational acceleration and a modified FRI point is proposed. Finally, we find that the CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% The International Journal of Robotics Research Vol. 24, No. 12, December 2005, pp. 1013-1032, DOI: 10.1177/0278364905058363 ©2005 SAGE Publications Figures 1 and 3–9 appear in color online: http://jrp.sagepub.com of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking. KEY WORDS—legged locomotion, control, biomechanics, human, zero moment point, center of pressure, foot rotation indicator, centroidal moment pivot 1. Nomenclature ai = body segment icenter of mass acceleration α = parameter used for optimization of human model mass parameters D = relative mass distribution described by a 16-component vector DA = average relative mass distribution (Winter 1990) DR = resulting relative mass distribution DS = subject specific relative mass distribution obtained by equal density assumption D S = relative mass of the ith link F = net force acting on a whole body (in free fall Fx = Fy = 0, Fz = −Mg) Fankle = net force at the stance foot ankle joint exerted from the rest of the body FG.R. = ground reaction force FG.R. ⊥ = component of the ground reaction force normal to the surface FR. = reaction force (general surface) F x = net zero force in x-direction corresponding to the moment balance strategy