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

Abstract

The Zero Moment Point (ZMP) and Centroidal Moment Pivot (CMP) are important ground reference points used for motion identification and control in biomechanics and legged robotics. Using a consistent mathematical notation, we define and compare the ground reference points. We outline the various methodologies that can be employed in their estimation. Subsequently, we analyze the ZMP and CMP trajectories for level-ground, steady-state human walking. We conclude the chapter with a discussion of the significance of the ground reference points to legged robotic control systems. In the Appendix, we prove the equivalence of the ZMP and the center of pressure for horizontal ground surfaces, and their uniqueness for more complex contact topologies. 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 this hypothesis 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 CMP never leaves the ground support base, and the mean separation distance between the CMP and ZMP is small (14% of foot length), highlighting how closely the human body regulates spin angular momentum in level ground walking.