This paper proposes a concept of center of gravity (COG) viscoelasticity to associate joint viscoelasticity with the inverted pendulum model of humanoid dynamics. Although COG viscoelasticity is based on the well-known kinematic relationship between joint stiffness and end-effector stiffness, it provides practical advantages for both analysis and control of humanoid motions. There are two main contributions. The first is that the COG viscoelasticity allows us to analyze fall risk. In a previous study, the author proposed a fall detection method based on the maximal output admissible (MOA) set, which is computed from feedback gain of the inverted pendulum model. The COG viscoelasticity associates joint viscoelasticity with the feedback gain and allows us to compute the corresponding MOA set when an arbitrary joint viscoelasticity is given. The second contribution is that the COG viscoelasticity can be also utilized in motion control. After we design a feedback gain in the inverted pendulum model utilizing the control theory, the COG viscoelasticity can directly transform it to the joint viscoelasticity. The validity of the COG viscoelasticity is verified with whole-body dynamics simulations.
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