Estimation and closed-loop control of COG/ZMP in biped devices blending CoP measures and kinematic information

Abstract

The zero moment point (ZMP) and the linearized inverted pendulum model linking the ZMP to the center of gravity (COG) have an important role in the control of the postural equilibrium (balance) of biped robots and lower-limb exoskeletons. A solution for balance real time control, closing the loop from the joint actual values of the COG and ZMP, has been proposed by Choi. However, this approach cannot be practically implemented: While the ZMP actual value is available from the center of pressure (CoP) measured under the feet soles, the COG is not measurable, but it can only be indirectly assessed from the joint-angle measures, the knowledge of the kinematics, and the usually poorly known weight distribution of the links of the chain. Finally, the possible presence of unknown external disturbance forces and the nonlinear, complex nature of the kinematics perturb the simple relationship between the ZMP and COG in the linearized model. The aim of this paper is to offer, starting from Choi's model, a practical implementation of closed-loop balance control fusing CoP and joint-angle measures, eliminating possible inconsistencies. In order to achieve this result, we introduce a model of the linearized inverted pendulum for an extended estimation, not only of COG and ZMP, but also of external disturbances. This model is then used, instead of Choi's equations, for estimation and balance control, using H∞ theory. As the COG information is recovered from the joint-angle measures, the identification of a statistically equivalent serial chain (SESC) linking the COG to the joint angles is also discussed.