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Balancing is a fundamental need for legged robots due to their unstablefloating-base nature. Balance control has been thoroughly studied for simplemodels such as the linear inverted pendulum thanks to the concept of theinstantaneous capture point (ICP), yet the constant center of mass heightassumption limits the application. This paper explores balancing of thevariable-height inverted pendulum (VHIP) model by introducing the\emph{instantaneous capture input} (ICI), an extension of the ICP based on itskey properties. Namely, the ICI can be computed as a function of the state, andwhen this function is used as the control policy, the ICI is renderedstationary and the system will eventually come to a stop. This characterizationinduces an analytical region of capturable states for the VHIP, which can beused to conceptually guide where to step. To further address state and controlconstraints during recovery, we present and theoretically analyze an explicitICI-based controller with online optimal feedback gains. Simulationsdemonstrate the validity of our controller for capturability maintenancecompared to an approach based on the divergent component of motion.

Instantaneous Capture Input for Balancing the Variable Height Inverted Pendulum