This paper proposes a real-time balance control technique that can be implemented to bipedal robots (exoskeletons, humanoids) whose ankle joints are powered via variable physical stiffness actuators. To achieve active balancing, an abstracted biped model, torsional spring-loaded flywheel, is utilized to capture approximated angular momentum and physical stiffness, which are of importance in postural balancing. In particular, this model enables us to describe the mathematical relation between Zero Moment Point and physical stiffness. The exploitation of variable physical stiffness leads to the following contributions: i) Variable physical stiffness property is embodied in a legged robot control task, for the first time in the literature to the authors' knowledge. ii) Through experimental studies conducted with our bipedal exoskeleton, the advantages of variable physical stiffness strategy are demonstrated with respect to the optimal constant stiffness strategy. The results indicate that the variable stiffness strategy provides more favorable results in terms of external disturbance dissipation, mechanical power reduction, and ZMP/CoM position regulation.

We extend the classical integral Input-to-State Stability (iISS) theory to systems evolving on complete Riemannian manifolds and admitting multiple disjoint invariant sets, so as to allow a much broader variety of dynamical behaviors of interest. Building upon a recent extension of the Input-to-State (ISS) theory for this same class of systems, we provide characterizations of the iISS concept in terms of dissipation inequalities and integral estimates as well as connections with the Strong iISS notion. Finally, we discuss some examples within the domain of mechanical systems.

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