Nonlinear orbital ℋ∞-stabilization of underactuated mechanical systems with unilateral constraints

The present investigation introduces a novel control strategy for hybrid dynamic systems with unilateral constraints. Sufficient conditions are presented to ensure internal asymptotic stability and external disturbances attenuation. The developed synthesis is applied to the orbital stabilization of an underactuated bipedal robot periodically touching the ground. Good performance of the closed-loop system is obtained not only in the presence of external disturbances, affecting the gait of the biped between impacts and under uncertainties at the velocity restitution when the ground collision occurs.