Bibliography

(eng): The hybrid invariance of the collocated virtual holonomic constraints for general underactuated mechanical systems is studied here. The collocated virtual holonomic constraints involve directly actuated coordinates only and they preserve the kinetic symmetry and the Lagrangian character of the corresponding restricted dynamics. Their hybrid invariance can be combined with the walking design during the swing phase based on the kinetic symmetry to achieve the exponential stable multi-step walking. Results are illustrated by the case study of the planar four link mechanical chain and its walking-like movement.