Robust stabilization of hybrid periodic orbits of passive walking mechanisms

In this paper, we develop a control law to stabilize passive periodic orbits (without external enregy) of a class of autonomous mechanical systems subject to model uncertainties. The dynamic model of such systems is Lagrangian and include multiple phases (modes) and discrete jumps (e. g walking robots). The approach is based in the notion of controlled symmetry (due to spong) which capture the effect of the control input on the invariance of the system Lagrangian under group action. Simulation results are given for a simple robotic system.