  The variable-height inverted pendulum (VHIP) model enables a new balancing
strategy by height variations of the center of mass, in addition to the
well-known ankle strategy. We propose a biped stabilizer based on linear
feedback of the VHIP that is simple to implement, coincides with the
state-of-the-art for small perturbations and is able to recover from larger
perturbations thanks to this new strategy. This solution is based on
"best-effort" pole placement of a 4D divergent component of motion for the VHIP
under input feasibility and state viability constraints. We complement it with
a suitable whole-body admittance control law and test the resulting stabilizer
on the HRP-4 humanoid robot.
