  Capturability analysis of the linear inverted pendulum (LIP) model enabled
walking with constrained height based on the capture point. We generalize this
analysis to the variable-height inverted pendulum (VHIP) and show how it
enables 3D walking over uneven terrains based on capture inputs. Thanks to a
tailored optimization scheme, we can compute these inputs fast enough for
real-time model predictive control. We implement this approach as open-source
software and demonstrate it in dynamic simulations.
