  Reduced-order template models are widely used to control high
degree-of-freedom legged robots, but existing methods for template-based
whole-body control rely heavily on heuristics and often suffer from robustness
issues. In this letter, we propose a template-based whole-body control method
grounded in the formal framework of approximate simulation. Our central
contribution is to demonstrate how the Hamiltonian structure of rigid-body
dynamics can be exploited to establish approximate simulation for a
high-dimensional nonlinear system. The resulting controller is passive, more
robust to push disturbances, uneven terrain, and modeling errors than standard
QP-based methods, and naturally enables high center of mass walking. Our
theoretical results are supported by simulation experiments with a 30
degree-of-freedom Valkyrie humanoid model.
