  This paper proposes a technique for automatic gain tuning of a momentum based
balancing controller for humanoid robots. The controller ensures the
stabilization of the centroidal dynamics and the associated zero dynamics.
Then, the closed-loop, constrained joint space dynamics is linearized and the
controller's gains are chosen so as to obtain desired properties of the
linearized system. Symmetry and positive definiteness constraints of gain
matrices are enforced by proposing a tracker for symmetric positive definite
matrices. Simulation results are carried out on the humanoid robot iCub.
