  This paper presents a new condition, the fully physical consistency for a set
of inertial parameters to determine if they can be generated by a physical
rigid body. The proposed condition ensure both the positive definiteness and
the triangular inequality of 3D inertia matrices as opposed to existing
techniques in which the triangular inequality constraint is ignored. This paper
presents also a new parametrization that naturally ensures that the inertial
parameters are fully physical consistency. The proposed parametrization is
exploited to reformulate the inertial identification problem as a manifold
optimization problem, that ensures that the identified parameters can always be
generated by a physical body. The proposed optimization problem has been
validated with a set of experiments on the iCub humanoid robot.
