The inverse dynamics τ_id = M(q)vd_d + C(q, v)v - τ_g(q) - τ_app contain the mass matrix M(q) which in turn contains all the spatial inertias of the links. I'm curious what point these spatial inertias are about and what frame they are expressed in.
My application is system identification. I now have these inertias (obtained from the inverse dynamic equations) but I want to double-check whether my frames are correct.
The mass matrix M(q) is the inertia matrix for the whole system in generalized coordinates (that is, accounting for the interconnections). It doesn't generally contain the 6x6 spatial inertias of individual links, unless they are just lone free links. Even in that case the inertias must be compatible with the generalized coordinates, which relate a joint's parent frame F and child frame M (those are our conventional frame names; sorry for the re-use of "M"). That is, the coordinates represent X_FM(q), V_FM(v), and A_FM(vdot). So the inertias in the mass matrix will be about the M origin (Mo) and expressed in F.