The authors of the paper under discussion did an excellent job in formulating the problem in an invariant, i.e., coordinate-free, form. Now, while they discussed problem (c) in full detail, they only gave a sketch of the solution of problem (b). There are some shortcomings in the solution proposed by the authors, as this reviewer describes below.
The authors chose the Rodrigues parameters to represent the unknown rotation matrix in this problem. However, Rodrigues parameters being unbounded, they invariably lead to ill-conditioning and overflow. In fact, Rodrigues parameters can be dispensed with, in favor of what is known as Euler parameters or, as they are also called sometimes, Euler-Rodrigues parameters. These parameters are isomorphic to quaternions.
