Natural principal connections on the principal gauge prolongation of a principal bundle

Let Γ be a principal connection on a principal bundle π: P → M and let Λ be a linear connection on M. We describe all possible natural prolongations of Γ, with respect to Λ, to principal connections on the principal gauge prolongation Wr P of P. For r = 1, 2 we give the full classification, for r ≥ 3 we give a base of natural operators which generates all possible natural principal connections on WrP.