Thanks everybody for replying. I know that the r-th homotopy groups of $S^k$ are a difficult problem for r bigger than k. In this case, I am only interested in the case r smaller or equal to p.q = dim Gr (p,q).

Prof Budney, I just would like to know, if there exists such a description, the r-homotopy groups of the Grassmannian for r less or equal than the dim of the grassmannian itself. Sorry if I don't manage to be more specific, but it is exactly because I don't understand what can appears there....

I mean r less or equal than the dimension of the grassmannia Gr (p,q)