Free affine groups acting properly discontinuously

Consider a real semisimple group G and a representation rho of G on a vector space V. We ask the following question: does the affine group G |x V (semidirect product of G by V) have a Zariski-dense, nonabelian free subgroup that acts properly discontinuously on V?

We are going to present a simple algebraic criterion on the representation rho that is sufficient (and conjecturally necessary) for the answer to be affirmative. We will then talk about the problem of explicit classification of representations satisfying this criterion.