This paper proposes a simple numerical technique for the steering of a
rbitrary analytic systems with no drift. It is based on the generation
of ''nonsingular loops'' which allow linearized controllability along
suitable trajectories. Once such loops are available, it is possible
to employ standard Newton or steepest descent methods, as classically
done in numerical control. The theoretical justification of the approa
ch relies on recent results establishing the genericity of nonsingular
control, as well as a simple convergence lemma.