## Main parameters of the model.

(A) We take the theoretical optic flow vector () to be the opposite of the 3-D speed vector () experienced by the hoverfly. We calculated a horizontal () and a vertical () component of this theoretical optic flow vector in the hoverfly’s reference frame (*R*_{fly}) depending on the estimated pitch orientation. (B) The force produced by the hoverflies’ flapping wings () is assumed to be orthogonally oriented with respect to the body pitch orientation [11]. Moving forward is then achieved by pitching down from the head and moving backward, or braking, by pitching up from the head. Lift force () corresponds to the vertical component of in the inertial reference frame and thrust force () to the horizontal component. As depicted in [35], we assumed a pure active control of the pitch torque which is seen to occur during a fraction of the wingstroke, about half of a wing beat period (i.e., about 2ms for an hoverfly, see [3]).