A backstepping procedure for a class of underactuated system with tree structure

In the present paper, we propose to transform via a change of coordinates and control law the structure of a subclass of underactuated mechanical system in tree structure to a chain one. By this way, we allow extension of some classical control design as backstepping and feedback linearization to a class of underactuated system to which these approaches fail to be applied initially. Specially, a systematic backstepping strategy is applied to stabilize the Tora system to show the effectiveness of the procedure. However, due to the transformation, one assumption in the control scheme is verified only on a domain rather then the hole space. The control law derived from this procedure can still be applied but the stability is not global. In order to make the latter global, we propose to switch to an other control near the singularities. The simulation results for using the hybrid switching control are given.