Control Design Schemes for Underactuated Mechanical Systems

In this chapter, the stabilization issue for UMSs is considered. The strategy employed is based on the classification of Seto and Baillieul for these systems. The authors of this classification proposed a systematic control design procedure of backstepping type for the chain structure only. We are therefore concerned here with the problem of synthesizing control laws for each of the structures of this classification; thus, providing a general treatment of all the UMSs. For this, we shall firstly extend the procedure of Seto and Baillieul to a subclass of the tree structure that can be transformed to a chain structure under some conditions. Next, a procedure to control the remaining tree structure that cannot be transformed into a chain structure is presented. Finally, the control of the isolated vertex structure, which is the most difficult structure to control, is proposed.

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