Abstract
Different from the VUMs discussed in the last section, a planar underactuated manipulator (PUM)Planar Underactuated Manipulator (PUM) moves in a horizontal plane without the gravity. Both space manipulators [1] and underwater vehicles [2] belong to this kind of system. The study on this kind of system is meaningful for the aeronautics and astronautics engineering and deep-sea detecting engineering. For such a system, since the linear approximation model of its equilibrium point is uncontrollable [3, 4, 5], control methods for the VUM are not suitable for the PUM. This chapter mainly discusses the planar n-link ( $$n\geqslant 2$$ ) manipulators with a passive first joint (i.e., planar PA $$^{n-1}$$ ( $$n\geqslant 2$$ ) manipulator Planar PA () manipulator) [6]. Such planar manipulators can be divided into two kinds. One is the planar two-link underactuated manipulator (i.e., planar Acrobot Planar Acrobot), which is a holonomic system [7]. The other is the planar manipulators with three or more links, which can be classified as the first-order nonholonomic system [8]. The motion-state constraints and stable control methods of these two kinds of manipulators are different. This chapter will also provide the motion-state constraint analysis and the respective control methods in details.
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