| Nonholonomic system is a very important branch of analytical mechanics. Since1788when “Nonholonomic” was put forward to now, the development of it has been hundreds ofyears. Because of its complexity, which is diferent with holonomic system, its theoreticalresearch is also more difcult. However, The nonholonomic system is of important theoreticalvalue and practical signifcance of the huge attracted the attention of scholars at home andabroad. So in recent years, the achievements of this feld are signifcant. In this article, wefrst do from the two forms of nonholonomic system，combining the dynamic model andkinematics model system with each other to begin a series of theoretical research. Finally,we take a special kind of nonholonomic system, the underactuated ship mode, into studyingand direct at dealing with the problem of the fnite-time tracking controller. In detail, wecan show all of them as the following three parts:(1)From the kinematics model with nonholonomic constraints, transform the kinematicsmodel into a dynamic model with the extended chain form by a diferential homeomorphismcoordinate transformation. And then we use a method of sliding mode control to design thecontrol law and ensure that the tracking errors reach zero in fnite time.(2)In this part, we frst establish a robot dynamics equation by using the Lagrangeequation, and fnd out its kinematic constraint matrix and constraint equations. Finally,the global stability is guaranteed and the system states accurately track the states of thereference model in fnite time via the method of NSTM.(3)Underactuated ship system, in essence, is a kind of nonholonomic system. In thefourth chapter of this article, it studies the complete state tracking control of an under-actuated ship with only two control, namely surge force and yaw moment. A novel fnitetime switching controller is developed which is based on the inherent cascade interconnectedstructure of the ship dynamics under a more relaxed assumption. |
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