Trajectory Tracking of Multibody Systems
The methods of feedback linearization and feedforward control based on exact model inversion are powerful tools for output trajectory tracking of nonlinear systems. Using these methods, one key step is the determination of the input–output normal form. In
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Trajectory Tracking of Multibody Systems
The methods of feedback linearization and feedforward control based on exact model inversion are powerful tools for output trajectory tracking of nonlinear systems. Using these methods, one key step is the determination of the input–output normal form. In general, this step depends heavily on symbolic calculations of Lie derivatives of the system outputs in state space. However, establishing a symbolical state space description of a multibody system requires the symbolical inversion of the mass matrix. This yields, even in small mechanical systems, very complex state space descriptions. Therefore, the straightforward application of these nonlinear control methods to multibody systems is, in general, limited to systems with very few degrees of freedom. In this chapter, it is shown that it is often possible to determine the input– output normal form and the resulting control laws by direct symbolic manipulations on the second order differential equations of motion of a multibody system. Thereby, no explicit utilization of their state space description is necessary, since the special structure of the equations of motion of multibody systems is utilized. However, in order to get a full understanding of this procedure and the underlying differential geometric control techniques, it is very important to relate to the corresponding theory in state space, which is presented in the previous chapter. In the following, different cases of holonomic multibody systems are investigated, whereby the main focus is put on underactuated multibody systems, which possess fewer control inputs than degrees of freedom. The techniques presented in this chapter are mainly applied to trajectory tracking control and working point chances of multibody systems, which normally include large nonlinear motions and require nonlinear control techniques. In contrast, it should be noted that stabilization and regulation around a stationary point might be often more efficiently accomplished by Jacobian linearization and linear control techniques. This chapter is organized in three sections. In the first section, fully actuated multibody systems are briefly presented. Here the main focus is put on inverse dynamics, which is the most simple form of nonlinear control of multibody systems. In the second section, an emphasis is placed on underactuated multibody systems, which are much more difficult to handle than fully actuated multibody systems. Firstly, general
R. Seifried, Dynamics of Underactuated Multibody Systems, Solid Mechanics and Its Applications 205, DOI: 10.1007/978-3-319-01228-5_4, © Springer International Publishing Switzerland 2014
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4 Trajectory Tracking of Multibody Systems
underactuated systems are analyzed and classified. Then, different types of system outputs and the consequences for control design are discussed in detail. Afterwards these methods are applied to the control of a manipulator with a passive joint. In the last section, a design approach for bounded and causal feedforwa
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