Titlebook: Geometric Control of Mechanical Systems; Modeling, Analysis, Francesco Bullo,Andrew D. Lewis Textbook 2005 Springer-Verlag New York 2005 g

著名

https://doi.org/10.1007/978-3-642-53994-7ure in a mechanical system that can be exploited for analysis and control. This chapter discusses an important class of manifolds, called Lie groups, that arise naturally in rigid body kinematics, as well as the properties of mechanical systems defined on Lie groups or possessing Lie group symmetries.

Dendritic-Cells

l signals: periodic, large-amplitude, high-frequency signals, which we refer to as oscillatory; and small-amplitude signals. For both classes of signals, we perform a perturbation analysis that predicts, with some specified level of accuracy, the behavior of the resulting forced affine connection system.

Sinus-Rhythm

Terrace

Lie groups, systems on groups, and symmetriesure in a mechanical system that can be exploited for analysis and control. This chapter discusses an important class of manifolds, called Lie groups, that arise naturally in rigid body kinematics, as well as the properties of mechanical systems defined on Lie groups or possessing Lie group symmetries.

CLEAR

Perturbation analysisl signals: periodic, large-amplitude, high-frequency signals, which we refer to as oscillatory; and small-amplitude signals. For both classes of signals, we perform a perturbation analysis that predicts, with some specified level of accuracy, the behavior of the resulting forced affine connection system.

Infirm

Stabilization and tracking using oscillatory controlsctive is to exploit the averaging analysis obtained in Chapter 9 for the purpose of control design. In particular, we shall present results on stabilization and tracking that are applicable to systems that are not linearly controllable. As in the perturbation analysis in Chapter 9, we shall consider smooth systems.

遺留之物

Stability.14. So-called invariance principles were later developed to establish stability properties of dynamical systems on the basis of weaker requirements than those required by Lyapunov’s original criteria. Early work on invariance principles in stability is due to Barbashin and Krasovski? [1952]; LaSall

焦慮

Controllabilityg controllability is currently unresolved, although there have been many deep and insightful contributions. While we cannot hope to provide anything close to a complete overview of the literature, we will mention some work that is commensurate with the approach that we take here. Sussmann has made v

largesse

Low-order controllability and kinematic reductionLynch [2001], and considered here in Section 8.3. While the controllability results of Section 8.2 have more restrictive hypotheses than those of Chapter 7, it turns out that the restricted class of systems are those for which it is possible to develop some simplified design methodologies for motion

頂點

Motion planning for underactuated systems3b]. The kinematic reduction results of Section 8.3 provide a means of reducing the order of the dynamical systems being considered from two to one. The idea of lowering the complexity of representations of mechanical control systems can be related to numerous previous efforts, including work on hyb