Underactuated Case Research Articles

Augmented Hamiltonian Formulation and Energy-Based Control Design of Uncertain Mechanical Systems

This paper mainly investigates augmented Hamiltonian formulation for both fully actuated and underactuated uncertain mechanical systems. First, a high-order partial derivative operator, called the unified partial derivative operator (UPDO), is given, and its properties are investigated, which plays a very important role in presenting the main results of this paper. Secondly, using the tool UPDO, the idea of shaping potential energy, and the pre-feedback technique, an augmented Hamiltonian structure with dissipation is provided for both fully actuated and underactuated uncertain mechanical systems. It is shown that the augmented Hamiltonian formulation has some nice properties for further analysis and control, and at the same time, its matching condition in the underactuated case becomes a set of algebraic equations, which are much easier to solve in comparison with solving a set of partial differential equations. Finally, as an application, the energy-based robust adaptive control is studied by using the augmented Hamiltonian formulation, and a new energy-based adaptive L 2 disturbance attenuation controller is designed for the uncertain mechanical systems. Study of an illustrative example with simulations shows that the controller obtained in this paper works very well in handling disturbances and uncertainties in the systems.

Kinematic analysis of a flexible six-DOF parallel mechanism

In this paper, a new type of six-degrees of freedom (DOF) flexible parallel mechanism (FPM) is presented. This type of parallel mechanism possesses several favorable properties: (1) its number of DOFs is independent of the number of serial chains which make up the mechanism; (2) it has no kinematical singularities; (3) it is designed to move on rails, and therefore its workspace is much larger than that of a conventional parallel manipulator; and (4) without changing the number of DOFs and the kinematics of the mechanisms, the number of the serial chains can be reconfigured according to the needs of the tasks. These properties make the mechanism very preferable in practice, especially for such tasks as joining huge ship blocks, in which the manipulated objects vary dramatically both in weights and dimensions. Furthermore, the mechanism can be used as either a fully actuated system or an underactuated system. In the fully actuated case, the mechanism has six DOF motion capabilities and manipulation capabilities. However, in the underactuated case, the mechanism still has six DOF motion capabilities, but it has only five DOF manipulation capabilities. In this paper, both the inverse and forward kinematics are studied and expressed in a closed form. The workspace and singularity analysis of the mechanism are also presented. An example is presented to illustrate how to calculate the kinematics of the mechanism in both fully-actuated and underactuated cases. Finally, an application of such a mechanism to manufacturing industry is introduced.