Planar Multibody Systems Research Articles

Nonlinear control of planar multibody systems in shape space

Modeling, reduction, and nonlinear control of planar multibody systems motivated by the classicalcat-fall problem and the practical problem of reorientation of free-floating multibody satellites with rotational joints using angular-momentum-preserving controls is studied. The system model considered is reduced by the first integral (the system angular momentum) resulting in a Hamiltonian system with a configuration space of relative joint angles (shape space). Reconstruction of dynamics is applied to modify the shape-space model and track the phase shift of the absolute angles. An important reachability result is then proved in the unreduced configuration space. Control synthesis can then be found in a feedback form, solving the reorientation problem completely. Surprisingly, the reachability result breaks down in the case of the planar coupled two-body system with zero angular momentum, proving that the cat-fall phenomenon is definitely nonplanar.

Planar reorientation maneuvers of space multibody systems using internal controls

In this paper a reorientation maneuvering strategy for an interconnection of planar rigid bodies in space is developed. It is assumed that there are no exogeneous torques, and torques generated by joint motors are used as means of control so that the total angular momentum of the multibody system is a constant, assumed to be zero in this paper. The maneuver strategy uses the nonintegrability of the expression for the angular momentum. We demonstrate that large-angle maneuvers can be designed to achieve an arbitrary reorientation of the multibody system with respect to an inertial frame. The theoretical background for carrying out the required maneuvers is briefly summarized. Specifications and computer simulations of a specific reorientation maneuver, and the corresponding control strategies, are described. I. Introduction I N this paper we develop a reorientation strategy for a system of N planar rigid bodies in space that are interconnected by ideal frictionless pin joints in the form of an open kinematic chain. Angular momentum preserving controls, e.g., torques generated by joint motors, are considered. The TV-body system is assumed to have zero initial angular momentum. Our earlier work1'2 demonstrated that reorientation of a planar multibody system with three or more interconnected bodies using only joint torque inputs is an inherently nonlinear control problem that is not amenable to classical methods of nonlinear control. The goal of this study is to indicate how control strategies can be explicitly constructed to achieve the desired absolute reorientation of the TV-body system. There are many physical advantages in using internal controls, e.g., joint torque controls, to carry out the desired multibody reorientation maneuvers. First of all, this control approach does not modify the total angular momentum of the multibody system. In addition, internal controls have obvious advantages in terms of energy conservation. Moreover, they can be implemented using standard electrical servo motors, a simple and reliable control actuator technology. The formal development in this paper is concerned with control of a multibody interconnection in space that has zero angular momentum. Although these results are formulated in a general setting, we have been motivated by several classes of specific problems. Several potential applications of our general results are now described. Manipulators mounted on space vehicles and space robots have been envisioned to carry out construction, maintenance, and repair tasks in an external space environment. These space systems are essentially multibody systems satisfying the assumptions of this paper. To carry out the desired tasks, they must be capable of performing a variety of reorientation maneuvers. Previous research on maneuvering of such space multibody systems has mainly focused on maneuvers that achieve desired orientation of some of the bodies, e.g., an end effector, whereas the orientation of some of the remaining bodies cannot be specified, at least using the methodologies employed.38 Using the approach suggested in this paper, maneuvers that achieve any desired reorientation for all of the

On the Mathematical Modeling of ROV'S

Remotely operated underwater vehicles (ROV’s) are important tools for inspection and maintenance tasks in off-shore engineering and for submarine structures as well as for exploration and exploitation in deep sea mining. The communication, power, and control connection to the operation basis is usually performed by means of a tether cable (umbilical) which has a significant influence on the overall behavior of the system. In order to optimize the vehicle construction and to design an appropriate control system, knowledge about general characteristics of the dynamics of the system is required. The aim of this paper is to concentrate on the dynamic behavior of the cable and to outline a strategy to divide the cable into a quasistatic and dynamic part in order to reduce calculation time for on-line control purposes. For the numerical simulations hydrodynamic effects must properly be taken into account. In this fundamental investigation the cable is modeled as a planar multibody system with twenty elements; the generation of the symbolic equations of motion is performed by using computer algebra packages. The simulation of a typical robot manoeuver indicates the strong influence of the cable even for moderate currents.

Continuous/discrete modeling and analysis of elastic planar multi-body systems

The modeling and analysis of continuous/discrete multi-body systems are described, with emphasis on applications to elastic planar closed-loop systems. Whereas the continuous formulations presented can be applied to simplified models (with less effort) to help isolate the dominant factors for parametric evaluations in preliminary analysis studies, on the other hand, the finite element formulations described are, in general, applicable for more complex geometries and larger problems. In this regard, an explicit self-starting velocity-based time integration architecture is employed for the numerical simulation of multi-body dynamics with several inherent attractive features. Numerical test cases for planar multi-body dynamic situations employing the Timoshenko beam theory are presented from a generalized viewpoint in conjunction with the present formulations to validate the applicability of the proposed formulations.