Abstract

In the last years modeling, simulation, and control of flexibel structures have made an essential progress, especially stimulated by the requirements of space operations. For this working field, flexible lightweight robots can enhance the work space of space robots very well, if the length of the robot arm is variable.

Contributions in the corresponding literature mostly consider models of special configurations and perform simple approximations or even assume linear models to describe the elastic motions of the robot. However, especially in the case of lightweight robots undergoing large reference motion, its nonlinear dynamic behaviour should be modeled as exact as possible.

The mechanical system should be controlled to improve its dynamical behaviour. Unfortunately, it is not possible to measure the position of the endeffector. The only measurements that can be done are that of the strains of the beam. The control input should be the velocity (translational and rotational) transmitted to the base of the beam. This includes a correction of the actual path planning values as a kinematical control.

Here the specified task is solved in two parts:

Firstly, the variable length, the geometric nonlinear beam behaviour and the large reference motion of the driven joint are taken into consideration with a systematic modeling approach in (Söffker, 1995b; Söffker, 1995c).

Nonlinear control approaches can often be used only for special classes of problems assumptions have to be made, which cannot be generally fulfilled in practice. Here a new controller is developed which is realizable for on-line applications with the mentioned restrictions. Therefore, in a second part the mechanical plant will be controlled by a new observer-based dynamic compensation scheme.

Based on a linear time-invariant model, nonlinear effects and unmodeled dynamics are estimated in a first step by an Proportinal-Integral (PI) observer scheme, whereby the nonlinearities and the effects of the non-considered time-varying parameters etc. are assumed as external disturbances.

The used PI-observer (Söffker, 1995a) estimates the states of the system and the external disturbances under some weak assumptions.

Using this informations about the external disturbances to the nominal time-invariant system, the task of an extended regulator scheme is to compensate these effects in a second step. Because of the structure of the given mechanical system, usual static disturbance compensation schemes are not useful. Therefore a new dynamic approach is developed, which uses the estimations of the extended observer. The developed method does not depend on the structure of the physical problem and can be also used more generally. This is mainly due to the robustness of the observer-based dynamic compensation scheme.

Two examples of a very flexible spatial telescopic robot arm demonstrate the effects of disturbances compensation and control of the elastic vibrations induced by the initial conditions and the reference motion.

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