Modeling Of Flexible-link Manipulators Research Articles

Modeling and control of flexible link manipulators for unmodeled dynamics effect

Flexible link manipulators are mostly prefered in applications where energy consumption and faster operation are critically important. Since distributed nature of flexibility makes the system depend on not only time variable but also a spatial variable, the dynamics of flexible structures are expressed by partial differential equations. In the virtue of this kind of modeling, the designers encounter with infinite dimensional systems which means that the system has an infinite number of degrees of freedom. To cope with infinite dimensional systems, one of the most relevant techniques is to truncate the model into a definite order. However, this may yield the unmodeled dynamics that cause performance degradation and even instability. In this paper, the main motivation is to propose control techniques to compensate unwanted effects of unmodeled dynamics which may occur in truncation process. In order to achieve this goal, the linear quadratic Gaussian and the weighted [Formula: see text] controller design are adopted. The performances of the designed controllers are demonstrated on the experimental setup. Besides this motivation, traditional lumped parameter model of the flexible link manipulator which is widely seen in the literature is considered and the superiority of the partial differential equation model is shown on the experimental setup.

Modeling of flexible-link manipulators with prismatic joints

The axially translating flexible link in flexible manipulators with a prismatic joint can be modeled using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, we present a nondimensional form of the Euler-Bernoulli beam equation using the concept of group velocity and present conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions lead to a time-dependent frequency equation for the translating flexible beam. We present a novel method to solve this time-dependent frequency equation by using a differential form of the frequency equation. We then present a systematic modeling procedure for spatial multi-link flexible manipulators having both revolute and prismatic joints. The assumed mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. We show, using a model-based control law, that the closed-loop dynamic response of modal variables become unstable during retraction of a flexible link, compared to the stable dynamic response during extension of the link. Numerical simulation results are presented for a flexible spatial RRP configuration robot arm. We show that the numerical results compare favorably with those obtained by using a finite element-based model.