A new approach to the control of indirect simultaneous positioning of deformable objects is presented. Many manufacturing processes that deal with deformable objects such as clothes and rubber sheets involve a positioning of multiple points on a deformable object. The multiple points should be guided simultaneously to the desired locations. Moreover, these positioned points cannot be manipulated directly. This operation is referred to as indirect simultaneous positioning. In this article, we will propose a new control law for indirect simultaneous positioning of a deformable object based on its uncertain model and will show the robustness of the proposed control law. First, a simplified physical model of a deformable object is developed for its positioning operation. Second, indirect simultaneous positioning of an extensible object is formulated. Based on a linearized model of an extensible object, we will propose a novel control law for indirect simultaneous positioning. Next, we will prove the robustness of the proposed control law theoretically. Finally, experimental results will show the robustness of our proposed control law against the discrepancy between a real fabric and its uncertain model.
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