Error Compensation in Position and Orientation of Mobile Platform of Cable-Driven Robots via Tensile Forces Measurement

Abstract

The paper deals with a problem of position and orientation errors of mobile platform of large-sized parallel cabledriven robots. The advantages of parallel cable-driven robots are simplicity of structure and scalability. At the same time, parallel cable-driven robots are difficult to design due to the specific problems such as collision of cables, geometric and structural nonlinearity in the mathematical models of the main elements of the robot. In this paper, we consider the problem of eliminating the uncertainty associated with deformations of the elements of the robot structure. Such a configuration of the cable system is selected, in which the proximal anchor points of some cables can be considered without errors relatively to given positions. The cable system of a large-sized robot is mounted on the towers. The errors in the proximal anchor points relatively to given positions become significant due to the significant deformations of upper sections of the towers. The deformations of the towers in lower sections can be considered insignificant, and the proximal anchor points have to be located no higher than the middle of the tower to be considered corresponding to a given position. The aim is to compensate the position and orientation errors of the mobile platform of large-sized parallel cable-driven robot due to deformations of the cables and towers. The task suppose uncertainty about the coordinates of the proximal anchor points of the upper cables. Cable deformations are determined from Hooke’s law using tensile forces measurement in cables. The problem of compensations is solved in two stages. At the first stage, the approximate bias of the center of mass of the mobile platform along the vertical coordinate is found. It is defined as the height of the truncated pyramid, the edges of which are formed by stretched lower cables. At the second stage, rotation angles of the mobile platform are determined. Using the rotation matrix, biases in the heights of each distal anchor points are found in the tool coordinate system. In the studied cases PID regulation is used, however, more advanced techniques of automatic regulation, for example, optimal control, can provide better results. The tasks are applied to the model of large-sized symmetric parallel eight-cable-driven robot.