OPTIMIZATION OF THE ANGULAR MANIPULATOR'S PLACEMENT RELATIVE TO THE END EFFECTOR'S STRAIGHT-LINE TRAJECTORY

The problem of creating a universal approach to analyzing the efficiency of the manipulator placement location is considered using the example of the problem of optimizing the placement of a two-link angular manipulator relative to a given vector of movement of the working element according to the criteria of energy consumption and maximum power per cycle. The concept of the possible manipulator placements area is introduced, which is the basis for forming matrices of indicators of the optimality of the manipulator placement based on various criteria. The Lagrange equations of the second kind are used to determine the energy consumption and maximum power of a manipulator placed at a specific point. Each element of the matrix corresponding to specific coordinates of the manipulator placement is filled with the value of consumed energy or maximum power per cycle. The resulting matrices of energies and maximum powers allow determining the optimal placement of the manipulator with an accuracy of the grid step. The analysis of the obtained results showed the significant impact of the manipulator placement on its energy efficiency. It is shown that the optimal locations for placing the manipulator according to the criteria of minimum energy and power consumption do not coincide, and the functions describing these criteria have several local extrema. In this regard, it is proposed to use a preliminary determination of the optimal placement according to the criteria matrices with subsequent refinement by local minima search algorithms. The proposed method for determining the optimal placement of the manipulator is universal, since it can also be used to optimize placement according to other criteria (including multi-criteria optimization) and in the presence of several local minima of the criterion functions. The described materials are the basis for the formation of a systematic approach to the study of the effectiveness of optimizing the layout of a robotic cell, not only according to the criteria of energy efficiency, but also according to the criteria of speed, accuracy and payload.