Формування методу аналітичного розв’язку зворотної задачі кіне-матики маніпуляторів промислового робота
The work is conditioned by the need for analytical expressions, which aresolutions of the inverse problem of kinematics for the synthesis of the control influence, at a given position of the grip of the manipulator and satisfythe condition of unity. The work presents an analysis of the problem and t...
Збережено в:
| Дата: | 2023 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Ukrainian |
| Опубліковано: |
V.M. Glushkov Institute of Cybernetics of NAS of Ukraine
2023
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| Теми: | |
| Онлайн доступ: | https://jais.net.ua/index.php/files/article/view/19 |
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| Назва журналу: | Problems of Control and Informatics |
Репозитарії
Problems of Control and Informatics| Резюме: | The work is conditioned by the need for analytical expressions, which aresolutions of the inverse problem of kinematics for the synthesis of the control influence, at a given position of the grip of the manipulator and satisfythe condition of unity. The work presents an analysis of the problem and thereasons that made such a solution difficult. It is shown that the constructionbased on the condition of equality of sub-matrices, which represent the position of the link in the projective space, is a system of nine equations withthree unknowns. An excessive number of equations and their solution by direct analytical methods is the reason for its non-uniformity. The propertiesof the vectors, which always set the position of the gripper, have beenproved, which allows for the simplification of systems of equations. It isproposed to transform the system due to the grouping of equations, using theestablished properties of the gripper position vectors. Such transformationsreduce the system of nine equations to a system of three equations withthree unknowns and obtain a single solution of the inverse problem of manipulator kinematics. The simulation of the conditions of analytical determination of the gripper position by the direct method was carried out and acomparison with the results obtained by analytical solutions shows that therelative error lies within the range from 10–16 to 10–13. The use of such expressions allows you to determine quickly the angles of rotation, which inturn allows you to describe analytically the kinematics and dynamics of themanipulator links. |
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