Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse
The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approxima...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Polish Academy of Sciences
2015-03-01
|
| Series: | Archives of Control Sciences |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/acsc.2015.25.issue-1/acsc-2015-0003/acsc-2015-0003.xml?format=INT |
| id |
doaj-4ab9f564037f4a668d0f89d9bbda8b0a |
|---|---|
| record_format |
Article |
| spelling |
doaj-4ab9f564037f4a668d0f89d9bbda8b0a2020-11-25T02:33:32ZengPolish Academy of SciencesArchives of Control Sciences2300-26112015-03-01251355010.1515/acsc-2015-0003acsc-2015-0003Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverseRatajczak Joanna0Electronics Faculty, Wroclaw University of Technology, ul. Janiszewskiego 11/17, 50–372 Wroclaw, PolandThe paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory.http://www.degruyter.com/view/j/acsc.2015.25.issue-1/acsc-2015-0003/acsc-2015-0003.xml?format=INTredundant manipulatorinverse kinematicsJacobianapproximation |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ratajczak Joanna |
| spellingShingle |
Ratajczak Joanna Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse Archives of Control Sciences redundant manipulator inverse kinematics Jacobian approximation |
| author_facet |
Ratajczak Joanna |
| author_sort |
Ratajczak Joanna |
| title |
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse |
| title_short |
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse |
| title_full |
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse |
| title_fullStr |
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse |
| title_full_unstemmed |
Design of inverse kinematics algorithms: extended Jacobian approximation of the dynamically consistent Jacobian inverse |
| title_sort |
design of inverse kinematics algorithms: extended jacobian approximation of the dynamically consistent jacobian inverse |
| publisher |
Polish Academy of Sciences |
| series |
Archives of Control Sciences |
| issn |
2300-2611 |
| publishDate |
2015-03-01 |
| description |
The paper presents the approximation problem of the inverse kinematics algorithms for the redundant manipulators. We introduce the approximation of the dynamically consistent Jacobian by the extended Jacobian. In order to do that, we formulate the approximation problem and suitably defined approximation error. By the minimization of this error over a certain region we can design an extended Jacobian inverse which will be close to the dynamically consistent Jacobian inverse. To solve the approximation problem we use the Cholesky decomposition and the Ritz method. The computational example illustrates the theory. |
| topic |
redundant manipulator inverse kinematics Jacobian approximation |
| url |
http://www.degruyter.com/view/j/acsc.2015.25.issue-1/acsc-2015-0003/acsc-2015-0003.xml?format=INT |
| work_keys_str_mv |
AT ratajczakjoanna designofinversekinematicsalgorithmsextendedjacobianapproximationofthedynamicallyconsistentjacobianinverse |
| _version_ |
1724813435151056896 |