Global inverse kinematics via mixed-integer convex optimization
<jats:p>In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints: a major improvement over existing a...
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| Diğer Yazarlar: | |
| Materyal Türü: | Makale |
| Dil: | English |
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SAGE Publications
2021
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| Online Erişim: | https://hdl.handle.net/1721.1/136519 |
| _version_ | 1826200752747446272 |
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| author | Dai, Hongkai Izatt, Gregory Tedrake, Russ |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Dai, Hongkai Izatt, Gregory Tedrake, Russ |
| author_sort | Dai, Hongkai |
| collection | MIT |
| description | <jats:p>In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints: a major improvement over existing approaches, which either solve the problem in only a local neighborhood of the user initial guess through nonlinear non-convex optimization, or address only a limited set of kinematics constraints. Specifically, we propose a mixed-integer convex relaxation of non-convex [Formula: see text] rotation constraints, and apply this relaxation on the IK problem. Our formulation can detect if an instance of the IK problem is globally infeasible, or produce an approximate solution when it is feasible. We show results on a seven-joint arm grasping objects in a cluttered environment, an 18-degree-of-freedom quadruped standing on stepping stones, and a parallel Stewart platform. Moreover, we show that our approach can find a collision free path for a gripper in a cluttered environment, or certify such a path does not exist. We also compare our approach against the analytical approach for a six-joint manipulator. The open-source code is available at http://drake.mit.edu .</jats:p> |
| first_indexed | 2024-09-23T11:41:13Z |
| format | Article |
| id | mit-1721.1/136519 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:41:13Z |
| publishDate | 2021 |
| publisher | SAGE Publications |
| record_format | dspace |
| spelling | mit-1721.1/1365192023-03-01T14:45:16Z Global inverse kinematics via mixed-integer convex optimization Dai, Hongkai Izatt, Gregory Tedrake, Russ Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory <jats:p>In this paper, we present a novel formulation of the inverse kinematics (IK) problem with generic constraints as a mixed-integer convex optimization program. The proposed approach can solve the IK problem globally with generic task space constraints: a major improvement over existing approaches, which either solve the problem in only a local neighborhood of the user initial guess through nonlinear non-convex optimization, or address only a limited set of kinematics constraints. Specifically, we propose a mixed-integer convex relaxation of non-convex [Formula: see text] rotation constraints, and apply this relaxation on the IK problem. Our formulation can detect if an instance of the IK problem is globally infeasible, or produce an approximate solution when it is feasible. We show results on a seven-joint arm grasping objects in a cluttered environment, an 18-degree-of-freedom quadruped standing on stepping stones, and a parallel Stewart platform. Moreover, we show that our approach can find a collision free path for a gripper in a cluttered environment, or certify such a path does not exist. We also compare our approach against the analytical approach for a six-joint manipulator. The open-source code is available at http://drake.mit.edu .</jats:p> 2021-10-27T20:35:46Z 2021-10-27T20:35:46Z 2019 2021-01-27T17:58:57Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/136519 en 10.1177/0278364919846512 International Journal of Robotics Research Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf SAGE Publications MIT web domain |
| spellingShingle | Dai, Hongkai Izatt, Gregory Tedrake, Russ Global inverse kinematics via mixed-integer convex optimization |
| title | Global inverse kinematics via mixed-integer convex optimization |
| title_full | Global inverse kinematics via mixed-integer convex optimization |
| title_fullStr | Global inverse kinematics via mixed-integer convex optimization |
| title_full_unstemmed | Global inverse kinematics via mixed-integer convex optimization |
| title_short | Global inverse kinematics via mixed-integer convex optimization |
| title_sort | global inverse kinematics via mixed integer convex optimization |
| url | https://hdl.handle.net/1721.1/136519 |
| work_keys_str_mv | AT daihongkai globalinversekinematicsviamixedintegerconvexoptimization AT izattgregory globalinversekinematicsviamixedintegerconvexoptimization AT tedrakeruss globalinversekinematicsviamixedintegerconvexoptimization |