Intrinsic Optimal Control for Mechanical Systems on Lie Group
The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal pr...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/6302430 |
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| _version_ | 1850230411248009216 |
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| author | Chao Liu Shengjing Tang Jie Guo |
| author_facet | Chao Liu Shengjing Tang Jie Guo |
| author_sort | Chao Liu |
| collection | DOAJ |
| description | The intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance. |
| format | Article |
| id | doaj-art-290d6a70b5cc4393842c1bc225a4fcf7 |
| institution | OA Journals |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-290d6a70b5cc4393842c1bc225a4fcf72025-08-20T02:03:52ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/63024306302430Intrinsic Optimal Control for Mechanical Systems on Lie GroupChao Liu0Shengjing Tang1Jie Guo2Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, ChinaKey Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, ChinaKey Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, ChinaThe intrinsic infinite horizon optimal control problem of mechanical systems on Lie group is investigated. The geometric optimal control problem is built on the intrinsic coordinate-free model, which is provided with Levi-Civita connection. In order to obtain an analytical solution of the optimal problem in the geometric viewpoint, a simplified nominal system on Lie group with an extra feedback loop is presented. With geodesic distance and Riemann metric on Lie group integrated into the cost function, a dynamic programming approach is employed and an analytical solution of the optimal problem on Lie group is obtained via the Hamilton-Jacobi-Bellman equation. For a special case on SO(3), the intrinsic optimal control method is used for a quadrotor rotation control problem and simulation results are provided to show the control performance.http://dx.doi.org/10.1155/2017/6302430 |
| spellingShingle | Chao Liu Shengjing Tang Jie Guo Intrinsic Optimal Control for Mechanical Systems on Lie Group Advances in Mathematical Physics |
| title | Intrinsic Optimal Control for Mechanical Systems on Lie Group |
| title_full | Intrinsic Optimal Control for Mechanical Systems on Lie Group |
| title_fullStr | Intrinsic Optimal Control for Mechanical Systems on Lie Group |
| title_full_unstemmed | Intrinsic Optimal Control for Mechanical Systems on Lie Group |
| title_short | Intrinsic Optimal Control for Mechanical Systems on Lie Group |
| title_sort | intrinsic optimal control for mechanical systems on lie group |
| url | http://dx.doi.org/10.1155/2017/6302430 |
| work_keys_str_mv | AT chaoliu intrinsicoptimalcontrolformechanicalsystemsonliegroup AT shengjingtang intrinsicoptimalcontrolformechanicalsystemsonliegroup AT jieguo intrinsicoptimalcontrolformechanicalsystemsonliegroup |