Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2010
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| Online Access: | http://hdl.handle.net/1721.1/59934 |
| _version_ | 1826188628183744512 |
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| author | Rust, Ian Charles |
| author2 | Jean-Jacques E. Slotine. |
| author_facet | Jean-Jacques E. Slotine. Rust, Ian Charles |
| author_sort | Rust, Ian Charles |
| collection | MIT |
| description | Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010. |
| first_indexed | 2024-09-23T08:02:36Z |
| format | Thesis |
| id | mit-1721.1/59934 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:02:36Z |
| publishDate | 2010 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/599342022-01-13T07:54:36Z Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm Rust, Ian Charles Jean-Jacques E. Slotine. Massachusetts Institute of Technology. Dept. of Mechanical Engineering. Massachusetts Institute of Technology. Department of Mechanical Engineering Mechanical Engineering. Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2010. Cataloged from PDF version of thesis. Includes bibliographical references (p. 54). Underactuated robotics, though surrounded by an established body of work, has certain limitations when nonlinear adaptive control principles are applied. This thesis applies a nonlinear adaptative controller that avoids many of these limitations using alterations inspired by the control of a similar underactuated system, the cart-pole. Due to the complexity of the system, a sums-of-squares MATLAB toolbox is used to generate a suitable Lyapunov Candidate used for proofs of stability, with claims of local stability made using Barbalat's Lemma. This provides us with a local domain of attraction for the altered classical nonlinear adaptive controller. In addition, the algorithm known as LQR Trees is applied to the system in order to create a controller with a larger region of attraction and lower torque requirements, though without an adaptive component. Both control systems are implemented in simulations using MATLAB. by Ian Charles Rust. S.B. 2010-11-08T17:48:29Z 2010-11-08T17:48:29Z 2010 2010 Thesis http://hdl.handle.net/1721.1/59934 676831500 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 55 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering. Rust, Ian Charles Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title | Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title_full | Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title_fullStr | Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title_full_unstemmed | Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title_short | Control of a nonlinear underactuated system with adaptation, numerical stability verification, and the use of the LQR Trees algorithm |
| title_sort | control of a nonlinear underactuated system with adaptation numerical stability verification and the use of the lqr trees algorithm |
| topic | Mechanical Engineering. |
| url | http://hdl.handle.net/1721.1/59934 |
| work_keys_str_mv | AT rustiancharles controlofanonlinearunderactuatedsystemwithadaptationnumericalstabilityverificationandtheuseofthelqrtreesalgorithm |