Control design along trajectories with sums of squares programming
Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of invariance ar...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2014
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| Online Access: | http://hdl.handle.net/1721.1/90910 https://orcid.org/0000-0002-9383-6071 https://orcid.org/0000-0002-8712-7092 |
| _version_ | 1811078749077110784 |
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| author | Majumdar, Anirudha Ahmadi, Amir Ali Tedrake, Russell Louis |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Majumdar, Anirudha Ahmadi, Amir Ali Tedrake, Russell Louis |
| author_sort | Majumdar, Anirudha |
| collection | MIT |
| description | Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities. These certificates, together with our proposed polynomial controllers, can be efficiently obtained via semidefinite optimization. Our approach can handle time-varying dynamics resulting from tracking a given trajectory, input saturations (e.g. torque limits), and can be extended to deal with uncertainty in the dynamics and state. The resulting controllers can be used by space-filling feedback motion planning algorithms to fill up the space with significantly fewer trajectories. We demonstrate our approach on a severely torque limited underactuated double pendulum (Acrobot) and provide extensive simulation and hardware validation. |
| first_indexed | 2024-09-23T11:04:55Z |
| format | Article |
| id | mit-1721.1/90910 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:04:55Z |
| publishDate | 2014 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/909102022-10-01T01:02:11Z Control design along trajectories with sums of squares programming Majumdar, Anirudha Ahmadi, Amir Ali Tedrake, Russell Louis Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Majumdar, Anirudha Tedrake, Russell Louis Motivated by the need for formal guarantees on the stability and safety of controllers for challenging robot control tasks, we present a control design procedure that explicitly seeks to maximize the size of an invariant “funnel” that leads to a predefined goal set. Our certificates of invariance are given in terms of sums of squares proofs of a set of appropriately defined Lyapunov inequalities. These certificates, together with our proposed polynomial controllers, can be efficiently obtained via semidefinite optimization. Our approach can handle time-varying dynamics resulting from tracking a given trajectory, input saturations (e.g. torque limits), and can be extended to deal with uncertainty in the dynamics and state. The resulting controllers can be used by space-filling feedback motion planning algorithms to fill up the space with significantly fewer trajectories. We demonstrate our approach on a severely torque limited underactuated double pendulum (Acrobot) and provide extensive simulation and hardware validation. United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014-09-1-1051) Siebel Scholars Foundation 2014-10-14T13:51:32Z 2014-10-14T13:51:32Z 2013-05 Article http://purl.org/eprint/type/ConferencePaper 978-1-4673-5643-5 978-1-4673-5641-1 1050-4729 http://hdl.handle.net/1721.1/90910 Majumdar, Anirudha, Amir Ali Ahmadi, and Russ Tedrake. “Control Design Along Trajectories with Sums of Squares Programming.” 2013 IEEE International Conference on Robotics and Automation (May 2013). https://orcid.org/0000-0002-9383-6071 https://orcid.org/0000-0002-8712-7092 en_US http://dx.doi.org/10.1109/ICRA.2013.6631149 Proceedings of the 2013 IEEE International Conference on Robotics and Automation Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Majumdar, Anirudha Ahmadi, Amir Ali Tedrake, Russell Louis Control design along trajectories with sums of squares programming |
| title | Control design along trajectories with sums of squares programming |
| title_full | Control design along trajectories with sums of squares programming |
| title_fullStr | Control design along trajectories with sums of squares programming |
| title_full_unstemmed | Control design along trajectories with sums of squares programming |
| title_short | Control design along trajectories with sums of squares programming |
| title_sort | control design along trajectories with sums of squares programming |
| url | http://hdl.handle.net/1721.1/90910 https://orcid.org/0000-0002-9383-6071 https://orcid.org/0000-0002-8712-7092 |
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