Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variation...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Communications in Analysis and Mechanics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2023001?viewType=HTML |
| _version_ | 1797366705819746304 |
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| author | Efstratios Stratoglou Alexandre Anahory Simoes Leonardo J. Colombo |
| author_facet | Efstratios Stratoglou Alexandre Anahory Simoes Leonardo J. Colombo |
| author_sort | Efstratios Stratoglou |
| collection | DOAJ |
| description | We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the reduced optimality conditions from a reduced variational principle via symmetry reduction techniques in both settings continuous-time, and discrete-time. We apply the results to a collision and obstacle avoidance problem for multiple vehicles evolving on $ SE(2) $ in the presence of a static obstacle. |
| first_indexed | 2024-03-08T17:08:30Z |
| format | Article |
| id | doaj.art-0c1cd23b50284e54bfbe79c10abdff4d |
| institution | Directory Open Access Journal |
| issn | 2836-3310 |
| language | English |
| last_indexed | 2024-03-08T17:08:30Z |
| publishDate | 2023-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Communications in Analysis and Mechanics |
| spelling | doaj.art-0c1cd23b50284e54bfbe79c10abdff4d2024-01-04T03:24:07ZengAIMS PressCommunications in Analysis and Mechanics2836-33102023-03-0115212310.3934/cam.2023001Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groupsEfstratios Stratoglou 0Alexandre Anahory Simoes1Leonardo J. Colombo21. Programa de Doctorado de Automática y Robótica, Universidad Politécnica de Madrid (UPM), 28006 Madrid, Spain2. IE School of Sciences and Technology, P. Castellana, 259E, 28046 Madrid, Spain3. Centre for Automation and Robotics (CSIC-UPM), Ctra. M300 Campo Real, Km 0,200, Arganda del Rey - 28500 Madrid, SpainWe study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the reduced optimality conditions from a reduced variational principle via symmetry reduction techniques in both settings continuous-time, and discrete-time. We apply the results to a collision and obstacle avoidance problem for multiple vehicles evolving on $ SE(2) $ in the presence of a static obstacle.https://www.aimspress.com/article/doi/10.3934/cam.2023001?viewType=HTMLlagrangian systemssymmetry reductioneuler-poincaré equationsmulti-agent control systemslie-poisson integrators |
| spellingShingle | Efstratios Stratoglou Alexandre Anahory Simoes Leonardo J. Colombo Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups Communications in Analysis and Mechanics lagrangian systems symmetry reduction euler-poincaré equations multi-agent control systems lie-poisson integrators |
| title | Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups |
| title_full | Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups |
| title_fullStr | Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups |
| title_full_unstemmed | Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups |
| title_short | Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups |
| title_sort | reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi agent system on lie groups |
| topic | lagrangian systems symmetry reduction euler-poincaré equations multi-agent control systems lie-poisson integrators |
| url | https://www.aimspress.com/article/doi/10.3934/cam.2023001?viewType=HTML |
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