Scalable Optimal Motion Planning for Multi-Agent Systems by Cosserat Theory of Rods
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914832282812416 |
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| author | Golestaneh, Amirreza Fahim Hammond, Maxwell Cichella, Venanzio |
| author_facet | Golestaneh, Amirreza Fahim Hammond, Maxwell Cichella, Venanzio |
| contents | We address the motion planning problem for large multi-agent systems, utilizing Cosserat rod theory to model the dynamic behavior of vehicle formations. The problem is formulated as an optimal control problem over partial differential equations (PDEs) that describe the system as a continuum. This approach ensures scalability with respect to the number of vehicles, as the problem's complexity remains unaffected by the size of the formation. The numerical discretization of the governing equations and problem's constraints is achieved through Bernstein surface polynomials, facilitating the conversion of the optimal control problem into a nonlinear programming (NLP) problem. This NLP problem is subsequently solved using off-the-shelf optimization software. We present several properties and algorithms related to Bernstein surface polynomials to support the selection of this methodology. Numerical demonstrations underscore the efficacy of this mathematical framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_07684 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scalable Optimal Motion Planning for Multi-Agent Systems by Cosserat Theory of Rods Golestaneh, Amirreza Fahim Hammond, Maxwell Cichella, Venanzio Optimization and Control Numerical Analysis Dynamical Systems We address the motion planning problem for large multi-agent systems, utilizing Cosserat rod theory to model the dynamic behavior of vehicle formations. The problem is formulated as an optimal control problem over partial differential equations (PDEs) that describe the system as a continuum. This approach ensures scalability with respect to the number of vehicles, as the problem's complexity remains unaffected by the size of the formation. The numerical discretization of the governing equations and problem's constraints is achieved through Bernstein surface polynomials, facilitating the conversion of the optimal control problem into a nonlinear programming (NLP) problem. This NLP problem is subsequently solved using off-the-shelf optimization software. We present several properties and algorithms related to Bernstein surface polynomials to support the selection of this methodology. Numerical demonstrations underscore the efficacy of this mathematical framework. |
| title | Scalable Optimal Motion Planning for Multi-Agent Systems by Cosserat Theory of Rods |
| topic | Optimization and Control Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2406.07684 |