Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
Autor: | Efstratios Stratoglou, Alexandre Anahory Simoes, Leonardo J. Colombo |
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Jazyk: | angličtina |
Rok vydání: | 2023 |
Předmět: | |
Zdroj: | Communications in Analysis and Mechanics, Vol 15, Iss 2, Pp 1-23 (2023) |
Druh dokumentu: | article |
ISSN: | 2836-3310 |
DOI: | 10.3934/cam.2023001?viewType=HTML |
Popis: | 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. |
Databáze: | Directory of Open Access Journals |
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