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
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	lagrangian systems symmetry reduction euler-poincaré equations multi-agent control systems lie-poisson integrators Analytic mechanics QA801-939
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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