@article{Stratoglou2023, 
author = {Efstratios Stratoglou and Alexandre Anahory Simoes and Leonardo J. Colombo},
title = {Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups},
year = {2023},
journal = {Communications in Analysis and Mechanics},
volume = {15},
number = {2},
pages = {1-23},
keywords = {Lagrangian systems, symmetry reduction, Euler-Poincaré equations, multi-agent control systems, Lie-Poisson integrators},
url = {https://www.sciopen.com/article/10.3934/cam.2023001},
doi = {10.3934/cam.2023001},
abstract = {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    S  E  (  2  ) in the presence of a static obstacle.}
}