Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups

Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups

Blog Article

We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent bushranger awning 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 aptamil allerpro multiple vehicles evolving on $ SE(2) $ in the presence of a static obstacle.