Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
arXiv preprint arXiv:2207.06806, 2022•arxiv.org
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 …
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 …
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 in the presence of a static obstacle.
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