Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
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 variation...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-03-01
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| Series: | Communications in Analysis and Mechanics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/cam.2023001?viewType=HTML |
| Summary: | 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. |
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| ISSN: | 2836-3310 |