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...
| Authors: | , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Consejo Superior de Investigaciones Científicas (CSIC) |
| Repository: | DIGITAL.CSIC. Repositorio Institucional del CSIC |
| OAI Identifier: | oai:digital.csic.es:10261/369137 |
| Online Access: | http://hdl.handle.net/10261/369137 |
| Access Level: | Open access |
| Keyword: | Lagrangian systems symmetry reduction Euler-Poincaré equations multi-agent control systems Lie-Poisson integrators |
| 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 S E(2) in the presence of a static obstacle. |
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