Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
DOI10.3934/cam.2023001zbMath1518.70027arXiv2207.06806OpenAlexW4323244459MaRDI QIDQ6107332
Alexandre Anahory Simoes, Efstratios Stratoglou, Leonardo Colombo
Publication date: 3 July 2023
Published in: Communications in Analysis and Mechanics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2207.06806
optimality conditionEuler-Poincaré equationssymmetry reductionLagrangian systemLie-Poisson integratormultiple vehicle dynamicsreduced variational principle
Variational methods for problems in mechanics (70G75) Control of mechanical systems (70Q05) Dynamics of multibody systems (70E55) Symmetries, Lie group and Lie algebra methods for problems in mechanics (70G65) Lagrange's equations (70H03)
Cites Work
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- State estimation for invariant systems on Lie groups with delayed output measurements
- Clebsch optimal control formulation in mechanics
- Reduction theory for symmetry breaking with applications to nematic systems
- Hamilton-Pontryagin integrators on Lie groups. I: Introduction and structure-preserving properties
- Symmetries and conservation laws for Hamiltonian systems with inputs and outputs: A generalization of Noether's theorem
- The Euler-Poincaré equations and semidirect products with applications to continuum theories
- Geometric reduction in optimal control theory with symmetries
- General symmetries in optimal control
- Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. E Crouch, J. E. Marsden and D. Zenkov. With scientific input from P. S. Krishnaprasad and R. M. Murray
- Semidirect Products and Reduction in Mechanics
- Discrete mechanics and variational integrators
- The structure of nonlinear control systems possessing symmetries
- Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry and Lagrangian Reduction
- Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping
- Symmetry Reduction for Performance Certification of Interconnected Systems
- Optimal Control Problems with Symmetry Breaking Cost Functions
- Translational and Rotational Invariance in Networked Dynamical Systems
- Discrete Euler-Poincaré and Lie-Poisson equations
- Motion control of drift-free, left-invariant systems on Lie groups
- Symmetry Reduction of Optimal Control Systems and Principal Connections
- Nonlinear Complementary Filters on the Special Orthogonal Group
- Symmetry-Preserving Observers
- Gradient-Like Observers for Invariant Dynamics on a Lie Group
- Coordinated Motion Design on Lie Groups
- Collision Avoidance of Multiagent Systems on Riemannian Manifolds
- Optimal Control on Lie Groups: The Projection Operator Approach
- Reduction of Sufficient Conditions for Optimal Control Problems With Subgroup Symmetry
- Optimality, reduction and collective motion
- Symmetry Reduction in Optimal Control of Multiagent Systems on Lie Groups
- Lie groups beyond an introduction
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