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This paper introduces a learning framework for synthesizing robust controllers for dynamical systems on Lie groups by jointly training a robust control contraction metric (RCCM) and a neural feedback controller. The method enforces contraction conditions on the Lie group manifold, respecting geometric constraints and establishing disturbance-dependent trajectory bounds. Applied to quadrotor control, the learned controller demonstrates performance comparable to geometric controllers in simulations.
Guaranteeing robustness for neural controllers on Lie groups is now possible, opening doors for safer and more reliable control of complex robotic systems.
In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.
