Flat Output

Flat output identification aims to simplify the control and planning of complex robotic systems by finding a minimal set of variables that completely determine the system's behavior. Current research focuses on leveraging the system's inherent symmetries, particularly using tools from Riemannian geometry and Lie group theory, to construct "geometric flat outputs" which are globally valid and respect the system's structure. This approach, often formulated as a numerical optimization problem, promises more systematic and automated methods for finding flat outputs, overcoming limitations of previous analytical techniques. The resulting advancements will improve the efficiency and robustness of robotic control algorithms across various applications.