Welde, JakeKvalheim, Matthew D.Kumar, Vijay2023-10-242023-10-242023-07-04J. Welde, M. D. Kvalheim and V. Kumar, "The Role of Symmetry in Constructing Geometric Flat Outputs for Free-Flying Robotic Systems," 2023 IEEE International Conference on Robotics and Automation (ICRA), London, United Kingdom, 2023, pp. 12247-12253, doi: 10.1109/ICRA48891.2023.10160628.https://doi.org/10.1109/ICRA48891.2023.10160628http://hdl.handle.net/11603/303652023 IEEE International Conference on Robotics and Automation (ICRA); London, United Kingdom; 29 May 2023 - 02 June 2023Mechanical systems naturally evolve on principal bundles describing their inherent symmetries. The ensuing factorization of the configuration manifold into a symmetry group and an internal shape space has provided deep insights into the locomotion of many robotic and biological systems. On the other hand, the property of differential flatness has enabled efficient, effective planning and control algorithms for various robotic systems. Yet, a practical means of finding a flat output for an arbitrary robotic system remains an open question. In this work, we demonstrate surprising new connections between these two domains, for the first time employing symmetry directly to construct a flat output. We provide sufficient conditions for the existence of a trivialization of the bundle in which the group variables themselves are a flat output. We call this a geometric flat output, since it is equivariant (i.e. maintains the symmetry) and is often global or almost-global, properties not typically enjoyed by other flat outputs. In such a trivialization, the motion planning problem is easily solved, since a given trajectory for the group variables will fully determine the trajectory for the shape variables that exactly achieves this motion. We provide a partial catalog of robotic systems with geometric flat outputs and worked examples for the planar rocket, planar aerial manipulator, and quadrotor.7 pagesen-US© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.Text