Towards Automatic Identification of Globally Valid Geometric Flat Outputs via Numerical Optimization
Abstract
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system. In this work, we leverage recent results elucidating the role of symmetry in constructing flat outputs for free-flying robotic systems. Using the tools of Riemannian geometry, Lie group theory, and differential forms, we cast the search for a globally valid, equivariant flat output as an optimization problem. An approximate transcription of this continuum formulation to a quadratic program is performed, and its solutions for two example systems achieve precise agreement with the known closed-form flat outputs. Our results point towards a systematic, automated approach to numerically identify geometric flat outputs directly from the system model, particularly useful when complexity renders pen and paper analysis intractable.
Cite
@article{arxiv.2305.09442,
title = {Towards Automatic Identification of Globally Valid Geometric Flat Outputs via Numerical Optimization},
author = {Jake Welde and Vijay Kumar},
journal= {arXiv preprint arXiv:2305.09442},
year = {2023}
}
Comments
To appear as a contributed paper in the "Geometric Representations" workshop at the 2023 International Conference on Robotics and Automation (ICRA)