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arXiv · 2305.09442

Towards Automatic Identification of Globally Valid Geometric Flat Outputs via Numerical Optimization

Jake Welde·Vijay Kumar
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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.

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Jake Welde, Vijay Kumar. 2023-05-16. Towards Automatic Identification of Globally Valid Geometric Flat Outputs via Numerical Optimization. https://arxiv.org/abs/2305.09442

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