数値最適化による大域的幾何学的フラット出力の自動同定に向けて
Towards Automatic Identification of Globally Valid Geometric Flat Outputs via Numerical Optimization
対称性を利用し、リーマン幾何学とリー群論に基づいてフラット出力の探索を最適化問題として定式化し、二次計画問題に変換して既知の解と一致することを示した。
著者: Jake Welde, Vijay Kumar
分類: cs.RO, math.DG, math.OC
原文アブストラクト
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.
