PHODCOS: ピタゴラスホドグラフに基づく微分可能座標系
PHODCOS: Pythagorean Hodograph-based Differentiable Coordinate System
曲線に沿って移動する座標系を、近似なしで微分可能かつ高連続に生成するアルゴリズムを提案し、月ゲートウェイのNRHO軌道で有効性を示した。
著者: Jon Arrizabalaga, Fausto Vega, Zbyněk ŠÍR, Zachary Manchester, Markus Ryll
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
This paper presents PHODCOS, an algorithm that assigns a moving coordinate system to a given curve. The parametric functions underlying the coordinate system, i.e., the path function, the moving frame and its angular velocity, are exact -- approximation free -- differentiable, and sufficiently continuous. This allows for computing a coordinate system for highly nonlinear curves, while remaining compliant with autonomous navigation algorithms that require first and second order gradient information. In addition, the coordinate system obtained by PHODCOS is fully defined by a finite number of coefficients, which may then be used to compute additional geometric properties of the curve, such as arc-length, curvature, torsion, etc. Therefore, PHODCOS presents an appealing paradigm to enhance the geometrical awareness of existing guidance and navigation on-orbit spacecraft maneuvers. The PHODCOS algorithm is presented alongside an analysis of its error and approximation order, and thus, it is guaranteed that the obtained coordinate system matches the given curve within a desired tolerance. To demonstrate the applicability of the coordinate system resulting from PHODCOS, we present numerical examples in the Near Rectilinear Halo Orbit (NRHO) for the Lunar Gateway.
