SE(3)上の軌道バンドル法によるブラックボックス固定翼機の軌道最適化
Trajectory Bundle Method in SE(3) for Black-Box Fixed-Wing Aircraft Trajectory Optimization
微分情報が使えないブラックボックス力学系に対し、リー代数上のバンドルを用いてSE(3)上で直接軌道最適化を行う手法を提案し、固定翼機のアクロバティックな衝突回避機動で有効性を示した。
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著者: Matthew D. Osburn, Cameron K. Peterson, John L. Salmon
分類: cs.RO
原文アブストラクト
Dynamically feasible trajectory optimization for rigid-body systems is naturally formulated on the special Euclidean group SE(3) but is challenging when dynamics are available only as black-box computations without derivatives. This paper formulates the Trajectory Bundle Method (TBM) for motion planning implicitly on SE(3). Bundles are constructed in the Lie algebra and propagated through nonlinear rigid-body dynamics using exponential and logarithmic maps, enabling derivative-free planning of non-Euclidean trajectories. We show that Euclidean TBM interpolation error is bounded quadratically by bundle diameter and extend this result to SE(3), where the bound additionally depends on a local Lipschitz constant of the Log map. Numerical experiments corroborate these bounds. Finally, we demonstrate SE(3) TBM by optimizing an acrobatic, collision-free fixed-wing maneuver through a rotated aperture without explicit models or derivatives of the vehicle dynamics, aerodynamics, or collision model.
