SE(3)中的轨迹束方法用于黑箱固定翼飞行器轨迹优化
Trajectory Bundle Method in SE(3) for Black-Box Fixed-Wing Aircraft Trajectory Optimization
- Brigham Young University（杨百翰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出SE(3)上的轨迹束方法，利用李代数构造束并通过指数/对数映射传播，实现无导数的黑箱固定翼轨迹优化，并证明了误差界及实验验证。
AI中文摘要：
刚体系统的动态可行轨迹优化自然地在特殊欧几里得群SE(3)上表述，但当动力学仅作为无导数的黑箱计算可用时，这一优化具有挑战性。本文在SE(3)上隐式地提出了轨迹束方法（TBM）用于运动规划。束在李代数中构造，并通过指数映射和对数映射在非线性刚体动力学中传播，从而实现对非欧几里得轨迹的无导数规划。我们证明了欧几里得TBM插值误差由束直径二次有界，并将此结果扩展到SE(3)，其中界限还依赖于Log映射的局部Lipschitz常数。数值实验证实了这些界限。最后，我们通过优化一个通过旋转孔径的特技、无碰撞固定翼机动来展示SE(3) TBM，无需车辆动力学、空气动力学或碰撞模型的显式模型或导数。
英文摘要：
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.
