Trajectory Bundle Method in SE(3) for Black-Box Fixed-Wing Aircraft Trajectory Optimization

2026-09-10

AI Summary

本文提出了一种在SE(3)上使用轨迹束方法解决刚体系统（如固定翼飞机）的黑盒轨迹优化问题，无需显式动力学模型或导数。

Abstract

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.

Problem

• trajectory optimization
• SE(3)
• black-box dynamics
• rigid-body systems
• derivative-free

Innovation

• Trajectory Bundle Method
• SE(3)
• derivative-free optimization
• rigid-body dynamics
• black-box computations