基于几何方法求解固定翼飞机飞行轨迹的逆动力学问题。
Geometric Inverse Flight Dynamics on SO(3) and Application to Tethered Fixed-Wing Aircraft
- 在SO(3)上建立无坐标系依赖的逆飞行动力学模型，分离平动与转动方程。
- 推导出零侧滑条件下的解析解，可直接计算所需姿态角与攻角组合。
- 适用于系绳固定翼飞机的轨迹设计，尤其适合研究离心力平衡机制。
本文提出一种面向机器人学的、无坐标依赖的固定翼飞机逆飞行动力学框架，定义于SO(3)空间。平动平衡以世界坐标系表达，旋转动力学在机体坐标系中建模；气动力方向（阻力、升力、侧向力）通过几何方式定义，避免使用局部姿态坐标。在保持协调飞行（无侧滑）条件下，推导出从轨迹到控制输入的闭式映射，可获得姿态、角速度及推力-攻角对，并逐分量恢复气动力矩系数。将该映射应用于沿球面纬线的系绳飞行，得到所需滚转角的解析表达式，并识别出一个特定零滚转轨迹，在此轨迹上缆绳张力恰好抵消离心效应，凸显气动协调性与表观重力矢量间的解耦特性。在简单的升阻律假设下，最小推力攻角亦具闭式表达。当轨迹与旋转动力学为时不变时，这些点态准稳态解即退化为稳态配平解。该框架连接了航空领域的逆仿真与机器人学中的几何建模，为轨迹设计与可行性验证提供严谨基础。
原文摘要 · Abstract (English)
We present a robotics-oriented, coordinate-free formulation of inverse flight dynamics for fixed-wing aircraft on SO(3). Translational force balance is written in the world frame and rotational dynamics in the body frame; aerodynamic directions (drag, lift, side) are defined geometrically, avoiding local attitude coordinates. Enforcing coordinated flight (no sideslip), we derive a closed-form trajectory-to-input map yielding the attitude, angular velocity, and thrust-angle-of-attack pair, and we recover the aerodynamic moment coefficients component-wise. Applying such a map to tethered flight on spherical parallels, we obtain analytic expressions for the required bank angle and identify a specific zero-bank locus where the tether tension exactly balances centrifugal effects, highlighting the decoupling between aerodynamic coordination and the apparent gravity vector. Under a simple lift/drag law, the minimal-thrust angle of attack admits a closed form. These pointwise quasi-steady inversion solutions become steady-flight trim when the trajectory and rotational dynamics are time-invariant. The framework bridges inverse simulation in aeronautics with geometric modeling in robotics, providing a rigorous building block for trajectory design and feasibility checks.
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