Geometric Inverse Flight Dynamics on SO(3) and Application to Tethered Fixed-Wing Aircraft

2026-02-19

AI Summary

This work addresses the challenge of coordinate-free inverse flight dynamics modeling for fixed-wing aircraft, particularly the difficult mapping from trajectory to control inputs in tethered flight. The authors propose a novel coordinate-independent inverse dynamics framework formulated on the SO(3) manifold, which places force equilibrium in the world frame and angular momentum equations in the body frame, while geometrically defining aerodynamic force directions. Under the no-sideslip constraint, they derive a closed-form mapping from trajectory to attitude, angular velocity, and thrust–angle-of-attack pairs. By innovatively integrating geometric robotics with aerospace inverse simulation, the study reveals—for the first time—the precise balance mechanism between tether tension and centrifugal force under a zero-roll special solution, thereby decoupling aerodynamic coordination from apparent gravity. Key results include analytical expressions for roll angle in spherical parallel-circle flight and a closed-form solution for minimum-thrust angle of attack, establishing a rigorous theoretical foundation for steady-state trim and trajectory feasibility.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Intelligent Robots: State Estimation
• Machine Learning: Learning with Manifolds

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

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.

Problem

• inverse flight dynamics
• SO(3)
• tethered aircraft
• coordinated flight
• geometric modeling

Innovation

• geometric inverse dynamics
• SO(3)
• coordinate-free formulation
• tethered fixed-wing aircraft
• coordinated flight