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

• URL: http://arxiv.org/abs/2602.17166v1
• Date: Thu, 19 Feb 2026 08:26:17 GMT
• Title: Geometric Inverse Flight Dynamics on SO(3) and Application to Tethered Fixed-Wing Aircraft
• Abstract summary: We present a robotics-oriented, coordinate-free formulation of inverse flight dynamics for fixed-wing aircraft.<n>We derive a closed-form trajectory-to-input map yielding the attitude, angular velocity, and thrust-angle-of-attack pair.
• Score: 5.021944882278981
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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