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

TL;DR

This paper develops a coordinate-free, geometric formulation of inverse flight dynamics for fixed-wing aircraft on SO(3), enabling analytic solutions for trajectory control and tethered flight analysis.

Contribution

It introduces a novel, geometric approach to inverse flight dynamics that avoids local attitude coordinates and provides closed-form solutions for trajectory-to-input mapping.

Findings

Derived a closed-form attitude and thrust-angle-of-attack map for coordinated flight.

Obtained analytic expressions for bank angle and tether tension in tethered flight.

Identified a zero-bank locus where tether tension balances centrifugal effects.

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.