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.
Aerial manipulation with multirotors has seen rapid progress, but endurance constraints limit long-duration tasks. To overcome this, recent works introduced the non-stop flight paradigm, where multiple carriers move perpetually while holding a cable-suspended load at a fixed pose [1], [2]. Those results show that, for three or more carriers, one can synthesize coordinated, phase-shifted, cyclic trajectories that keep the load static while each carrier never stops, thus enabling energyefficient manipulation beyond multirotor hover endurance. However, in that line of work, the dynamics of each carrier are abstracted as double integrators, i.e., the aerodynamic and rigid-body actuation dynamics of aircraft are not included.
Robotics formulations for quadrotor aerial manipulation of cable-suspended loads model a thrust-vectoring rotorcraft on SE(3) coupled to a pendular load on S2 , enabling differentialflatness and geometric-control design [3], [4], [5]. While powerful for multirotors, these models do not capture fixedwing aerodynamics (lift, angle of attack, aerodynamic moment coupling, coordinated-flight constraint), and are therefore not directly applicable to fixed-wing carriers. This motivates a geometric, world-frame composition with explicit aerodynamic directions suitable for fixed-wing inverse synthesis.
Related Work. To the best of our knowledge, aircraftbased manipulation remains essentially unexplored within the robotics community. Arguably, the only preliminary attempt is [6], which, however, neglects the dynamic coupling between the cable and the aircraft. By contrast, the airborne wind energy (AWE) literature has long studied tethered wings and their flight mechanics [7], but not the robotics-oriented inverse synthesis that produces realizable input and orientation trajectories directly from task-space specifications (and certainly not for manipulation). At the same time, the aeronautics community offers (i) inverse simulation methods that recover control histories using local angles [8], [9]; (ii) nonlinear dynamic inversion (NDI) and incremental NDI (INDI) for control-law design [10], [11], [12]; and (iii) coordinated-turn relations linking curvature, load factor, and bank [13], [14]. Yet, a concise robotics-oriented, coordinate-free, SO(3)-based inverse synthesis for fixed-wing aircraft is still missing.
Relative to classical inverse simulation [8], [9], our approach is coordinate-free and world-frame geometric, making it directly accessible for robotics planning (as in multirotor flatness methods [15], [16], [17]). Relative to NDI/INDI [10], [11], we focus on trajectory inversion and synthesis of the attitude, angular velocity, thrust, and angle of attack rather than a control-law structure. Relative to AWE [7], we target robotics use-cases that require geometric inverse synthesis with explicit feasibility checks and manipulation-oriented external forces. Differently from control-line aero models, where the pilot controls the aerodynamic surfaces of the aircraft using one or more tethers [18], in our model, the tether is attached at the center of mass, and it is not directly connected to the inputs of the aircraft. Such a modeling choice is instrumental for the manipulation of cable-supended loads. Crucially, this work complements our prior non-stop flight results [1], [2] by contributing the aircraft-level building block needed to move from abstractions toward aircraft-based manipulation.
The main contributions of the work are as follows.
(1) Geometric SO(3) model for fixed-wing aircraft. We formulate Newton-Euler dynamics in a z-up world frame, with globally valid aerodynamic directions and rate-damping moments, remaining compatible with standard coefficient maps and stability derivatives [13], [19]. We believe that such a problem formulation may represent a useful starting point for the robotics community to design motion and interaction controllers. (2) Inverse flight dynamics (IFD) in closed form. Given a desired Center of Mass (CoM) trajectory and external loads, we construct the attitude and body angular velocity geometrically, and solve the 2D force balance for the thrust and the angle of attack under coordinated flight. We also recover the required aerodynamic moment coefficients componentwise.
(3) Tethered fixed-wing on a spherical parallel. We apply the theory to an aircraft tethered to the origin, flying on a spherical parallel at constant speed, and subject to the cable tension. We derive analytic expressions for the required bank angle, identifying a specific zero-bank locus where the tether tension exactly counteracts centrifugal effects, decoupling aerodynamic coordination from the apparent gravity vector. (4) Minimal-thrust angle of attack. Under a simple lift-drag law, the value of the angle of attack that minimizes thrust admits a closed-form solution (Cardano), yielding constant angle of attack and minimum thrust for constant-speed circular motion.
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