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Dynamic System Emulation: Fixed Wing Dynamics on a Multicopter

Abdelhakim Amer, Andriy Sarabakha

arXiv:2609.06520v1eess.SYcs.ROcs.SY

TL;DR

Fixed-wing and multicopter dynamics differ, making it nontrivial to reproduce fixed-wing behavior on a multicopter. The paper derives a DFL-based framework for multicopter camera-pose mimicry and reports successful simulation tracking of steady and aggressive trajectories.

  • Problem

    Fixed-wing and multicopter dynamics differ in constraints, stall behavior, and actuation, raising questions about whether mimicry is feasible and how to control it in practice.

    Source: §I · p. 1

  • Method

    The paper designs a DFL-based framework and control laws for a two-axis-gimbal multicopter to mimic fixed-wing camera-pose trajectories.

    Source: §I · p. 1, B. Camera-Pose Mimicry · p. 3, §IV · p. 4

  • Results

    The simulated multicopter-gimbal system achieves camera-pose mimicry for both steady and aggressive trajectories, with precise tracking of the coupled nonlinear dynamics.

    Source: A. Trajectory 1: Level Flight · p. 6, B. Trajectory 2: Aerobatic Loop · p. 6, C. Discussion · p. 7

  • Takeaways & Limitations

    The framework provides a practical method for high-fidelity physical-to-physical mimicry, with potential application to algorithm validation and operator training in real-world conditions.

    Source: §VI · p. 7

    Validation is conducted in simulation, including tracking simulations using a multicopter-gimbal system and a fixed-wing aerobatic aircraft.

    Source: §I · p. 1, §V · p. 5

Abstract

from arXiv · show

This work presents a control framework that enables a multicopter equipped with a two-axis gimbal to emulate the flight dynamics of a fixed-wing aircraft. The goal is to provide an operationally simple platform for training and simulation that avoids the aerodynamic constraints of fixed-wing vehicles, such as minimum airspeed and nonholonomic constraints. A state-input mapping between the two platforms is derived using dynamic feedback linearization. The framework is evaluated on representative fixed-wing manoeuvres. Results show high-fidelity emulation under nominal conditions. While evaluations are conducted in simulation, the approach establishes a practical path toward hardware deployment for pilot training, autonomy research, and controller benchmarking.

I. INTRODUCTION

The paper proposes physical-to-physical emulation to address the differences between fixed-wing and multicopter dynamics, using a DFL-based framework to mimic fixed-wing camera-pose trajectories. It motivates the approach against limits of virtual and pilot-in-the-loop simulation and describes the aircraft model used for the comparison.

I. INTRODUCTION

  • Physical-to-physical emulation controls a manoeuvrable multicopter with a gimbal to replicate a more constrained fixed-wing aircraft’s motion and camera viewpoint.The introduction contrasts this approach with virtual simulation’s sim-to-real gap and pilot-in-the-loop systems’ inability to provide real-time sensor data responsive to current state and actions.Source: §I · p. 1
  • Fixed-wing and multicopter dynamics differ fundamentally, motivating formal feasibility analysis and control methods such as dynamic feedback linearization for practical emulation.The paper identifies nonholonomic constraints, stall behavior, and unmatched actuation as key differences; it notes MPC’s computational cost can hinder embedded real-time use.Source: §I · p. 1
  • The work proposes proving camera-pose controllability and mimicry, designing DFL control laws, and validating the framework in simulations of increasingly complex manoeuvres.Source: §I · p. 1

II. PRELIMINARIES

  • Quaternions are scalar-first, with conjugates denoted by q̄ and R(q) denoting the corresponding rotation matrix.Source: §II · p. 2

A. Fixed-Wing Aircraft Dynamics

  • The fixed-wing aircraft is modeled as an underactuated system with engine thrust, aileron, elevator, and rudder inputs, and Newton–Euler kinematics and dynamics.The model includes aerodynamic forces and torques acting on the aircraft.Source: A. Fixed-Wing Aircraft Dynamics · p. 2

B. Multicopter with 2-Axis Gimbal Dynamics

The multicopter model couples vehicle motion with a two-axis roll-pitch gimbal carrying a camera. Its control inputs include vehicle thrust and torques, along with gimbal inputs, and its output is the camera pose.

B. Multicopter with 2-Axis Gimbal Dynamics

III. CAMERA-POSE CONTROLLABILITY AND MIMICRY ON SE(3)

The camera-pose setup assumes a body-aligned fixed-wing camera at a fixed lever arm, while the multicopter’s camera position includes lever-arm coupling. The described multicopter rotational inputs include gimbal rates and free-body yaw rate.

III. CAMERA-POSE CONTROLLABILITY AND MIMICRY ON SE(3)

  • The fixed-wing camera is assumed body-aligned and located at a fixed lever arm expressed in the aircraft body frame.Source: §III · p. 3
  • The rotational inputs used for mimicry include gimbal roll and pitch rates and the multicopter’s free yaw rate, which does not alter thrust direction.Source: §III · p. 3
  • The multicopter’s camera position is expressed in the world frame and includes known lever-arm coupling terms.Source: §III · p. 3
  • The fixed-wing camera assumption can be relaxed with a planner that avoids the singular set.Source: §III · p. 3

A. Output Full Actuation & STLC on SE(3)

The camera-pose input Jacobian has full rank almost everywhere, establishing output full actuation and small-time local controllability on SE(3). The translational and rotational rank arguments have distinct conditions, with a global result noted for a three-axis gimbal.

A. Output Full Actuation & STLC on SE(3)

B. Camera-Pose Mimicry

The multicopter and gimbal can match the fixed-wing camera pose by coordinating position and orientation control. Under the stated assumptions, this works for any feasible fixed-wing camera trajectory.

B. Camera-Pose Mimicry

  • The multicopter thrust, torque, and gimbal angle and rate limits must remain within authority along trajectories of interest.Source: B. Camera-Pose Mimicry · p. 3
  • Camera-position matching commands the multicopter to a lever-arm-compensated target, then tracks the resulting desired acceleration.The matched positions are pM + R(qM)tG and pA + R(qA)tAC.Source: B. Camera-Pose Mimicry · p. 3
  • Camera-orientation matching requires qM ⊗ qG = qA, with the gimbal supplying a relative roll-pitch quaternion.The multicopter attitude is decomposed into thrust-setting tilt and free yaw; the relative camera quaternion is chosen to cancel yaw and lie in the roll-pitch submanifold.Source: B. Camera-Pose Mimicry · p. 3
  • Under Assumptions 1 and 2, control inputs realize camera-pose mimicry for any feasible fixed-wing camera trajectory.With identical camera intrinsics, the rendered image streams are indistinguishable to the viewer.Source: B. Camera-Pose Mimicry · p. 3

IV. PROPOSED METHOD

The method maps fixed-wing camera-pose trajectories to multicopter and gimbal inputs using dynamic feedback linearization. A dynamic compensator addresses the failure of static feedback to decouple the system’s inputs and outputs.

IV. PROPOSED METHOD

  • The method computes multicopter and gimbal inputs so their camera pose tracks the fixed-wing camera trajectory, using dynamic feedback linearization for nonlinear tracking.DFL transforms a nonlinear system into an equivalent linear, controllable, and observable one through a change of variables.Source: §IV · p. 4
  • Static state feedback cannot solve input-output decoupling because the decoupling matrix is singular and thrust affects acceleration without other control inputs.The relative-degree sum is 9 while N = 14; the proposed dynamic compensator adds state variables and delays thrust’s appearance to higher acceleration derivatives.Source: §IV · p. 4
  • Replacing thrust with the output of a double integrator makes thrust an internal state and adds its second derivative as a new control input.The other inputs remain unchanged in the extended system.Source: §IV · p. 4
  • For the extended system, the input-output decoupling condition is satisfied, making dynamic feedback control solvable.The passage reports the extended system’s values as ˆN = 16 and a relative-degree vector whose sum satisfies the condition.Source: §IV · p. 4

V. VALIDATION RESULTS

The validation simulates a multicopter with a two-axis gimbal tracking an aerobatic fixed-wing aircraft. It tests both level flight and an aerobatic loop against the camera-pose mimicry condition.

V. VALIDATION RESULTS

  • The simulation uses a two-axis-gimbal multicopter to track a Red Bull Edge 540 aerobatic aircraft.The Edge 540 is selected for aggressive manoeuvring, and the Freefly Alta-X for its high thrust-to-weight ratio and required control authority.Source: §V · p. 5
  • The evaluation tests level flight and an aerobatic loop against the camera-pose mimicry condition.Source: §V · p. 5
  • Table I is identified as the source of vehicle parameters.Source: Table I · p. 5

A. Trajectory 1: Level Flight

In level flight, the gimbal camera tracks the fixed-wing aircraft’s position and orientation even as the multicopter pitches to generate forward thrust. The results also show tracking without steady-state error in the stated nonsingular region.

A. Trajectory 1: Level Flight

  • The fixed-wing level-flight baseline uses a constant elevator deflection of −0.05 rad to counteract gravity.Fig. 5 depicts the aircraft, multicopter, and gimbal-camera trajectories for this flight.Source: A. Trajectory 1: Level Flight · p. 5, Figure 5 · p. 5
  • 30° multicopter pitch is countered by gimbal rotation, keeping camera orientation aligned with the fixed-wing attitude during level flight.The camera position also tracks the fixed-wing reference with negligible error across the six degrees of freedom.Source: A. Trajectory 1: Level Flight · pp. 5–6, Figure 4 · p. 5
  • Rapid gimbal response and no steady-state error indicate operation within the stated nonsingular region, maintaining full actuation authority throughout the trajectory.Source: A. Trajectory 1: Level Flight · p. 6

B. Trajectory 2: Aerobatic Loop

During the vertical loop, the gimbal camera tracks the fixed-wing reference through rapid changes in direction and gravitational load, despite aggressive multicopter motion. Position tracking has brief high-acceleration transients, but remains stable and converges.

B. Trajectory 2: Aerobatic Loop

  • The vertical loop uses a constant elevator deflection of −0.25 rad and produces rapid changes in position, velocity, orientation, airspeed, and load factor.The 3D trajectory view shows the camera path closely following the fixed-wing path through directional changes and varying gravitational loads.Source: B. Trajectory 2: Aerobatic Loop · p. 6, Figure 7 · p. 6
  • More than 60° of multicopter pitch at the loop top is decoupled from camera orientation, which remains tightly coupled to the fixed-wing reference with bounded tracking errors.The gimbal rapidly compensates for the multicopter’s aggressive body rotations while the thrust vector tracks the curved path.Source: Figure 6 · p. 6, Figure 7 · p. 6, B. Trajectory 2: Aerobatic Loop · p. 7
  • Position tracking shows brief transients during the loop’s highest-acceleration phases, but stability and convergence are maintained.The dynamic compensator extends relative degree to enable exact input-output decoupling.Source: B. Trajectory 2: Aerobatic Loop · p. 7

C. Discussion

The discussion reports successful camera-pose mimicry on both steady and aggressive trajectories, with the gimbal preserving smooth camera orientation despite large multicopter pitch oscillations. The conclusion presents the framework as a lower-cost, lower-risk option for training and algorithm validation than deploying high-value fixed-wing aircraft.

C. Discussion

  • Across steady and aggressive trajectories, simulations achieve camera-pose mimicry, with gimbal motion maintaining smooth camera orientation despite high-amplitude multicopter pitch oscillations.The discussion attributes the strong pitch oscillations to the need to reorient thrust to follow the aircraft’s velocity profile.Source: C. Discussion · p. 7

VI. CONCLUSIONS AND FUTURE WORK

  • The authors present the framework as a practical method for real-world algorithm validation and operator training at negligible cost and reduced operational risk versus high-value fixed-wing aircraft.They also state that the principles may generalize to other dissimilar systems, including ground or underwater vehicles.Source: §VI · p. 7
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