Submitted:
05 January 2026
Posted:
06 January 2026
You are already at the latest version
Abstract
Keywords:
1. Introduction
Related Work


2. Materials and Methods
2.1. Mathematical Modeling (VTOL Mode)
- the equations of motion of a rigid body with six degrees of freedom (6-DOF)
- the propulsion element model
- the distribution of forces and moments as a function of each rotor’s position
- : position in the inertial frame
- : Euler angles
- : linear velocities in the body frame
- : angular velocities of the body
2.2. Control Structure
- is the proportional gain.
- is the integral gain.
- is the derivative gain.
- is the first-order derivative filter time constant.
- is the integrator method for computing the integral in discrete-time controller.
- is the integrator method for computing the derivative filter in discrete-time controller.
2.3. Control Allocation Matrix for the Octo-I Configuration (in East-North-Down Coordinates)

2.4. PMSM Electric Motor Model[13] (Permanent-Magnet Synchronous Motor)
- is the applied voltage
- is the winding resistance
- is the winding inductance
- is the motor current
- is the back electromotive force (back-EMF)
2.5. Mechanical Equilibrium Equation
- is the rotor moment of inertia
- is the angular speed of the shaft
- is the motor torque
- is the load torque
- is the viscous friction coefficient
2.6. Electric Battery Model
- is the voltage delivered to the load
- is the open-circuit voltage
- is the internal resistance of the battery
- is the current delivered to the load
- is the battery capacity (Ah)
- is the consumed current (A)
2.6. Numerical Simulation Framework (Simscape/Matlab Model)



2.7. Parameters of the Simulation Network
| % Model Parameters of Octo_I_DRAGONFLY | |
| % operation environment | |
| air_temperature = 298; | % Kelvin |
| air_density = 1.225; | % kg/m3 |
| gravity = [0 0 -9.80665]; | % m/s^2 |
| % multirotor propeller | |
| propeller_Diameter = 1.447; | % m |
| propeller_kThrust = 0.0968; | |
| propeller_kPower = 0.0282; | |
| propeller_mass = 0.434; | % kg |
| propeller_center_of_mass = [[0 0 0]; | % m |
| propeller_inertia = [0.061, 0.0007, 0.062]; | % kg*m^2 |
| propeller_product_of_inertia = [[0 0 0]; | % kg*m^2 |
| % multirotor electric motor | |
| motor_max_torque = 64; | % motor_max_torque (Nm) |
| motor_max_power = 23000; | % motor_max_power (W) |
| motor_time_const = 0.010; | % motor_time_const (s) |
| motor_efficiency = 85; | % motor_efficiency (%) |
| motor_efficiency_spd = 1800; | % motor_efficiency_spd (rpm) |
| motor_efficiency_torque = 30; | % motor_efficiency_torque (Nm) |
| motor_rotor_damping = 1e-07; | % motor_rotor_damping (Nm/(rad/s) |
| % battery | |
| nominal_voltage = 100; | % V |
| internal_resistance = 0.002; | % ohm |
| voltage_v1 = 88.8; | % V |
| battery_capacity = 38000; | % Ah |
| charge_AH1 = 19000; | % Amperi.ora |
| batt_temperature = 298.15; | % K |
| fouselage_mass = 100; | % kg |
| frame_mass = 10; | % kg |
| pilot_mass = 70; | % kg |
| battery_mass = 13.2; | % kg |
| combustion engine_mass = 17.6; | % kg |
| fuel_tank = [0.304 0.304 0.304]; | % 28l / 21kg |




3. Results
3.1. DragonFly Model, Version 1 – VTOL Octocopter Configuration







3.2. Laboratory Testing of the VTOL System (Ground Testing)

3.3. Typical Step Responses (for the VTOL Mode)




4. Discussion
5. Conclusion
6. Future Work

7. Acknowledgements
References
- Beard, R.W.; McLain, T.W., Small Unmanned Aircraft: Theory and Practice Princeton University Press, 2012. [CrossRef]
- Stevens, B.L.; Lewis, F.L.; Johnson, E.N, Aircraft Control and Simulation, 3rd ed.Wiley, 2015. [CrossRef]
- Austin, R., Unmanned Aircraft Systems: UAVS Design, Development and Deployment. Wiley, 2010. [CrossRef]
- Ducard, G.J.J., Fault-Tolerant Flight Control and Guidance Systems. Springer, 2009. [CrossRef]
- Sun, Y.; Zhang, Y.; Guo, S., “Survey of Optionally Piloted Vehicles: Architectures and Challenges.”,Aerospace, 2021,8, 326. [CrossRef]
- Bartolini, G.; Fridman, L.; Levant, A.; Usai, E., Sliding Mode Control in Electro-Mechanical Systems, CRC Press, 2019. [CrossRef]
- Bouabdallah, S.; Murrieri, P.; Siegwart, R, “Design and Control of an Indoor Micro Quadrotor.”, ICRA, 2004. [CrossRef]
- Mahony, R.; Kumar, V.; Corke, P., “Multirotor Aerial Vehicles: Modeling, Estimation, and Control.”, IEEE Robotics & Automation Magazine, 2012, 19, 20–32. [CrossRef]
- Pounds, P.; Mahony, R.; Corke, P., “Modelling and Control of a Quad-Rotor Robot.” Aerospace Control Conference, 2006. [CrossRef]
- Anderson, J.D., Aircraft Performance and Design, McGraw-Hill, 1999, ISBN: 978-0070019714.
- MathWorks, Simscape Multibody User’s Guide, 2023.
- Raffo, G.V.; Ortega, M.G.; Rubio, F.R., “An Integral Predictive/Nonlinear H∞ Control Structure for a Quadrotor, Automatica, 2010, 46, 29–39. [CrossRef]
- Cook, M.V., Flight Dynamics Principles, 3rd ed, Butterworth-Heinemann, 2012. [CrossRef]
- Skogestad, S.; Postlethwaite, I., Multivariable Feedback Control, 2nd ed. Wiley, 2005. [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).