cs.ROSep 17, 2026

Dynamic Modeling and LQR Control of a Single Coaxial Drone with 2DOF Thrust Vectoring Mechanism

Authors: Ali Jokar, Amin Talaeizadeh, Aria Alasty

Organizations: Sharif AgRoLab School of Mechanical Engineering Sharif University of Technology Tehran, Iran

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Abstract

Coaxial rotor drones have generated considerable interest because of energy efficiency and small size, but they are afflicted with inherent underactuation for roll and pitch control, although systems like swashplates have circumvented this limitation at the cost of greater mechanical complexity. This work presents a novel coaxial drone supplemented by a two-degreesof-freedom pendulum mechanism for active thrust vectoring that offers a less mechanically complicated alternative. We develop a comprehensive Lagrangian dynamic model that does not ignore the inertial contributions of all the components, including body, servo arms, and motor assembly. A Linear Quadratic Regulator(LQR) is designed based on the linearized dynamics around the hover equilibrium. High-fidelity simulations taking actuator dynamics and sensor noise into account validate the proposed architecture. An Extended Kalman Filter (EKF) blends GPS, barometer, and IMU estimates with high accuracy for state estimation. The findings verify the potential and reliability of this approach for power-saving, rapid coaxial UAVs.

Figures & tables

Fig. 1: Schematic of a coaxial drone with coordinates indicating the pendulum mechanism structure
ParameterValueUnit
Gravitational acceleration ( gg )9.81m/s2\text{m/s}^{2}
Structural offset d1d_{1}0.05m
Structural offset d2d_{2}0.09m
Structural offset d3d_{3}0.30m
Thrust coefficient ( kfk_{f} )1.3×10−31.3\times 10^{-3}N⋅s2\text{N}\cdot\text{s}^{2}
Torque coefficient ( ktk_{t} )6.7×10−46.7\times 10^{-4}N⋅m⋅s2\text{N}\cdot\text{m}\cdot\text{s}^{2}
TABLE I: Physical and aerodynamic system parameters
ParameterValueUnit
Body mass ( mbm_{b} )0.45kg
Moment of inertia IxxI_{xx}0.002kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IyyI_{yy}0.001kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IzzI_{zz}0.002kg⋅m2\text{kg}\cdot\text{m}^{2}
TABLE II: Main body physical specifications
ParameterValueUnit
Servo arm mass ( ms1m_{s_{1}} )0.07kg
Moment of inertia IxxI_{xx}0.00002kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IyyI_{yy}0.000025kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IzzI_{zz}0.00003kg⋅m2\text{kg}\cdot\text{m}^{2}
TABLE III: First servo arm physical specifications
ParameterValueUnit
Servo arm mass ( ms2m_{s_{2}} )0.07kg
Moment of inertia IxxI_{xx}0.00002kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IyyI_{yy}0.000025kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IzzI_{zz}0.00003kg⋅m2\text{kg}\cdot\text{m}^{2}
TABLE IV: Second servo arm physical specifications
ParameterValueUnit
Motor mass ( mmm_{m} )0.16kg
Moment of inertia IxxI_{xx}0.00006kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IyyI_{yy}0.00004kg⋅m2\text{kg}\cdot\text{m}^{2}
Moment of inertia IzzI_{zz}0.00006kg⋅m2\text{kg}\cdot\text{m}^{2}
TABLE V: Motor assembly physical specifications
ParameterValueUnit
Solverode45-
Time step ( Δt\Delta t )0.001s
Simulation duration ( tt )[-2, 60]s
TABLE VI: Simulation parameters for the torque input scenario
Fig. 2: 3D trajectory of the UAV with torque inputs as control signals
Fig. 3: Roll, pitch, and yaw angles of the UAV with torque inputs as control signals
Fig. 4: Position of the UAV with torque inputs as control signals
Fig. 5: Control signals of the UAV with torque inputs as control signals
Fig. 6: 3D trajectory of the UAV with EKF
Fig. 7: Position of the UAV with EKF
Fig. 8: Roll, pitch, and yaw angles of the UAV with EKF
Fig. 9: Control signals of the UAV with EKF
Fig. 10: Filtering IMU sensor data using the EKF
Fig. 11: Fusion of GPS and barometer data using the EKF
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