Scale Factor Estimation for Quadrotor Monocular-Vision Positioning Algorithms
Abstract
:1. Introduction
2. Materials and Methods
2.1. Quadrotor Dynamics
2.2. Available Sensors
2.2.1. Scaled Position
2.2.2. Specific Acceleration
2.2.3. Attitude and Heading Reference Systems
2.2.4. Vertical Speed
2.3. Immersion and Invariance Observers
- is positively invariant,
- A1
- For all and y the map satisfies
- A2
- The dynamic system
3. Observer and Estimator Design
3.1. Observation and Estimation Problems
3.2. Velocity Observer
3.3. Scale Factor Estimator
4. Numerical Simulations
4.1. Matlab-Simulink
4.2. Gazebo
4.2.1. Calculation of
4.2.2. Monocular-Vision Algorithm
4.2.3. Trajectory Tracking Control Using the Scale Factor Estimator
5. Conclusions
- The velocity observer does not neglect the Coriolis term, offering greater accuracy in fast flights.
- The scale factor estimator allows taking advantage of all the benefits of monocular cameras, obtaining the accuracy of a stereoscopic camera without increasing the processing power.
- Lyapunov’s arguments prove asymptotic convergence to zero of the observer and estimator errors, and the simulations validate the correct performance and use of the proposed theory.
- It is illustrated that the scale factor is not the same in all axes, as some authors assume. It is even different from experimenting in the same environment if the initial conditions change.
- The proposed approach allows for position trajectory tracking to be performed directly using the measurements of a monocular-vision positioning algorithm, removing the limitations of a GPS or a motion capture system.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Proof of Theorem 1
Appendix B. Proof of Proposition 1
References
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Symbol | Variable | Units |
---|---|---|
Translational position in inertial coordinates | m | |
Rotation matrix from body to inertial coordinates | dimensionless | |
Translational velocity in body frame coordinates | m/s | |
Angular velocity in body coordinates | rad/s | |
Moments generated by the differential thrust, and reaction moment between the four rotors | Nm | |
m | Quadrotor mass | kg |
g | Gravity acceleration constant | m/s |
Total thrust generated by the four rotors | N | |
Parameter related to aerodynamic drag force [27] | kg/s | |
Quadrotor inertia matrix | kg m |
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Gómez-Casasola, A.; Rodríguez-Cortés, H. Scale Factor Estimation for Quadrotor Monocular-Vision Positioning Algorithms. Sensors 2022, 22, 8048. https://doi.org/10.3390/s22208048
Gómez-Casasola A, Rodríguez-Cortés H. Scale Factor Estimation for Quadrotor Monocular-Vision Positioning Algorithms. Sensors. 2022; 22(20):8048. https://doi.org/10.3390/s22208048
Chicago/Turabian StyleGómez-Casasola, Alejandro, and Hugo Rodríguez-Cortés. 2022. "Scale Factor Estimation for Quadrotor Monocular-Vision Positioning Algorithms" Sensors 22, no. 20: 8048. https://doi.org/10.3390/s22208048
APA StyleGómez-Casasola, A., & Rodríguez-Cortés, H. (2022). Scale Factor Estimation for Quadrotor Monocular-Vision Positioning Algorithms. Sensors, 22(20), 8048. https://doi.org/10.3390/s22208048