Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs
Abstract
:1. Introduction
2. Artificial Asymmetrical Potential Field as Nonlinear Proportional Term
3. Nonlinear Integral Term of PID Control Loop
4. Nonlinear Derivative Term of PID Control Loop
5. Numerical Simulations
5.1. Lateral Wind Gust Case
5.2. Longitudinal wind Gust Case
6. Results
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Symbol | Description |
---|---|
UAV | Unmanned aerial vehicle |
APF | Artificial potential field |
AAPF | Asymmetrical artificial potential field |
Proportional integral derivative controller (function of x, y, or z) | |
Proportional term (function of x, y, or z) | |
Integral term (function of x, y, or z) | |
Derivative term (function of x, y, or z) | |
Proportional–integral term (function of x, y, or z) | |
Tracked point velocity | |
Gain coefficients of AAPF (proportional term) | |
Rotation matrix of angular rate of heading angle | |
Gain coefficient of rotation matrix | |
Angular rate of heading angle of tracked point | |
Asymmetrical artificial potential function | |
Gradient of artificial potential function | |
Velocity vector field | |
, | Gain coefficients of integral term for x |
Gain coefficient of integral term for y | |
Gain coefficient of integral term for z | |
, | Gain coefficients of derivative term for x |
, | Gain coefficients of derivative term for y |
, | Gain coefficients of derivative term for z |
Controller (Subfigure) | ||||||||
---|---|---|---|---|---|---|---|---|
P (1a) | 10.0 | 10.0 | 0.01 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
P (1b) | 10.0 | 10.0 | 1 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
P (1c) | 10.0 | 10.0 | 10.0 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
PI (2a) | 10.0 | 10.0 | 1 | 0.3 | 0.1 | 0.1 | 0.0 | 0.0 |
PI (2b) | 10.0 | 10.0 | 1 | 0.3 | 1.0 | 1.0 | 0.0 | 0.0 |
PI (2c) | 10.0 | 10.0 | 1 | 0.3 | 10.0 | 10.0 | 0.0 | 0.0 |
PID (3a) | 10.0 | 10.0 | 1 | 0.3 | 1.0 | 1.0 | 0.1 | 0.1 |
PID (3b) | 10.0 | 10.0 | 1 | 0.3 | 1.0 | 1.0 | 1.0 | 1.0 |
PID (3c) | 10.0 | 10.0 | 1 | 0.3 | 1.0 | 1.0 | 10.0 | 10.0 |
Controller (Subfigure) | ||||||||
---|---|---|---|---|---|---|---|---|
P (1a) | 0.1 | 0.1 | 10.0 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
P (1b) | 1.0 | 1.0 | 10.0 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
P (1c) | 10.0 | 10.0 | 10.0 | 0.3 | 0.0 | 0.0 | 0.0 | 0.0 |
PI (2a) | 1.0 | 1.0 | 10.0 | 0.3 | 0.1 | 0.1 | 0.0 | 0.0 |
PI (2b) | 1.0 | 1.0 | 10.0 | 0.3 | 1.0 | 1.0 | 0.0 | 0.0 |
PI (2c) | 1.0 | 1.0 | 10.0 | 0.3 | 10.0 | 10.0 | 0.0 | 0.0 |
PID (3a) | 1.0 | 1.0 | 10.0 | 0.3 | 1.0 | 1.0 | 0.1 | 0.1 |
PID (3b) | 1.0 | 1.0 | 10.0 | 0.3 | 1.0 | 1.0 | 1.0 | 1.0 |
PID(3c) | 1.0 | 1.0 | 10.0 | 0.3 | 1.0 | 1.0 | 10.0 | 10.0 |
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Kownacki, C.; Ambroziak, L. Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs. Sensors 2022, 22, 5474. https://doi.org/10.3390/s22155474
Kownacki C, Ambroziak L. Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs. Sensors. 2022; 22(15):5474. https://doi.org/10.3390/s22155474
Chicago/Turabian StyleKownacki, Cezary, and Leszek Ambroziak. 2022. "Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs" Sensors 22, no. 15: 5474. https://doi.org/10.3390/s22155474
APA StyleKownacki, C., & Ambroziak, L. (2022). Asymmetrical Artificial Potential Field as Framework of Nonlinear PID Loop to Control Position Tracking by Nonholonomic UAVs. Sensors, 22(15), 5474. https://doi.org/10.3390/s22155474