Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory
The aim of the present research work is to design a control law for a quadcopter drone based on the Virtual Attractive-Repulsive Potentials (VARP) theory. VARP theory, originally designed to enable path following by a small wheeled robot, will be tailored to control a quadcopter drone, hence allowin...
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MDPI AG
2022-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/7/1104 |
| _version_ | 1797438536082784256 |
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| author | Simone Fiori Luca Bigelli Federico Polenta |
| author_facet | Simone Fiori Luca Bigelli Federico Polenta |
| author_sort | Simone Fiori |
| collection | DOAJ |
| description | The aim of the present research work is to design a control law for a quadcopter drone based on the Virtual Attractive-Repulsive Potentials (VARP) theory. VARP theory, originally designed to enable path following by a small wheeled robot, will be tailored to control a quadcopter drone, hence allowing such device to learn flight planning. The proposed strategy combines an instance of VARP method to control a drone’s attitude (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>-VARP) and an instance of VARP method to control a drone’s spatial location (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mn>3</mn></msup></semantics></math></inline-formula>-VARP). The resulting control strategy will be referred to as double-VARP method, which aims at making a drone follow a predefined path in space. Since the model of the drone as well as the devised control theory are formulated on a Lie group, their simulation on a computing platform is performed through a numerical analysis method specifically designed for these kinds of numerical simulations. A numerical simulation analysis is used to assess the salient features of the proposed regulation theory. In particular, resilience against shock-type disturbances are assessed numerically. |
| first_indexed | 2024-03-09T11:38:21Z |
| format | Article |
| id | doaj.art-9017f00f97fe416f97ae445c2ecd147c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T11:38:21Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9017f00f97fe416f97ae445c2ecd147c2023-11-30T23:37:14ZengMDPI AGMathematics2227-73902022-03-01107110410.3390/math10071104Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials TheorySimone Fiori0Luca Bigelli1Federico Polenta2Department of Information Engineering, Marches Polytechnic University, 60121 Ancona, ItalyGraduate School of Mechatronic Engineering, Politecnico di Torino, 10129 Turin, ItalyGraduate School of Automation and Control Engineering, Politecnico di Milano, 20133 Milan, ItalyThe aim of the present research work is to design a control law for a quadcopter drone based on the Virtual Attractive-Repulsive Potentials (VARP) theory. VARP theory, originally designed to enable path following by a small wheeled robot, will be tailored to control a quadcopter drone, hence allowing such device to learn flight planning. The proposed strategy combines an instance of VARP method to control a drone’s attitude (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>SO</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula>-VARP) and an instance of VARP method to control a drone’s spatial location (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mn>3</mn></msup></semantics></math></inline-formula>-VARP). The resulting control strategy will be referred to as double-VARP method, which aims at making a drone follow a predefined path in space. Since the model of the drone as well as the devised control theory are formulated on a Lie group, their simulation on a computing platform is performed through a numerical analysis method specifically designed for these kinds of numerical simulations. A numerical simulation analysis is used to assess the salient features of the proposed regulation theory. In particular, resilience against shock-type disturbances are assessed numerically.https://www.mdpi.com/2227-7390/10/7/1104VARP control theoryfeedback controlLie groupautonomous quadcopter controlpath followingvirtual potentials |
| spellingShingle | Simone Fiori Luca Bigelli Federico Polenta Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory Mathematics VARP control theory feedback control Lie group autonomous quadcopter control path following virtual potentials |
| title | Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory |
| title_full | Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory |
| title_fullStr | Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory |
| title_full_unstemmed | Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory |
| title_short | Lie-Group Type Quadcopter Control Design by Dynamics Replacement and the Virtual Attractive-Repulsive Potentials Theory |
| title_sort | lie group type quadcopter control design by dynamics replacement and the virtual attractive repulsive potentials theory |
| topic | VARP control theory feedback control Lie group autonomous quadcopter control path following virtual potentials |
| url | https://www.mdpi.com/2227-7390/10/7/1104 |
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