Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach
This article addresses the problem of balancing an inverted spherical pendulum on a quadrotor. The full dynamic model is obtained via the Euler-Lagrange formalism, where the dynamics of the pendulum is coupled to the dynamics of the quadrotor, taking as control inputs the torques associated with the...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/11/6/578 |
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| author | Adrian H. Martinez-Vasquez Rafael Castro-Linares Abraham Efraím Rodríguez-Mata Hebertt Sira-Ramírez |
| author_facet | Adrian H. Martinez-Vasquez Rafael Castro-Linares Abraham Efraím Rodríguez-Mata Hebertt Sira-Ramírez |
| author_sort | Adrian H. Martinez-Vasquez |
| collection | DOAJ |
| description | This article addresses the problem of balancing an inverted spherical pendulum on a quadrotor. The full dynamic model is obtained via the Euler-Lagrange formalism, where the dynamics of the pendulum is coupled to the dynamics of the quadrotor, taking as control inputs the torques associated with the yaw, roll, and pitch dynamics, and a control input for the vertical displacement in height. A trajectory tracking control scheme is proposed by means of an active disturbance rejection control based on a discontinuous extended state observer (ADRC-DESO) that allows controlling the system in the translational dynamics of the quadrotor including the rotational dynamics and the inverted pendulum dynamics. To address this problem, the dynamic model is linearized around an equilibrium point, taking into consideration that the system operates in close vicinity of the equilibrium points, thus considerably simplifying the dynamic model. Proving that the linear model is controllable and therefore differentiable flat, flat outputs are proposed around the displacements associated with the three cartesian axes of the Euclidean space, including a dynamic associated with the yaw dynamics of the quadrotor allowing to parameterize the full linear system. Simulation results as well as a convergence analysis validate the performance of the strategy. |
| first_indexed | 2024-03-11T02:13:27Z |
| format | Article |
| id | doaj.art-69104d34061d457886db82b0f35f811d |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-11T02:13:27Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Machines |
| spelling | doaj.art-69104d34061d457886db82b0f35f811d2023-11-18T11:20:06ZengMDPI AGMachines2075-17022023-05-0111657810.3390/machines11060578Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer ApproachAdrian H. Martinez-Vasquez0Rafael Castro-Linares1Abraham Efraím Rodríguez-Mata2Hebertt Sira-Ramírez3Mechatronics Section, Electrical Engineering Department, Cinvestav-IPN, Mexico City 07360, MexicoMechatronics Section, Electrical Engineering Department, Cinvestav-IPN, Mexico City 07360, MexicoDivisión de Estudios de Posgrado e Investigación, Tecnologico Nacional de Mexico Campus Chihuahua, Av. Tecnológico #2909, Chihuahua 31310, MexicoMechatronics Section, Electrical Engineering Department, Cinvestav-IPN, Mexico City 07360, MexicoThis article addresses the problem of balancing an inverted spherical pendulum on a quadrotor. The full dynamic model is obtained via the Euler-Lagrange formalism, where the dynamics of the pendulum is coupled to the dynamics of the quadrotor, taking as control inputs the torques associated with the yaw, roll, and pitch dynamics, and a control input for the vertical displacement in height. A trajectory tracking control scheme is proposed by means of an active disturbance rejection control based on a discontinuous extended state observer (ADRC-DESO) that allows controlling the system in the translational dynamics of the quadrotor including the rotational dynamics and the inverted pendulum dynamics. To address this problem, the dynamic model is linearized around an equilibrium point, taking into consideration that the system operates in close vicinity of the equilibrium points, thus considerably simplifying the dynamic model. Proving that the linear model is controllable and therefore differentiable flat, flat outputs are proposed around the displacements associated with the three cartesian axes of the Euclidean space, including a dynamic associated with the yaw dynamics of the quadrotor allowing to parameterize the full linear system. Simulation results as well as a convergence analysis validate the performance of the strategy.https://www.mdpi.com/2075-1702/11/6/578differential flatnessdiscontinuous observerinverted pendulumlyapunov analysis |
| spellingShingle | Adrian H. Martinez-Vasquez Rafael Castro-Linares Abraham Efraím Rodríguez-Mata Hebertt Sira-Ramírez Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach Machines differential flatness discontinuous observer inverted pendulum lyapunov analysis |
| title | Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach |
| title_full | Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach |
| title_fullStr | Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach |
| title_full_unstemmed | Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach |
| title_short | Spherical Inverted Pendulum on a Quadrotor UAV: A Flatness and Discontinuous Extended State Observer Approach |
| title_sort | spherical inverted pendulum on a quadrotor uav a flatness and discontinuous extended state observer approach |
| topic | differential flatness discontinuous observer inverted pendulum lyapunov analysis |
| url | https://www.mdpi.com/2075-1702/11/6/578 |
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