Asymptotic stabilization of a transformed quadrotor model using energy-shaping method: Theory and experiments

Gumer Rodríguez-Martínez; Jose Guadalupe Romero; A Mosco-Luciano; H Rodríguez-Cortés

doi:10.1016/j.isatra.2023.04.034

Asymptotic stabilization of a transformed quadrotor model using energy-shaping method: Theory and experiments

ISA Trans. 2023 Aug:139:739-749. doi: 10.1016/j.isatra.2023.04.034. Epub 2023 May 10.

Authors

Gumer Rodríguez-Martínez¹, Jose Guadalupe Romero², A Mosco-Luciano³, H Rodríguez-Cortés⁴

Affiliations

¹ Departamento Académico de Sistemas Digitales, ITAM, Río Hondo 1, Col. Progreso Tizapán, Ciudad de México, 01080, Mexico. Electronic address: gumer.rodriguez@itam.mx.
² Departamento Académico de Sistemas Digitales, ITAM, Río Hondo 1, Col. Progreso Tizapán, Ciudad de México, 01080, Mexico. Electronic address: jose.romerovelazquez@itam.mx.
³ Sección de Mecatrónica, Departamento de Ingeniería Eléctrica, CINVESTAV-IPN, Av, IPN 2508, Col. San Pedro Zacatenco, Ciudad de México, 07360, Mexico. Electronic address: alan.mosco@cinvestav.mx.
⁴ Sección de Mecatrónica, Departamento de Ingeniería Eléctrica, CINVESTAV-IPN, Av, IPN 2508, Col. San Pedro Zacatenco, Ciudad de México, 07360, Mexico. Electronic address: hrodriguez@cinvestav.mx.

PMID: 37230906
DOI: 10.1016/j.isatra.2023.04.034

Abstract

This note presents a new passivity-based controller that ensures asymptotic stability for quadrotor position without solving partial differential equations or performing a partial dynamic inversion. After a resourceful change of coordinates, a pre-feedback controller, and a backstepping stage on the yaw angle dynamic, it is possible to identify new quadrotor cyclo passive outputs. Then, a simple proportional-integral controller of these cyclo-passive outputs completes the design. The cyclo-passive outputs allow the construction of an energy-based Lyapunov function that includes five out of six quadrotor degrees of freedom and guarantees asymptotic stability of the desired equilibrium. Moreover, the constant velocity reference tracking problem is solved with a slight modification to the proposed controller. Finally, the approach is validated through simulations and real-time experimental results.

Keywords: Asymptotic stability; Lyapunov functions; PI controllers; Quadrotor model; Real-time control.