Arellano-Muro, Carlos A.; Osuna-González, Guillermo; Castillo-Toledo, Bernardino; Bayro-Corrochano, Eduardo Newton-Euler modeling and control of a multi-copter using motor algebra \(\mathrm{G}^+_{3,0,1} \). (English) Zbl 1440.93161 Adv. Appl. Clifford Algebr. 30, No. 2, Paper No. 19, 22 p. (2020). In the present paper, on the base of the geometric algebra framework specifically using the motor algebra \(G^{+}_{3,0,1}\), the dynamic model and the nonlinear control for a multi-copter have been developed. The kinematics of the aircraft model is presented and the dynamics through Newton-Euler formalism is described. The block-control technique is applied in combination with super twisting including an internal dynamics estimator driven by maneuvers away from the origin. Finally, the stability of the presented control scheme is shown. Reviewer: Clementina Mladenova (Sofia) MSC: 93C85 Automated systems (robots, etc.) in control theory 93C10 Nonlinear systems in control theory 93B25 Algebraic methods 15A66 Clifford algebras, spinors Keywords:Newton-Euler equations of motion; algebra of rotors; motor algebra \(G^{+}_{3,0,1}\); multi-copter control; adaptive estimator PDFBibTeX XMLCite \textit{C. A. Arellano-Muro} et al., Adv. Appl. Clifford Algebr. 30, No. 2, Paper No. 19, 22 p. (2020; Zbl 1440.93161) Full Text: DOI References: [1] Bouabdallah, S., Siegwart, R.: Full control of a quadrotor. In: IEEE/RSJ international conference on intelligent robots and systems (IROS), San Diego, CA, USA (2007) [2] Wang, X., Yu, C.: Feedback linearization regulator with coupled attitude and translation dynamics based on unit dual quaternion. In: 2010 IEEE international symposium on intelligent control, pp. 2380-2384 (2010) [3] Abaunza, H., Cariño, J., Castillo, P., Lozano, R.: Quadrotor dual quaternion control. In: 2015 workshop on research, education and development of unmanned aerial systems (RED-UAS), pp. 195-203 (2015) [4] Luque-Vega, L.; Castillo-Toledo, B.; Loukianov, AG, Robust block second order sliding mode control for a quadrotor, advances in guidance and control of aerospace vehicles using sliding mode control and observation techniques, J. Franklin Inst., 349, 719-739 (2012) · Zbl 1254.93050 · doi:10.1016/j.jfranklin.2011.10.017 [5] Arellano-Muro, C. A., Castillo-Toledo, B., Loukianov, A., Luque-Vega, L. F., Gonzalez-Jimenez, L.: Quaternion-based trajectory tracking robust control for a quadrotor. In: 10th annual system of systems engineering conference 2015 (SoSE 2015), San Antonio, USA (2015) [6] Loukianov, AG, Robust block decomposition sliding mode control design, Int J Math Probl Eng Theory Methods Appl, 8, 349-365 (2002) · Zbl 1059.93024 [7] Levant, A., Universal single-input-single-output (SISO) sliding-mode controllers with finite time convergence, IEEE Trans Automat Control, 46, 1785-1789 (2005) · Zbl 1365.93071 [8] Bayro-Corrochano, E., Geometric Computing For Wavlet Transform, Robot Vision, Learning, Control and Action. (2010), London: Springer, London · Zbl 1211.68463 [9] C. W. K.: Preliminary sketch of bi-quaternons. Proc. London Math. Soc., 4, 381-395 (1873) · JFM 05.0280.01 [10] Gessow, A., Myers, G. C.: Aerodynamics of the helicopter. In: Fifth printing, Frederick Unger Publishing Co., New York (1978) · Zbl 0048.19101 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.