Quadrotor Real-Time Simulation: A Temporary Computational Complexity-Based Approach

Gustavo Delgado-Reyes, Jorge Salvador Valdez-Martínez, Miguel Ángel Hernández-Pérez, Karina Ruby Pérez-Daniel and Pedro Javier García-Ramírez
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Gustavo Delgado-Reyes: Instituto de Ingeniería, Universidad Veracruzana, Juan Pablo II s/n, Boca del Río 94294, Veracruz, Mexico
Jorge Salvador Valdez-Martínez: Industrial Mechanics Academic Division, Universidad Tecnológica Emiliano Zapata del Estado de Morelos, Av. Universidad Tecnológica No. 1, Emiliano Zapata 62760, Morelos, Mexico
Miguel Ángel Hernández-Pérez: Instituto de Ingeniería, Universidad Veracruzana, Juan Pablo II s/n, Boca del Río 94294, Veracruz, Mexico
Karina Ruby Pérez-Daniel: Facultad de Ingeniería, Universidad Panamericana, Augusto Rodin No. 498, Insurgentes Mixcoac, Benito Juarez, Mexico City 03920, Mexico
Pedro Javier García-Ramírez: Instituto de Ingeniería, Universidad Veracruzana, Juan Pablo II s/n, Boca del Río 94294, Veracruz, Mexico

Mathematics, 2022, vol. 10, issue 12, 1-34

Abstract: The interaction of digital systems with dynamic systems requires synchrony and the accomplishment of time constrains, so the simulation of physical processes needs an implementation by means of real-time systems (RTS). However, as it can be expected, every simulation and/or implementation might demand too many computational resources, surpassing the capacity of the processor used by computational systems. This is the reason for the need to perform a temporary computational complexity analysis based on the study of the behavior of the execution times of the implemented simulation. In this regard, the Real-Time Operating Systems (RTOS) feature time managing tools, which allow their precise measurement and the establishment of scheduling criteria in process execution. Therefore, this research proposes accomplishing a temporary computational complexity analysis of the real-time simulation by an embedded system (ES) of an unmanned aerial vehicle (UAV) propelled by four rotors. Derived from this analysis, formal definitions are elaborated and proposed, which establish a close relationship between the temporary computational complexity and typical real-time temporary constraints. To the best of the author’s knowledge, the definitions presented in this article have not been reported in the literature. Furthermore, to perform the temporary computational complexity analysis of the UAV, the mathematical modeling based on the Euler–Lagrange approach is presented in detail. Finally, simulations were performed using a real-time system implemented on the Embedded Computer System (ECS) Raspberry Pi 2 Model B+, in order to validate the suggested definitions.

Keywords: real-time systems; temporary computational complexity; UAV modeling; real-time simulation; embedded computers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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