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

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.

Comprehensive Investigation of Unmanned Aerial Vehicles (UAVs): An In-Depth Analysis of Avionics Systems

“…For an object tracking-based UAV mission, when the Patch Color Group Feature (PCGF) framework was embedded on a Raspberry Pi 4, it resulted in 17 FPS offering a good execution speed with low PCGF computational complexities [200]. Older Raspberry Pi models, such as Raspberry Pi 2 B+, are effective in illustrating the relationship between time constraints of real-time systems and the analysis of temporary computational complexity [201], hence better managing failure possibilities in real-time processes. Figure 4 shows how Raspberry Pi 4 can flexibly make decisions concerning a UAV's flight by dynamically adapting to different communication protocols with only a few subsystems (e.g., sensors).…”

Fractional-Order Sliding Mode Observer for Actuator Fault Estimation in a Quadrotor UAV

“…The dynamics of the QUAV have been explored in existing literature. As outlined in [51], when considering small angular velocities, the dynamics of the QUAV can be expressed as follows:…”

An Adaptation of a Sliding Mode Classical Observer to a Fractional-Order Observer for Disturbance Reconstruction of a UAV Model: A Riemann–Liouville Fractional Calculus Approach

“…The movements described above must be controlled simultaneously in order for the quadrotor to follow the particular trajectories assigned via a flight plan. The non-linear dynamic model of the UAV is taken from [36], where it is presented in detail, and it is specified that the dynamics of the UAV are defined by combining translational and rotational dynamics, resulting in the following mathematical model:…”

“…with l representing the length of the arms of the UAV, g the acceleration due to gravity, u the thrust that defines the input to the translational dynamics, and the torques τ θ , τ φ and τ ψ representing the inputs to the rotational dynamics [36]. Finally, the forces f i generated by each one of the rotors incorporated into the quadrotor are defined as:…”

“…The linear model given in expression (8) has been discretized using the z-transform with a sampling period of 25 ms. This sampling period was chosen based on the technical specifications of synchronous communication operations of commercial sensors and the experiments reported in [36], where a real-time simulation of a quadrotor is discussed. Thus, the equivalent discrete-time domain linear model is defined as (9).…”