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Abstract

In this paper, a frequency-domain modeling methodology that can be applied to various multi-rotor aerial vehicles is introduced. The primary contribution of this work is a systematic integration of the first-principles modeling and system identification approaches to generate flight dynamics models with good accuracy. The first-principles modeling and model linearization are conducted to obtain an appropriate baseline model for the subsequent system identification. Next, a four-step parameter identification process, which consists of: (1) baseline model determination; (2) data collection and preprocessing; (3) mode-wise parameter identification; and (4) model fidelity validation, is performed in the frequency domain to identify the uncertain parameters. Our method has been applied to two custom-built multi-rotor aircraft (one X-type quadcopter and one QU4D quadcopter) for efficiency demonstration.

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... In this sense, a new control allocation method was proposed to consider aerodynamic effects, most notably those regarding blade flapping and inflow effects as described in [10], based on a function fitting neural network to replace the classic mixing matrix. This method allows us to improve the controller performance without the need for directly using aerodynamic effects equations in the control algorithm or the allocation problem. ...
... As aforementioned, rotor flapping causes the rotor plane to tilt and hence the thrust force will also be tilted and will have a horizontal component. The total thrust that appears in (4) results from the sum of the thrusts produced by each of the four propellers [10] ...
... where is called the thrust coefficient, and are detailed in Table II, as described by Riether [10]. ...
Article
This paper shows that the aerodynamic effects can be compensated in a quadrotor system by means of a control allocation approach using neural networks. Thus, the system performance can be improved by replacing the classic allocation matrix, without using the aerodynamic inflow equations directly. The network training is performed offline, which requires low computational power. The target system is a Parrot MAMBO drone whose flight control is composed of PD-PID controllers followed by the proposed neural network control allocation algorithm. Such a quadrotor is particularly susceptible to the aerodynamics effects of interest to this work, because of its small size. We compared the mechanical torques commanded by the flight controller, i.e., the control input, to those actually generated by the actuators and established at the aircraft. It was observed that the proposed neural network was able to closely match them, while the classic allocation matrix could not achieve that. The allocation error was also determined in both cases. Furthermore, the closed-loop performance also improved with the use of the proposed neural network control allocation, as well as the quality of the thrust and torque signals, in which we perceived a much less noisy behavior.
... Flight test data collection is an important phase to be accomplished before any application on the real-time system identification. During the experiment, manual frequency sweep signals with quasi-sinusoidal are injected to quadcopter as pilot input (Adiprawita et al., 2007;Cai et al., 2016;Sakulthong et al., 2018). The test pilot will manually excite the frequency sweep as an input signal to the quadcopter. ...
... Then, the pilot will reduce the sweep signal until the quadcopter enters the trim state. At one time, the pilot typically issued the frequency sweep into one input channel only, while another input channels will have uncorrelated and minimum signals to retain the quadcopter in hovering flight (Alexis et al., 2016;Cai et al., 2016). Normalise pilot control input and state output response were collected at 50 Hz sampling rate with noises cut off frequency at 10 Hz. ...
Article
Full-text available
In this paper, we present the performance analysis of a fully tuned neural network trained with the extended minimal resource allocating network (EMRAN) algorithm for real-time identification of a quadcopter. Radial basis function network (RBF) based on system identification can be utilised as an alternative technique for quadcopter modelling. To prevent the neurons and network parameters selection dilemma during trial and error approach, RBF with EMRAN training algorithm is proposed. This automatic tuning algorithm will implement the network growing and pruning method to add or eliminate neurons in the RBF. The EMRAN's performance is compared with the minimal resource allocating network (MRAN) training for 1000 input-output pair untrained attitude data. The findings show that the EMRAN method generates a faster mean training time of roughly 4.16 ms for neuron size of up to 88 units compared to MRAN at 5.89 ms with a slight reduction in prediction accuracy.
... Flight test data collection is an important phase to be accomplished before any application on the real-time system identification. During the experiment, manual frequency sweep signals with quasi-sinusoidal are injected to quadcopter as pilot input (Adiprawita et al., 2007;Cai et al., 2016;Sakulthong et al., 2018). The test pilot will manually excite the frequency sweep as an input signal to the quadcopter. ...
... Then, the pilot will reduce the sweep signal until the quadcopter enters the trim state. At one time, the pilot typically issued the frequency sweep into one input channel only, while another input channels will have uncorrelated and minimum signals to retain the quadcopter in hovering flight (Alexis et al., 2016;Cai et al., 2016). Normalise pilot control input and state output response were collected at 50 Hz sampling rate with noises cut off frequency at 10 Hz. ...
Article
Full-text available
In this paper, we present the performance analysis of a fully tuned neural network trained with the extended minimal resource allocating network (EMRAN) algorithm for real-time identification of a quadcopter. Radial basis function network (RBF) based on system identification can be utilised as an alternative technique for quadcopter modelling. To prevent the neurons and network parameters selection dilemma during trial and error approach, RBF with EMRAN training algorithm is proposed. This automatic tuning algorithm will implement the network growing and pruning method to add or eliminate neurons in the RBF. The EMRAN’sperformance is compared with the minimal resource allocating network (MRAN) training for 1000 input-output pair untrained attitude data. The findings show that the EMRAN method generates a faster mean training time of roughly 4.16 ms for neuron size of up to 88 units compared to MRAN at 5.89 ms with a slight reduction in prediction accuracy.
... There is a large volume of published studies [13], [16], [37] on system identification based on the frequency domain. Most of the aforementioned researchers used Comprehensive Identification from Frequency Responses (CIFER) software as an identification tool to implement frequency domain identification. ...
... Frequency domain result could be inaccurate and inconsistent because of the insufficient data in very low bandwidth frequency and the removal effect of some dynamic components. Even with the satisfactory identification results from the frequency domain, G. Cai et al. [16] suggested that more focus is needed in data collection and model architecture reconstruction in order to improve the model accuracy further. A complete comparison between frequency and timedomain system identification can be referred to in [20]. ...
Article
Full-text available
A quadcopter is a rotorcraft with a simple mechanical construction. It has the same hovering capability similar to the traditional helicopter, but it is easier to maintain. The quadcopter is hard to control due to its unstable system with highly coupled and non-linear dynamics. In order to design a robust control algorithm, it is crucial to obtain a precise quadrotor flight dynamics through system identification approach. System identification is a method of finding the mathematical model of the dynamics system using the input-output data measurement. Neural network (NN) based system identification is excellent alternative modeling because it reduces development costs and time by avoiding governing equations and large aerodynamic database. NN based system identification has successfully identified the quadcopter dynamics with good accuracy. This paper gives an overview of the characteristic of the quadcopter and presents a comprehensive survey of the modeling techniques used to determine the flight dynamics of a quadrotor with a particular focus on NN based system identification method. The presented research works have been classified into different categories such as the first principle modeling, system identification and implementation of NN based system identification in quadcopter platform. Finally, the paper highlights challenges that need to be addressed in developing efficient NN based system identification model for unmanned quadcopter system.
... There is a large volume of published studies [13], [16], [37] on system identification based on the frequency domain. Most of the aforementioned researchers used Comprehensive Identification from Frequency Responses (CIFER) software as an identification tool to implement frequency domain identification. ...
... Frequency domain result could be inaccurate and inconsistent because of the insufficient data in very low bandwidth frequency and the removal effect of some dynamic components. Even with the satisfactory identification results from the frequency domain, G. Cai et al. [16] suggested that more focus is needed in data collection and model architecture reconstruction in order to improve the model accuracy further. A complete comparison between frequency and timedomain system identification can be referred to in [20]. ...
Article
Full-text available
A quadcopter is a rotorcraft with simple mechanical construction. It has the same hovering capability, similar to the traditional helicopter, but it is easier to maintain. The quadcopter is very difficult to control due to its unstable system with highly coupled and non-linear dynamics. To design robust control algorithms, it is crucial to obtain precise quadrotor flight dynamics through system identification, which is a new method of finding the mathematical model of the dynamics system using the input-output data measurement. Neural network (NN) based system identification is excellent alternative modeling because it reduces development costs and time by avoiding governing equations and large aerodynamic database. NN based system identification has successfully identified the quadcopter dynamics with good accuracy. This paper gives an overview of the characteristic of the quadcopter, the first principle modeling, system identification of quadcopter, and implementation of NN based system identification in quadcopter platform.
... Due to the inherent strongly coupled and nonlinear dynamics of the models, complex control techniques are utilized or linearization and certain assumptions are used to obtain the model linear counterparts prior to designing the controllers [4][5][6]. Although firstprinciple models provide physical insight into the dynamics of quadcopters, they lack appropriate evaluation of their prediction accuracy [7]. As an alternative to models derived from first principles, system identification provides powerful algorithms to obtain quadcopter dynamic models [8,9]. ...
Article
Full-text available
This paper presents a method to precisely model a four rotor unmanned aerial vehicle, widely known as quadcopter autopilot system. Common system identification methods limit quadcopter models into first or second order systems, and do not count for noise characteristics. This leads to poor prediction accuracy of its longitudinal and lateral motion dynamics that ultimately affects the aircraft stabilization during flight and landing. To improve the quality of the estimated models, we utilized a statistically suitable discrete-time linear Box–Jenkins structure to model the plant and noise characteristics of the horizontal subsystems of a quadcopter autopilot system. The models were estimated using flight data acquired when the system were provided with pseudo-random binary sequence input. In this proposed method, by employing the prediction error method and least squares approach, the aircraft dynamics could be modeled up until the fifth order. The normalized root mean square fitness value showed that the predicted model output matches the experimental flight data by 94.72% in the one-step-ahead prediction test, and 84.52% in the infinite-step-ahead prediction test. These prediction results demonstrated an improvement of 52.8% when compared with a first and second order model structures proposed in previous works for the same quadcopter model. The output from this research works confirmed the effectiveness of the proposed method to adequately capture the autopilot dynamics and accurately predict the quadcopter outputs. These would greatly assist in designing robust flight controllers for the autopilot system.
... Reference [11] argues to provide a generic model but limits the multirotor architecture to "+" or "×" configurations. On [12] a more generalized model is presented. It even includes blade-flapping effects, but fails to address attitude planning and control allocation. ...
Conference Paper
This paper presents an architecture-independent framework for multirotor simulation based on a dynamic model for non-reversible rotors, a quaternion-based attitude planning, and null-space-based control allocation algorithm. This approach can be of use when investigating different multirotor architectures' characteristics and control algorithms for them, avoiding spending effort on attitude planning and control allocation for each different case. The framework is compared to current solutions by pointing out the advantages of the approach used here. Simulation results of three different architectures are presented aiming to explore the algorithm's robustness, without change, to arbitrary and non-symmetric rotor positions; under, fully or over-actuated architectures; and differently-sized rotors.
... The friction between the quadrotor body and the bench setup, and 15 the restricted quadrotor movement alter attitude dynamics and hence affect the identification results. Comprehensive Identification from FrEquency Responses (CIFER) were used by a few groups to identify quadrotor attitude dynamics in-flight [6,7,8,9]. In all cases, the proposed system identification methods requires a lot of time, expertise, and are computationally extensive which makes 20 them impractical for online identification. ...
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Designing high performance controllers for multirotors is a rigorous task that is often solved by trial and error approach. Trial and error tuning usually results in non-optimal controller parameters. Tuning controllers based on the existing quadrotor models would result in poor performance of quadrotors due to simplifications and inaccuracies in the underlying models. In this paper optimal tuning rules for quadrotor attitude dynamics are designed, which guarantees near-optimal performance and robustness. A single in-flight run of the Modified Relay Feedback Test that takes only few seconds with guaranteed stability is enough to have near-optimal tuning of the controller. The designed tuning rule is tested experimentally in-flight on a custom-built quadrotor. The results showed significant advantages in performance and robustness due to the proposed approach.
... It determines the accuracy of the dynamic model. In the previous studies for multirotor UAVs, the input variables of the filter are usually chosen as the control inputs, 24,25 while the output variables are chosen as the angular rates, accelerations, and so on. However, the dynamic model established by the above input-output variables cannot directly reflect the characteristics of the forces and moments. ...
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Chapter
Development of a reliable high-performance quadcopter requires an accurate and practical model of the vehicle dynamics. Generally, the key physical parameters of an object with six degrees of freedom (6-DOF) are mass and moments of inertia, where mass is easily obtainable while it is difficult to identify moments of inertia considering that it is not always measurable by static tests. In this paper, a precise and fast system identification technique in the frequency domain is proposed, which is directly applicable to the control system design. This technique has been experimentally implemented to two quadcopters. Transfer functions are extracted, and the moments of inertia are identified. The process has been firstly applied in a captive form to a quadcopter attached to the three degrees of freedom laboratory test stand. In addition, the tests are repeated for F450 quadcopter and the extracted dynamic models are verified. Moreover, delays of the rotors are also identified.
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This project presents the performance analysis of the radial basis function neural network (RBF) trained with Minimal Resource Allocating Network (MRAN) algorithm for real-time identification of quadcopter. MRAN's performance is compared with the RBF with Constant Trace algorithm for 2500 input-output pair data sampling. MRAN utilizes adding and pruning hidden neuron strategy to obtain optimum RBF structure, increase prediction accuracy and reduce training time. The results indicate that MRAN algorithm produces fast training time and more accurate prediction compared with standard RBF. The model proposed in this paper is capable of identifying and modelling a nonlinear representation of the quadcopter flight dynamics.
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In this paper, we consider the problem of controlling multiple quadrotor robots that cooperatively grasp and transport a payload in three dimensions. We model the quadro-tors both individually and as a group rigidly attached to a payload. We propose individ-ual robot control laws defined with respect to the payload that stabilize the payload along three-dimensional trajectories. We detail the design of a gripping mechanism attached to each quadrotor that permits autonomous grasping of the payload. An experimental study with teams of quadrotors cooperatively grasping, stabilizing, and transporting payloads along de-sired three-dimensional trajectories is presented with performance analysis over many trials for different payload configurations.
  • Sadeghzadeh I
Payload drop application using an unmanned quadrotor helicopter based on gain-scheduled PID and model predictive control
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