Hybrid fuzzybased slidingmode control approach, optimized by genetic algorithm for quadrotor unmanned aerial vehicles
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Abstract
According to the diverse applications of quadrotors in various military and space industries, this study attempts to focus on the modeling and simulation of a particular type of such robots, entitled unmanned aerial vehicles. The quadrotors are the vertical flying robots that contain four engines with impeller and it is possible to control this flyer with respect to the transitional force on these impellers. In fact, the quadrotors are the flyers with four propellers in a crisscross structure. These propellers allow the possibility of various movements to the quadrotors in such a way that control signals are applied to its operators and the difference in rotor speeds leads to the generation of different forces and movements. Such systems are dynamically unstable. Due to the nonlinear nature of quadrotor systems, modeling uncertainties and unmodeled dynamics in these systems, the need to design a suitable controller for optimal performance in different working conditions is strongly felt. In this paper, research on the modeling of unmanned flying robots in recent years is firstly reviewed and a mathematical model has been proposed for quadrotor robots with 6 degrees of freedom on the basis of the popular Newton–Euler equations. In the following, the capability of hybrid fuzzybased slidingmode control approach has been used to ensure the system stability. In addition, the genetic algorithm has been added to the control structure in order to optimize the proposed control system to meet the requirement of realizing fuzzybased control approach. The results of the simulations in Matlab software clearly demonstrate that the state variables of the quadrotor robot reach a certain situation and place at the right time, once the nominal inputs are considered.
Keywords
Unmanned aerial vehicles Quadrotor robot Newton/Euler equations Hybrid fuzzybased slidingmode control approachIntroduction
Nowadays, with regard to improvement in use of space capabilities, the process to design spatial robots regarding removal of human parameter keeps expanding, under which is expected that robotic systems play a major role in the future of space applications [1]. Therefore, the design of dynamic models from space robots has been increasingly drawn into attention [2, 3, 4].
Long time has passed from lifetime of fixedwing vehicles that such vehicles due to optimization of energy consumption have been widely drawn into attention, yet they have constantly suffered from the lack of power of maneuverability, at the affairs pertaining to unmanned vehicles. For instance, small air flasks can easily be controlled so far as there do not exist wind and turbulence. Under this state, natural lifting force causes moving aerial vehicle, yet causes decreasing its power of maneuverability. Helicopters have numerous advantages than fixedwing vehicles and balloons especially at control and the reason for this can be known in their ability in take off and land at small area of space as well as high power of maneuverability. In addition, static flight (hover) has been regarded as one of the capabilities of aerial vehicles, mentioned top of aims. On the other hand, these advantages lead to difficulty in control of helicopters for which different sensors as well as rapid processing boards are required. Unmanned aerial robots have been regarded as efficient and practical solutions to cope with this challenge in helicopters. Building unmanned aerial robots include synergic combination at different stages including design, selection of sensors and development of controllers. All the stages are fulfilled in an integrative and parallel way, so that, each one affects another one. To build autonomous unmanned aerial robots, high information on position and direction is required. Such information is provided through selfstabilizing sensors such as inertial navigation system (INS). Global positioning system (GPS) and/or sensors such as sound navigation and ranging (SONAR) [5]. With regard to increasing trend of research at the area of unmanned vehicles especially quadrotors, the present research will intend to examine, simulate and control aerial robots [6].
In recent years, aerial robots or unmanned aerial vehicles (UAVs) regarding removal of human operator have been drawn into attention as the aerial instruments with wide applications and capabilities [1]. With regard to high potential of aerial instruments for flying at points that the manned aerial vehicles fail to access them, investigation, analysis and control of such system have been transformed to an important issue. Nowadays, UAVs develop an important part of scientific studies pertaining to military industries. Unmanned aerial vehicles compared to the systems that are conducted by man’s intervention can have a high protective role in human’s life at hazardous environments.
Autonomous aerial vehicles have been witnessed with numerous commercial applications. Recent advancements at areas of energy storage with high density, integrated miniature operators. Microelectromechanical systems (MEMS), construction of miniature unmanned aerial robots has come to realize. This has opened the way towards complicated applications at military and nonmilitary markets. Currently, military applications propose the leading part of UAVs with huge increasing in industrial sector. With regard to growing increase of research at the area of UAVs especially quadrotor, the present research seeks to examine, simulate and control these UAVs [5].
Quadrotor has been mentioned as a useful tool for researchers at universities to engage in examining new ideas at different areas including flight control theory, guidance and navigation, realtime and robotic systems. In recent years, most of universities have conducted research on complex aerial maneuvers through quadrotors for which different controllers have been designed. Since quadrotors are so maneuverable, they can be beneficial under any environmental conditions quadrotors with the flight ability in an independent way can assist for removal of required manpower at hazardous situations, whereby this ability represents the main reason for increasing research on these systems in recent years [6].
With regard to significance of topic of this research, to date numerous activities have been conducted at the area of optimization of UAVs via nonlinear controllers, so that there are numerous ways to control an UAVs [4, 7, 8]. Use of fuzzy logic regarding capabilities of this method in controlling nonlinear systems is one way to control UAVs. For instance, in long lost past, a variety of research to improve membership functions in fuzzy controllers which had been used in UAVs have been conducted via genetic algorithm, that also this theory has been used to detect status of system, indicating such a theory as a suitable method to detect status of aerial robot. An adaptive neurofuzzy inference system to control position of an aerial robot at threedimensional space has been designed in reference [9], and a new idea which has integrated advantages of neural network method with advantages of fuzzy logic to control an aerial robot has been proposed in [10].
To date, numerous studies have been conducted at the area of control of quadrotor unmanned aerial robots. According to reference [11], slidingmode control approach has been used to regulate the force at quadrotor engines. This is in a way that a sliding surface entitled as the suitable return for force at four engines has been defined, aiming at sliding force to this sliding surface so far as the force at each of these engines removes from this return. These controllers due to sustainability of system at nonlinear models have been mentioned as a suitable item for control. Yet, the phenomenon of chattering has been found as a defect in these controllers for which no solution has been represented to cope with it.
In [12, 13], an output feedback adaptive fuzzy model following controller is proposed for a nonlinear and uncertain airplane model. The unknown nonlinear functions are approximated by fuzzy systems based on universal approximation theorem, where both the premise and the consequent parts of the fuzzy rules are tuned with adaptive schemes. Thus, prior knowledge and the number of fuzzy rules for designing fuzzy systems are decreased effectively. Also, to cope with fuzzy approximation error and external disturbances an adaptive discontinuous structure is used to make the controller more robust, as long as due to adaptive mechanism attenuates chattering effectively. All the adaptive gains are derived via Lyapunov approach thus asymptotic stability of the closedloop system is guaranteed.
Type2 fuzzy neural networks have a high ability to detect and control nonlinear systems and change systems over time as well as systems with uncertainties. In [14], the method of designing type2 fuzzy neural adaptive (inverse) controller has been studied in order to control online an example of a nonlinear dynamical system of flying robot. In this reference, the class structure of interval type2 fuzzy neural networks of TS model has been displayed first. It has seven layers that fuzzy operation is carried out by the first two layers, which contains type2 fuzzy nerves with uncertainty in the center of the Gaussian member functions. The third layer is the layer of rules and in the fourth layer, the operation of reducing degree is performed by matching nodes. Layers of fifth, sixth and seventh include the resulting layer, layers of calculating the center of gravity and layers of output, respectively. To teach network, decreasing gradient algorithm was used with adaptive training rate. Finally, in the section of the simulation of adaptive inverse online control with interval type2 fuzzy neural network of model TS and adaptive neurofuzzy inference system (ANFIS) for nonlinear dynamic system, a robot sample drone with certain parameters and with uncertain parameters were compared. The results of simulation show the effectiveness of the proposed method in this reference.
In [15], type2 fuzzy neural network with fuzzy clustering method is used to identify structures and update the parameters of the condition and the gradient algorithm is used to update the parameters of the result. Also in this reference, it has been indicated that the method of fuzzy clustering is not appropriate for identifying and online controlling. In recent years, various methods for training type2 fuzzy neural networks have been suggested, such as genetic algorithm [16] and PSO [17]. With the expansion of research in the field of type2 fuzzy systems, these systems have found wide applications, including the prediction of time series [18], linear motor control [19], slidingmode control [20] and control of robots [21].
For the first time Han et al. [22] have proposed an adaptive fuzzybased control of sliding mode, which estimates input and output parameters of member functions by means of matching rules that are extracted from a Lyapunov function. But in their approach, asymptotic stability is not guaranteed and it results in an error of permanent state. Recently, Lin and Hsu [23] designed a new method of controlling adaptive fuzzy sliding mode for controlling a servo motor in a manner that estimates the parameters of member functions of input and output by means of matching rules that are extracted from a Lyapunov function and they do not need to be specified by a designer. Furthermore, at the expense of having discontinuous control, they have asymptotic stability. But the method is only applicable to a particular motor system. Peng and Shi [24] presented a new and direct method of controlling adaptive fuzzy of sliding mode for a class of flying robots that estimates the parameters of member functions in input and output by means of matching rules that are extracted from a Lyapunov function. Therein a proportionalintegral adaptive controller is used to increase the consistency that ensures asymptotic stability.
In this investigation, with regard to an overview on the research in the area of modeling of the UAVs via Newton/Euler equation, a model has been proposed for quadrotor robot with 6 degrees of freedom. In following, the capability of fuzzybased slidingmode control approach, optimized by the genetic algorithm has been used to assure the sustainability of system.
This research has organized in line with five sections, while after introducing the key materials, in the second section, based on the equation of 6 degrees of freedom through Newton–Euler equation of rigid body, a nonlinear model for the drone robot of quadrotor UAV is extracted. It is to note that in the third section, the hybrid fuzzybased slidingmode control approach is realized to address the weaknesses of the structure of the traditional slidingmode control approach. In fact, there is the idea of combining it with the genetic algorithms and also fuzzybased approach to be newly proposed. Subsequently, in the fourth section, the results of the simulations regarding the hybrid fuzzybased slidingmode control approach, optimized by the abovereferenced genetic algorithm on UAV quadrotor model have been described and finally the last section is dedicated to conclusions.
The representation of a nonlinear dynamic model for quadrotor UAVs
Height and angle for setting robot in space are controlled through regulating speed of circulation at each of engines. Propellers at backward and forward rotate counterclockwise, yet the propellers at left and right sides rotate clockwise. This way for rotating blades meets the need to tail rotor. Four basic movements based on speed at rotation of engines are considered for a quadrotor. Movements roll, pitch, yaw and movement alongside axis z or height. To move alongside axis z, speed of four engines must be equal with each other, yet speed of the left engine is greater than the specified extent and speed of right engine is under the specified extent in movement roll, yet rest of engines have fixed speed, causing rotation around axis x, at movement pitch which rotates around axis y, the backward engine rotates with higher speed and the forward engine rotates with lower speed and rest of two engines rotate at fixed speed. Ultimately, at movement yaw, the left and right engines will rotate at lower speed and the backward and forward engines will rotate at higher speed at counterclockwise rotation by an angle \(\theta \) about the zaxis. At all basic movements, all the forces raised through engines must be equal to the force at first state which is movement alongside zaxis [26, 27].
 1.
x: Quadrotor’s movement in the direction of the axis x (surge);
 2.
y: Quadrotor’s movement in the direction of the axis y (sway);
 3.
z: Quadrotor’s movement in the direction of the axis z (heave);
 4.
\(\phi \): Quadrotor’s rotation around the axis x (roll), where \(\phi \in \left( {\frac{\pi }{2}\cdot \frac{\pi }{2}}\right) \);
 5.
\(\theta \): Quadrotor’s rotation around the axis y (pitch), where \(\theta \in \left( {\frac{\pi }{2}\cdot \frac{\pi }{2}}\right) \);
 6.
\(\Psi \): Quadrotor’s rotation around the axis z (yaw), where \(\Psi \in ({\pi \cdot \pi })\).

\(\Omega _1\) represents the impeller speed at the front part of the quadrotor;

\(\Omega _2 \) represents the impeller speed on left side of the quadrotor;

\(\Omega _3 \) represents the impeller speed at the back of the quadrotor;

\(\Omega _4 \) represents the impeller speed on left side of the quadrotor.

m: total mass of the quadrotor;

\(K_{i}\): constant coefficients of the drag;

g: gravity acceleration of the ground;

l: distance between the center of each rotor from the center of quadrotor mass;

\(I_{x},I_{y}\) and \(I_{z}\): the quadrotor’s moment of inertia;

\(J_{r}\): moment of inertia belonging to the impellers of each rotor;

b: the quadrotor’s ascending coefficient;

d: coefficient of drag for moment sampling.
Now, in this research, the first step is to model the behavior of the robot quadrotor and validate dynamic equations of the system for openloop. In Fig. 2, the response time of the state variables regarding the robot system without the presence of controller is shown.
The parameter’s values regarding the UAV model
Parameters  Value  Units 

m  2  kg 
\(I_{x} =I_{y}\)  1.25  \(\hbox {N}~\hbox {s}^{2}/\hbox {rad}\) 
\(I_{z}\)  2.2  \(\hbox {N}~\hbox {s}^{2}/\hbox {rad}\) 
\(K_1=K_2=K_3\)  0.01  \(\hbox {N}~\hbox {s}/\hbox {m}\) 
\(K_4 =K_5=K_6\)  0.012  \(\hbox {N}~\hbox {s}/\hbox {m}\) 
l  0.2  m 
\(J_{r}\)  1  \(\hbox {N}~\hbox {s}^{2}/\hbox {rad}\) 
b  2  \(\hbox {N}~\hbox {s}^{2}\) 
d  5  \(\hbox {N}~\hbox {m}~\hbox {s}^{2}\) 
g  9.8  \(\hbox {m}/\hbox {s}^{2}\) 
The hybrid fuzzybased slidingmode control approach realization
The parameter’s values regarding the realized slidingmode control
Parameters  Values  Parameters  Values 

\(\omega _1 \)  1  \(\omega _2 \)  3 
\(\xi _1 \)  1  \(\xi _2 \)  1 
\(m_1^{\prime } \)  5  \(m_2^{\prime } \)  5 
\(n_1^{\prime } \)  7  \(n_2^{\prime } \)  7 
\(m_1 \)  1  \(m_2 \)  1 
\(n_1 \)  3  \(n_2 \)  3 
\(\varepsilon _1 \)  10  \(\varepsilon _2 \)  10 
\(\eta _1 \)  \(L_1 /\left {s_2^{m_1 /n_1 } } \right +\delta _1 \)  \(\eta _2 \)  \(L_2 /\left {s_4^{m_2 /n_2 } } \right +\delta _2 \) 
\(c_1 \)  20  \(c_2 \)  22 
\(c_3 \)  8  \(\lambda \)  0.1 
\(\delta _1 \)  0.1  \(\delta _2 \)  0.1 
The results of applying the slidingmode control to the quadrotor UAV in Figs. 3, 4, 5, 6, 7 and 8 illustrate that the aforementioned slidingmode control designed in this research about subsystem (3) namely, the state variables z(t) and \(\psi (t)\) has acceptable performance, while regarding subsystem (4), namely, the state variables x(t), y(t), \(\phi (t)\) and \(\theta (t),\) it suffered a serious overshoot and had no optimal performance. Absence of sufficient flexibility in the nonlinear behavior can be considered as a major cause of inefficiency of slidingmode control in the stabilizing state variables of subsystem (4). In the following section, in order to deal with the weaknesses in the structure of the slidingmode controller, the idea of combining the controllers with intelligent algorithms will be implemented.
To implement the fuzzybased control approach, the fuzzy logic designer toolbox in Matlab software is directly used. Membership functions of the inputs and its output of the present control approach are shown in Figs. 10 and 11.
Despite the optimal impact of fuzzybased control on the performance of the slidingmode control approach, one of the weaknesses in the structure of the controller is lack of access to accurate information, in order to design the optimal system. Given that considering the model of quadrotor UAV, in this research, such information is not available; therefore, the designed fuzzybased slidingmode control approach is incomplete and its performance is not optimal. To deal with this problem, a lot of resources are analyzed, which led to the idea of adding the genetic algorithm optimization to the structure of hybrid fuzzybased slidingmode control approaches. The reason to choose the genetic algorithms is regarding their parallel nature of random search on the problem situation because each of the chromosomes randomly generated by this one is considered, as a new starting point to search for a part of the problem situation and search on all of them takes place, simultaneously. In addition, there is no limit on the search path and choosing random answers. In fact, the main purpose of implementing a genetic algorithm is to determine the rules of designing fuzzybased control approach in such a way that the control does not need information of the expert and be able to work, efficiently.
The results of the simulations
The designed parameters in the genetic algorithm
Parameters  Symbol  Value 

\(N_\mathrm{g}\)  Number of generations  125 
\(p_\mathrm{c}\)  Crossover probability  0.99 
\(N_\mathrm{c}\)  Number of crossover points  3 
\(p_\mathrm{m}\)  Mutation probability  0.01 
\(N_\mathrm{p}\)  Number of individuals in gen  30 
The best fuzzy rules obtained for the fuzzybased sliding mode control approach from the genetic algorithm
\(s_6/s_{6M}\)  \(s_5/s_{5M}\)  

NB  NS  ZE  PS  PB  
NB  NB  –  –  –  – 
NS  –  NS  NS  ZE  – 
ZE  –  NS  ZE  PS  – 
PS  –  ZE  –  PS  – 
PB  –  –  –  –  PB 
By applying the optimized results obtained from the genetic algorithm in the structure of designed fuzzybased slidingmode control approach, it is expected that improvements can be made in the objectives of the control system. To prove this claim, the results obtained in this study are compared with the results of research carried out in [30], where type2 fuzzybased control is realized to stabilize the robot of quadrotor, and are illustrated in terms of the state variables of six systems in Figs. 12, 13, 14, 15, 16 and 17.
Due to the limitations of the mechanical structure in modeled robot of quadrotor, the results obtained can be analyzed. The mission of the studied robot is that in a vertical axis it can be as high as 3 m from the ground and have a minor rotation around it (0.5 radians). According to Figs. 12, 13, 14, 15, 16 and 17, it can be argued that the designed control strategy in this article has been able to achieve these goals. Since the intended robot does not have the ability to move or rotate around the xaxis and yaxis, thus in order to prevent the diversion of robots from the required route and also for the realization of the desired control objectives, it is essential that other state variables of system converge to zero. The results indicate that these demands have been met when robot was flying. Importantly, the state variables of system are stabilized without the need for expert information for designing fuzzy control. Therefore, we can conclude that the proposed genetic algorithm in this article has implemented its task properly.
Comparing the results with respect to the potential benchmarks
Parameters  Reference  

Previous research  Current research  
Implemented control strategy  Fuzzytype 2 control  Fuzzybased SLIDINGMODE CONTROL control approach optimized by genetic algorithm 
Surface integral of control signal u1  68  79.5 
Surface integral of control signal u2  23  12.35 
Surface integral of control signal u3  38  31.875 
Surface integral of control signal u4  47  37 
Maximum overshoot or undershoot of state variables  125 m  60 m 
Highest settling time of state variables  Permanent oscillations  25 s 
To compare the results obtained in this study with previous potential similar benchmarks, the implemented control algorithm for fuzzytype 2 in the study [30] is investigated, in order to stabilize a drone robot of quadrotor. After the survey was conducted, the control parameters for both methods are extracted and compared with each other in Table 5. After integrating the absolute value of the output level for each controller in the designed method in this article and presented method in this study [30], the following results were achieved. As can be seen, the designed control strategy in this study could perform better both in reducing the amount of control efforts and in achieving of the control objectives.
Conclusion

ensuring the stability of nonlinear system of robot due to the use of slidingmode control;

ability to deal with the disturbance and uncertainty in the system due to the use of fuzzy control;

lack of need for expert information about the robot system so as to control design phase because of the use of genetic optimization algorithm.
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