Abstract

Tree branches near the electric power transmission lines are of great threat to the electricity supply. Nowadays, the tasks of clearing threatening tree branches are still mostly operated by hand and simple tools. Traditional structures of the multirotor aerial robot have the problem of fixed structure and limited performance, which affects the stability and efficiency of pruning operation. In this article, in order to obtain better environmental adaptability, an active deformable trees-pruning aerial robot is presented. The deformation of the aerial robot is implemented through two ways, arm telescopic and folding. In order to suppress the influence of internal and external disturbances on the system, Active Disturbance Rejection Control (ADRC) technology is adopted to build the flight controller. Firstly, active deformation aerial robot structure is given, followed by system dynamic model establishment under wind disturbance using the Newton–Euler method. Also, the analysis of the gusts influence on the system is considered. Then, the active deformation aerial robot system is decoupled into a combination of six SISO systems, so that a disturbance rejection controller is designed. Finally, the expanded state observer and the nonlinear state error feedback law are used to inspect and compensate the disturbance. Simulation results of attitude and position tracking as well as the antidisturbance capability show that the active deformation aerial robot with the ADRC flight controller designed in this paper has excellent attitude control capabilities during flight and trees-pruning operation.

1. Introduction

With the feature of complexity, intelligent systems have significant research values and huge application potential [1, 2]. In the giant and complex power grid, it has been always a tough issue that trees near the high-voltage transmission line channel often exceed the safe distance, causing the line to discharge through the trees to the ground, causing safety accidents such as power outages and fires, bringing huge inconvenience to social production and life. Therefore, the power sector consumes a lot of manpower and material resources every year for tree barrier cleaning. At present, most of its main methods use manpower, supplemented by simple tools such as hand saws. Not only is this kind of cleaning method limited in efficiency, but also human safety cannot be guaranteed. Casualties caused by such tasks in our country occur from time to time. Therefore, it is particularly necessary to develop and promote a set of efficient and safe tree barrier cleaning aerial robots that can replace manual cleaning methods.

The multirotor aerial robot that can take off and land vertically and hover in the air has the advantages of simple structure and good stability. The application research of using it as a work platform has attracted widespread attention [3–5].

However, the traditional structure of the multirotor aerial robot has the problem of fixed structure and limited performance, which affects the stability and efficiency of pruning operation.

In response to the above-mentioned problems of conventional multirotor aircraft, researchers have studied improving the controllability of the aircraft by optimizing the relative direction of the rotors or using tiltable rotors. Paper [6] puts forward a new type of rotor installation plan in which eight rotors are arranged in a cube structure in different directions through the analysis of the force and moment of ordinary motors. Paper [7] combines the advantages of conventional multirotor systems and omnidirectional control aircraft and proposes a new type of flying platform. Papers [8, 9] proposed a design scheme for a tiltable quadrotor and verified the effectiveness of the tiltable multirotor aircraft through simulation and actual flight experiments. Although these methods help achieve complex trajectories and operational tasks, they do not significantly change the shape of the multirotor aircraft frame.

On the contrary, only by directly changing the shape and structure of the multirotor aircraft during flight can this problem be effectively solved. Paper [10] focused on kinematics design and studied a new type of deformable quadrotor based on a scissor-like foldable structure, which can dynamically adjust the volume of the quadrotor to adapt to obstacles of various sizes and narrower space. Paper [11] proposed a deformable aircraft with four rotors connected in series, established its dynamic model, and designed an attitude LQI controller and a position PID controller to achieve the purpose of encircling the object and grasping it without additional gripping device. Paper [12] improved the diversity of aircraft deformation, divided the standard quadrotor structure into multiconnected platforms, and proposed a new control method that decoupled thrust control and rotor gimbal control and realized 3D folding. Paper [13] optimized the structure of the quadrotor and designed the automatic telescopic structure in the air and the manual folding structure after landing. The rational selection of materials and the strength check ensure the rationality of the airframe and can achieve the expected functions. Paper [14] designed a miniature deformable quadrotor, which achieved the purpose of deformation by using flexible materials to manufacture aircraft brackets and designing torsion spring and gear deformation mechanism. PID was selected as its flight control method.

The active deformation quadrotor is an aircraft that can actively change its shape during flight. Its shape changes have a strong influence on the mechanical properties, especially the expansion and folding of the arms, which not only directly change the position of the center of gravity and the inertia tensor of the aircraft but also change the mapping relationship between the lift generated by a single motor and the force and moment of the aircraft body [15]. This makes the active deformable quadrotor more uncertain and more coupled than the conventional quadrotor. In addition, the disturbance of the external environment during flight is inevitable, which makes the design of its controller more difficult. Researcher Han Jingqing inherited the essence of classic PID controllers and proposed Active Disturbance Rejection Control (ADRC) technology that requires low model accuracy and is easy to implement. ADRC has the advantages of fast control response speed and no overshoot, and transition process can be arranged. Also, the parameter adaptation range is large and has the ability to observe and compensate for disturbances inside and outside the system [16–18]. Because ADRC has obvious advantages in solving the control problems of nonlinear models with uncertainties and strong disturbances [19], researchers have tried ADRC on conventional quadrotor and verified the antidisturbance capability and robustness of the controller [20, 21]. Active Disturbance Rejection Control (ADRC) technology is a new type of control theory that does not require accurate modelling of the controlled object. A major feature of this theory is that it could effectively suppress the internal and external disturbances of the system, because it is able to estimate and compensate for the internal disturbances of the system and the unknown disturbances of the external environment in real time. During the operation of the tree barrier cleaning robot, the external force caused by the contact operation is a huge disturbance to the body, which brings about great challenges to the attitude stability control. In addition, ADRC has the characteristic of small amount of calculation, which makes it easy to realize real-time control of the robot's pose on the MCU (Microcontroller Unit).

With the purpose of pruning trees near the power transmission line, this paper proposes an active deformable aerial robot to improve environmental adaptability. The deformation forms are divided into arm telescopic and folding. In order to better suppress the internal and external disturbances of the system, this paper designs a flight control method based on Active Disturbance Rejection Control technology. First, the structural design is carried out, followed by the establishment of the dynamic model. Then analysis and calculation of the changes in the center of gravity and inertia matrix caused by the deformation are presented. Second, the system is decoupled and the attitude ADRC controller is designed. Then, the control distribution matrix form is given. Finally, through simulation, the deformation ability of the designed active deformation aerial robot and the effectiveness, anti-interference performance, and robustness of the ADRC controller are verified.

2. Structural Design of Active Deformation Aerial Robot

The active deformation aerial robot designed in this paper is mainly composed of the following four parts: (1) the centered fuselage, (2) the deformable arm, (3) the motor and the rotor, and (4) deformation of the arm to achieve the aerial robot deforming various steering gears. Assume that the deformable aerial robot is a rigid body, as shown in Figure 1. The earth fixed coordinate system is defined to be fixed to the ground, and the origin of the body coordinate system is fixed at the center of the robot fuselage. At the same time, the telescopic rudder of the active deformable active aerial robot is defined. The engine is installed at the midpoint of the arm, and the rotary servo is installed on the fuselage. For the convenience of writing, this article uses to represent the , . Define as the length of retractable arm. Define as the rotation angle of the arm around the axis of the machine system. When the arm rotates clockwise, is positive. Only is shown in Figure 1. The numbers of the arms and motors have been marked in the figure. Motors nos. 1 and 3 rotate counterclockwise, and motors nos. 2 and 4 rotate clockwise.

Figure 1 

Frames of actively deformable aerial robot.

The active deformation aerial robot has two deformation functions. (1) The arm is stretched and deformed by the telescopic steering gear; that is, the length of the arm is changed. (2) The arm is folded and deformed around the axis of the machine system by rotating the steering gear changing . Its four arms can be deformed individually or in combination. In the following of the paper, expansion and folding are used to represent these two kinds of deformation.

2.1. Kinematics and Dynamics

This article uses to represent the rotation matrix between coordinate systems, and represents the rotation matrix from the machine system to the earth’s fixed coordinate system (in the text, means , means , and means ):

The rigid body kinematics model of the actively deformed aerial robot iswhere and , respectively, represent the airframe position and triaxial velocity of the robot in the earth's fixed coordinate system, represents the Euler angle of the robot, and represents the triaxial angular velocity of the robot in the airframe coordinate system.

The force and moment changes caused by the deformation of the active deforming aerial robot are more complicated than the conventional aerial robots. The dynamic model of the active deforming aerial robot is analyzed and established below.

The fuselage is regarded as a mass point during the deformation process. As a six-degree-of-freedom rigid body, the dynamic model of the actively deformed aerial robot is obtained by Newton–Euler equations [22]. In this paper, the system translation equation is defined in the earth’s fixed coordinate system, and the rotation equation is defined in the body coordinate system:where represents the mass of the machine body and is the inertial matrix. Its value will change due to the deformation of the body, which will be analyzed in detail later.

The force analysis of the active deformation aerial robot system is carried out, and the following is obtained:where represents gravity. represents the lift generated by the rotor. represents the wind disturbance. represents the air resistance. is the lift coefficient of the rotor, and is the speed of the rotor.

Before analyzing the torque experienced by the active deformable aerial robot, the position of the center of mass and the inertia matrix are first analyzed. Compared with conventional quadrotors, the position of the center of mass and the inertia matrix of the actively deformed aerial robots will change due to the expansion and folding of the arms. Therefore, when the system is deformed, the position of the center of mass and the inertia matrix of the system need to be recalculated. The offset between the center of mass of the active deformed aerial robot and the origin of the system coordinates [23] is expressed as follows:where represents the mass of and represents the vector diameter from the origin of the machine system coordinates to . The meaning of each subscript English letter is shown in Table 1.

For the body inertia matrix of an actively deformed aerial robot, the parallel axis theorem can be used for calculation. Here are some assumptions: the fuselage containing the rotating steering gear is regarded as a rectangular parallelepiped with length and width of and height of . The cuboid length, width, and height are , , and , and the rotor and the motor are regarded as cylinders, in which the rotor radius is , the height is , the motor radius is , and the height is ; the telescopic steering gear is regarded as the cuboid with length, width, and height, respectively, of , , and . The calculation formula for the moment of inertia of each part [24] is as follows:where represents the inertia value of .

Considering that the motor, rotor, arm, and telescopic steering gear are actively deforming the aerial robot during folding and deformation, inertia must also be recalculated [25]. Since the inertia of the cylinder does not change when it is folded and deformed, this change can be ignored for the inertia of the motor and the rotor. Since the fuselage structure is fixedly connected to the fuselage coordinate system, the inertia of the fuselage does not need to be changed. Therefore, the rotation matrix is introduced to rerepresent them:

The rotation matrix is expressed as follows:

So, the inertia calculation formula can be expressed as

Analyzing the moment of the active deforming aerial robot, we getwhere is the torque generated by the lift of the rotor, is the rotation reaction torque of the rotor, is the system gyro effect item, and is the wind disturbance moment. Different from the conventional quadrotor, there is an additional gravitational moment .

The torque generated by the rotor thrust iswhere represents the coordinate vector of the lift application point of the rotor in the robot system. The expression is as follows:where is converted to angle system, namely, .

The antitorque expression is

The system gyro effect is mainly caused by the rotation of the body:

The expression of gravitational moment is

2.2. Wind Disturbance Modelling

The influence of the wind field environment on the multirotor aircraft is partly caused by the aerodynamic effect of the rotor and is also partly caused by the air resistance of the frame of the multirotor aircraft [26]. The active deformation aerial robot will inevitably be affected by the external wind field when it is flying, especially when it is deformed. So, wind gusts will have a certain impact on it. The wind disturbance model can calculate the forces and moments acting on the actively deformed aerial robot in a given wind field, so modelling and analysis of wind disturbance are essential [27].

The schematic diagram of the aerodynamic effect of the rotor under the action of the wind field is shown in Figure 2. In the figure, represents the wind speed, represents the induced speed, and represents the vector sum of the wind speed and the induced speed.

Figure 2 

Aerodynamics of rotor under wind gust.

According to the rotor slip flow theory [28], the calculation formula of induced speed is as follows:where represents the local air density and represents the radius of the rotor blade. When there is a wind field, the total aerodynamic force experienced by a single rotor [29] is

So, the wind disturbance force and wind disturbance moment of the rotor are as follows:

Thereby,

The air resistance calculation formula iswhere represents the coefficient of air resistance, represents the windward area, and represents the relative speed of the robot and the air; that is, . When calculating the windward area of a deformable robot, the robot is simplified as a cylinder, and the average windward area is taken as , where is the crosswind coefficient, is the height of the robot body, and is the average length of the arms, so

2.3. Control Distribution

Like the conventional quadrotor, the active deformation aerial robot system control force and moment are mainly the thrust and reaction torque generated by the rotor. Combining equations (4)–(24), and are used to represent the force and torque generated by the rotor. The dynamic model can be reexpressed:

The relationship between and and rotor speed is

Matrix is the control efficiency matrix. It can be seen that matrix is a time-varying matrix. The following verification matrix is singular only at the singular point , and the other matrices are all nonsingular.

Proof. Using the method of proof by contradiction and assuming that the square matrix is a singular matrix, its columns must not be full of rank. Because of only column 1 and column 3 or column 2 and column 4 are proportional. Let be the element in row and column for discussion:(1)Assuming that the sine and cosines of all angles are not 0, column 1 and column 3 are proportional. , so that is, , and derives which is further written as that is, which is also equivalent to At this time, only the situation where exists, but it is contrary to the assumption, so there is no solution.(2)Assuming that the sine and cosines of all angles are not 0, column 2 and column 4 are proportional: with the same principle, there is no solution.(3)Suppose that there are an angular sine and cosine of 0: when or , is or , and the empirical calculation is that only in the case of is matrix not full of rank, which is a singular matrix.Proof ends.
Since the deformation process of the actively deformed aerial robot in this paper does not involve the location of singular points, it can be considered that matrix is fully reversible. So, the form of control distribution is as follows:It can be seen from equations (25)–(28) that the active deformation aerial robot model has strong nonlinearity and coupling. The deformation causes the length and angle of the arm to change, which leads to the change of model parameters. Compared with the conventional aerial robot, the internal disturbance is greater. At the same time, external disturbances such as the wind field experienced by the actively deformed aerial robot cannot be ignored.

3. Design of Active Disturbance Rejection Flight Control Law

One of the significant features of Active Disturbance Rejection Control technology is that it has low dependence on the accuracy of the system modelling. It could estimate and dynamically compensate for the internal and external disturbances of the system as well, which contributes to the system's disturbance rejection and robustness ability. In this paper, Active Disturbance Rejection Control algorithms are implemented using the following three parts: tracking differentiator (TD), extended state observer (ESO), and nonlinear state error feedback (NLSEF).

3.1. Preliminary of the ARDC Law Design

There is a coupling between the position and attitude of the actively deformed aerial robot studied in this paper, which is an underactuated system. Only six-degree-of-freedom motion can be achieved in the incomplete sense, and the roll and pitch angles need to be changed while doing horizontal motion [30]. ADRC provides a more convenient way for the decoupling control of the multivariable coupling system, in which 6 states in the dynamic model of the active deformation aerial robot system are regarded as 6 channels, and ADRC can cause the coupling and deformation between the channels of the system. The parameter perturbation is treated as internal disturbance, and ESO is used to estimate and compensate for the internal and external disturbances of the system to realize the decoupling of the state of each channel. The virtual control quantity is introduced to realize the decoupling of system control, thereby converting the system description form from MIMO to six SISO systems combination. Therefore, the system's six-degree-of-freedom dynamic model equation (25) is rewritten in the following form:where is the uncertainty item and and are the disturbances caused by the external disturbance and deformation of the system, respectively. is an adjustable parameter with a size near . is an adjustable parameter with a size near , and is the introduced virtual control quantity.

Based on this, the control law adopts an inner and outer loop strategy, where the inner loop is attitude control and the outer loop is position control. The introduction of the control quantity , respectively, represents the expected value of the total lift and the expected value of the torque around the three axes of the machine system. The actual position value and the position expected value are used as the input of the outer loop position ADRC control law, and the expected values of roll and pitch angles and are output. The actual attitude value and the expected attitude value are input to the ADRC control law of the inner loop attitude. The output is . Finally, obtains the desired motor speed through control distribution, where the conversion relations between the virtual control variables and are

3.2. Design of Attitude Active Disturbance Rejection Control Law

Take the pitch angle channel as an example to illustrate the design process of the attitude ADRC control law:(1)Design a tracking differentiator (TD) to arrange the transition process with the given signal as a reference input: where is the transition value of TD from the initial value to . is the derivative value of , and the parameters are the fast factor and the filter factor, respectively.(2)Design an extended state observer (ESO) to use the system output and control input to observe the system state and disturbances in real time: where tracks . estimates the total disturbance , and is a set of adjustable parameters.(3)Design the nonlinear state error feedback (NLSEF) law, calculate , and combine it with disturbance compensation to calculate the control variable :

The parameter is an adjustable parameter.

The expressions of the fastest tracking control integrated function and nonlinear function are as follows:where . The design of the and channel control law is similar to that of the channel and will not be described in detail here.