Four-rotor unmanned aerial vehicle robust formation control method under communication topological structure constraint condition

Abstract

The invention discloses a quadrotor unmanned aerial vehicle robust formation control method under a communication topological structure constraint condition, is applied to the technical field of quadrotor automatic control, and aims to solve the problems that existing unmanned aerial vehicle cluster control mainly faces obstacle avoidance, collision avoidance and the like of an unmanned aerial vehicle cluster. The problem that the communication topological structure constraint between four-rotor unmanned aerial vehicles in a cluster and the overall robustness problem of a cluster system are not effectively analyzed and solved is solved; according to the quadrotor unmanned aerial vehicle robust formation control method under the communication constraint condition based on a guidance + control mode, the trajectory of the quadrotor unmanned aerial vehicle formation is controlled by quantitatively selecting controller parameters, and therefore the purpose of overall stability of the system is achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of quad-rotor automatic control, and in particular relates to a quad-rotor unmanned aerial vehicle robust formation control technology. Background Art

[0002] In recent years, with the continuous development of the field of quad-rotor drones, drone swarm technology is not only limited to the military field, but also shows great potential and diverse application scenarios in the civilian field. However, the communication between consumer-grade quad-rotor drone clusters is limited to less than 1 km in complex outdoor environments, which has brought certain obstacles to the quad-rotor drone clusters to perform regional coverage operations such as environmental monitoring, agricultural spraying, disaster relief, and logistics distribution. In addition, the complex external interference in outdoor operations also brings certain challenges to the stable control of the quad-rotor drones themselves. The existing drone cluster control mainly faces problems such as obstacle avoidance and collision avoidance of drone clusters. The communication topology constraints between quad-rotor drones within the cluster and the overall robustness of the cluster system have not been effectively analyzed and solved.

[0003] Therefore, it is necessary to complete the target task based on the existing communication conditions and control saturation constraints and achieve the goal of robust control of high-precision trajectory tracking of the cluster system. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a robust formation control method for quadrotor UAVs under communication topology constraints, and provides a robust formation control method for quadrotor UAVs under communication constraints based on the "guidance + control" mode. The trajectory of the quadrotor UAV formation is controlled by quantitatively selecting controller parameters, thereby achieving the purpose of overall system stability.

[0005] The technical solution adopted by the present invention is: a robust formation control method for quad-rotor drones under communication topology constraints, wherein the drone cluster includes multiple quad-rotor drones, and the multiple quad-rotor drones are formed in a unidirectional series, wherein the first quad-rotor drone obtains a reference signal, and the remaining quad-rotor drones unidirectionally obtain the status information and control information of the previous quad-rotor drone;

[0006] The reference signal is the status information and control signal of the virtual 0th quadrotor drone;

[0007] Each quad-rotor unmanned aerial vehicle includes a guidance module, a control gain module and an interference observer; the state information and control signal obtained by each quad-rotor unmanned aerial vehicle are input into the guidance module, the state information obtained by the unmanned aerial vehicle is outputted by the guidance module minus its own current state information to obtain a first result, the first result is added to the control signal obtained by the unmanned aerial vehicle after passing through the guidance module after passing through the gain module to obtain a second result; the second result is input into the interference observer; the input of the interference observer also includes the current state information of the quad-rotor unmanned aerial vehicle; the second result is minus the output of the interference observer to obtain a control signal for controlling the quad-rotor unmanned aerial vehicle.

[0008] Beneficial effects of the invention: The robust control method for a quad-rotor drone under communication constraints of the invention also has the following beneficial effects:

[0009] (1) By separating the guidance loop and the control loop, the control design is carried out in the "guidance + control" mode. The controller is simple, easy to use and conducive to stability analysis.

[0010] (2) For situations where communication is not ideal, an effective control design is given under the simplest communication topology, which can serve as the minimum guarantee in practical applications;

[0011] (3) By adding the uncertainty and disturbance estimator UDE to the controller, the overall robustness of the system is improved, and the quadcopter has a stronger ability to resist wind disturbances in actual outdoor flights;

[0012] (4) The present invention defines performance indicators, adopts singular perturbation theory to analyze the controller, and combines the stability analysis and robustness performance analysis of the controller into one according to the characteristics of singular perturbation theory. The analysis process is clear and organized, avoiding excessive cumbersome processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a communication topology diagram of a cluster formation of four-rotor drones of the present invention;

[0014] Figure 2 This is the data processing flow of the quad-rotor drone in the present invention;

[0015] Figure 3 The effect diagram of the simulation of the present invention. DETAILED DESCRIPTION

[0016] To facilitate those skilled in the art to understand the technical content of the present invention, the present invention is further explained below with reference to the accompanying drawings.

[0017] Example

[0018] like Figure 2The flowchart of the robust formation control method of a quad-rotor UAV under communication constraints based on the "guidance + control" mode of the present invention is shown. The design of the "guidance module" in the figure corresponds to step S3 below, and the design of the "interference observer" corresponds to step S4.2 below. In this embodiment, four quad-rotor UAVs are taken as an example to illustrate the content of the present invention. The specific implementation process includes the following steps:

[0019] S1. Establish the second-order subsystem of the quadrotor drone;

[0020] Define x i ,y i 、z i is the position of the i-th quadrotor drone, φ i ,θ i , i are the roll angle, pitch angle and yaw angle of the i-th quadrotor drone, respectively. The second-order subsystem of the quadrotor drone can be established as:

[0021]

[0022] where ξ i =[ψ i ,x i ,y i ,z i ] T , η i =[φ i ,θ i ] T represents the state vector, Represents ξ i and η i The second-order derivative of represents the virtual input vector, f i ξ =[f i ψ ,f i x ,f i y ,f i z ] T 、f i η =[f i φ ,f i θ ] T represents the aggregate interference vector;

[0023] S2. Establishing a formation communication topology diagram;

[0024] The communication topology of a quadrotor UAV formation is shown in the figure below. Figure 1As shown, only the first quadrotor drone can obtain the reference signal (i.e., the status information of the virtual 0th quadrotor drone), and the remaining i-th quadrotor drones can only obtain the status information of the i-1th quadrotor drone through communication, and all of them are one-way communications;

[0025] S3, design guidance rate;

[0026] Based on the above formation communication topology diagram, combined with the internal structure and control mechanism of the quadrotor drone, the formation control is realized in the ξ∈{ψ,x,y,z} channel; on the η∈{φ,θ} channel, each quadrotor drone is controlled separately;

[0027] The global reference for defining a quadrotor formation is:

[0028]

[0029] Among them, ξ0, and They represent the state of the virtual 0th quadrotor drone ξ∈{ψ,x,y,z} channel and the first and second order derivatives of its state, ξ d , represents the global reference state of the quadrotor formation ξ∈{ψ,x,y,z} channel and its derivative, represents the global expected input of the quadrotor UAV formation;

[0030] Then the formation reference that each quadrotor drone can obtain can be expressed as:

[0031]

[0032] Among them, ξ i-1 , represents the state of the i-1th quadrotor drone in the ξ∈{ψ,x,y,z} channel and its derivative, represents the input for controlling trajectory tracking of the i-1th quadrotor drone designed in step S4.1. For the first quadrotor drone, and Respectively represent the local reference of the i-th quadrotor UAV in the ξ∈{ψ,x,y,z} channel and the first and second order derivatives of the local reference under the communication topology constraint; △ i Represents the formation interval between the i-th quadrotor drone and the i-1-th quadrotor drone, when the interval between the quadrotors in the y direction is selected so as not to affect communication When i Can be designed as:

[0033]

[0034] Then△ i The first and second order derivatives of can be designed as:

[0035]

[0036] and:

[0037]

[0038] in, express The first and second order derivatives of ;

[0039] For the η∈{φ,θ} channel, the reference of each quadrotor drone is:

[0040]

[0041] in, represents the second-order derivative of the global reference of the quadrotor drone in the η∈{φ,θ} channel, Indicates the expected input of the quadrotor drone in this channel;

[0042] S4, establish a controller;

[0043] S4.1. Design a robust controller;

[0044] For the ξ∈{ψ,x,y,z} and η∈{φ,θ} channels of the quadrotor drone, the robust controller can be designed as:

[0045]

[0046] in, and represents the trajectory tracking input, and It is the uncertainty and disturbance estimator UDE (Uncertainty and Disturbance Estimator) designed in step S4.2;

[0047] The trajectory tracking error of the system is defined as:

[0048]

[0049] but and Can be designed as:

[0050]

[0051] in, and is the feedforward term, driving the system to move in the desired manner; and is the feedback term used to eliminate trajectory tracking error; are feedback gains;

[0052] S4.2, design uncertainty and disturbance estimator UDE;

[0053] For the ξ∈{ψ,x,y,z} channel of a quadrotor drone, The design in the frequency domain must meet the following requirements:

[0054]

[0055] Where s represents a complex variable and capital letters are used to represent the Laplace transform form of the corresponding signal (for example: yes The Laplace transform form of yes Laplace transform form of ); represents the transfer function matrix representing the degrees of freedom of the UDE, represent the designable transfer functions of the quadrotor drone in the ψ, x, y and z channels respectively, and is strictly regular and stable;

[0056] Substitute formula (8) into formula (11) and assume that the initial condition is zero, that is, ξ i (0) = 0, we can get:

[0057]

[0058] Further solving from formula (12) get:

[0059]

[0060] Where I is the unit matrix of compatible size; to ensure The physical feasibility of , we choose:

[0061]

[0062] Among them, T i ξ >0,ξ∈{ψ,x,y,z} represents the estimated bandwidth of UDE; Substituting formula (14) into formula (13) yields:

[0063]

[0064] Gain matrix Ti ξ satisfy:

[0065]

[0066] Where T i ψ , T i x , T i y , T i z are all positive numbers, representing the UDE parameters of the corresponding channels; the time domain form of formula (15) can be expressed as:

[0067]

[0068] Where t represents the time variable;

[0069] Since it can be seen from formula (8) that the controller form of the η∈{φ,θ} channel of the quadrotor drone is the same as that of the ξ∈{ψ,x,y,z} channel, the UDE design method of its channel is the same as that of the ξ∈{ψ,x,y,z} channel, and it is only necessary to replace ξ in each formula in step S4 with η; in order to save space, the present invention omits the reasoning process of the UDE design of the η∈{φ,θ} channel;

[0070] S5. Analyze the stability and robustness of the controller;

[0071] The present invention adopts singular perturbation theory to analyze the performance and stability of the controller. The specific method of analysis will be given in step S5. Since the controller stability and performance analysis methods of the ξ∈{ψ,x,y,z} channel and the η∈{φ,θ} channel of the quadrotor drone are the same, the controller stability and performance analysis of the η∈{φ,θ} channel is omitted in the present invention to avoid tediousness.

[0072] S5.1, parameter mapping;

[0073] To simplify parameter adjustment and facilitate subsequent analysis, the present invention provides the following parameter mapping:

[0074] T i ξ =εT i ξ* ,ξ∈{ψ,x,y,z} (18);

[0075] Where T i ξ* represents a positive constant, ε represents T i ξ With T i ξ* The mapping relationship between them;

[0076] S5.1. Construct the standard form of singular perturbation theory;

[0077] The estimated error of UDE is defined as:

[0078]

[0079] in, represents the estimation error of UDE;

[0080] Combining formula (11), formula (14) and formula (19), we can get the frequency domain representation of the UDE estimation error:

[0081]

[0082] Rewriting formula (20) into the time domain and combining it with the parameter mapping of formula (18), we can obtain:

[0083]

[0084] in, express The first derivative of ;

[0085] When the feedback gains of all quadrotor drones are exactly the same, that is:

[0086]

[0087] The tracking error equation can be expressed as:

[0088]

[0089] Formula (21) and formula (23) can constitute the standard form of singular perturbation theory;

[0090] S5.2. Define performance indicators;

[0091] The robustness index is defined as:

[0092]

[0093] in Represents the tracking error, the upper bound of the error It is a function that increases monotonically with the increase of ε and is always positive;

[0094] S5.3. Controller parameter selection and stability analysis

[0095] The singular perturbation theory is used to analyze the stability and performance of the controller. First, the condition of ε = 0 is substituted into formula (21), and we can get Quasi-steady-state model:

[0096]

[0097] for Quasi-steady-state model of

[0098] Then, substituting the quasi-steady-state model into formula (23) and applying the condition of ε = 0, the following simplified model can be obtained:

[0099]

[0100] in, is the system matrix in formula (23), is the trajectory tracking error, The definition of is given in formula (23), which represents the trajectory tracking error defined by formula (9) and The column vector composed of for The first derivative of ;

[0101] Then the boundary layer model of formula (21) can be obtained as follows:

[0102]

[0103] in, express The first derivative of ;

[0104] When selecting the parameter T i ξ >0,ξ∈{ψ,x,y,z} and When , it can be proved that both the simplified model and the boundary layer model are stable. According to Theorem 11.4 in "Nonlinear Systems", it can be concluded that there exists ε * >0, In f i ξ Under the premise that the second-order derivative of is bounded, the UDE estimation error equation represented by formula (21) and the tracking error equation represented by formula (23) are both stable;

[0105] S5.4. Controller robustness analysis

[0106] Solution of the simplified model It can be expressed as:

[0107]

[0108] According to Theorem 11.2 in "Nonlinear Systems", it can be concluded that there exists a positive constant k ξ ,right and There are the following inequalities:

[0109]

[0110] It can be further concluded that:

[0111]

[0112] According to the controller stability analysis in step S5.3, it can be concluded that It can be determined that there is a certain time and the upper bound of ε ** >0 and when ε→0 The positive boundary function And The following inequality can be obtained:

[0113]

[0114] When ε is reduced, the controller can achieve better robustness;

[0115] The simulation effect of the control method of the present invention in this embodiment is as follows: Figure 3 As shown, through reasonable design i , and By adopting appropriate control parameters, the control method of the present invention can achieve stable flight and formation change of a four-rotor UAV formation.

[0116] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A robust formation control method for quadrotor drones under communication topology constraints, characterized in that: The drone cluster includes multiple quad-rotor drones, and the formation communication of the quad-rotor drones is established. Specifically, the multiple quad-rotor drones are in a one-way series formation, in which the first quad-rotor drone obtains a reference signal, and the remaining quad-rotor drones obtain the status information and control information of the previous quad-rotor drone in a one-way manner; The reference signal is the status information and control signal of the virtual 0th quadrotor drone; Each quad-rotor unmanned aerial vehicle includes a guidance module, a control gain module and an interference observer; the state information and control signal obtained by each quad-rotor unmanned aerial vehicle are input into the guidance module, the state information obtained by the unmanned aerial vehicle is outputted by the guidance module minus its own current state information to obtain a first result, the first result is added to the control signal obtained by the unmanned aerial vehicle after passing through the guidance module after passing through the gain module to obtain a second result; the second result is input into the interference observer; the input of the interference observer also includes the current state information of the quad-rotor unmanned aerial vehicle; the second result is minus the output of the interference observer to obtain a control signal for controlling the quad-rotor unmanned aerial vehicle.

2. According to the method of robust formation control of quadrotor drones under communication topology constraints in claim 1, it is characterized in that: Based on the established formation communication topology, the formation control is realized in the ξ∈{ψ,x,y,z} channel; on the η∈{φ,θ} channel, each quadrotor is controlled individually; Among them, ψ represents the yaw angle of the quadrotor drone, x represents the coordinate of the quadrotor drone on the x-axis, y represents the coordinate of the quadrotor drone on the y-axis, z represents the coordinate of the quadrotor drone on the z-axis, φ represents the roll angle of the quadrotor drone, and θ represents the pitch angle of the quadrotor drone.

3. The robust formation control method for quadrotor drones under communication topology constraints according to claim 2 is characterized in that: The state information and control information of the ξ∈{ψ,x,y,z} channel are expressed as follows after the output of the guidance module: Among them, ξ i-1 represents the state of the i-1th quadrotor drone in the ξ∈{ψ,x,y,z} channel, Representative i-1 The first derivative of Indicates the control information obtained by the i-1th quadrotor drone. For the first quadrotor drone, represents the local reference of the i-th quadrotor UAV in the ξ∈{ψ,x,y,z} channel under the constraints of the formation communication topology graph, for The first derivative of for The second derivative of △ i Represents the formation interval between the i-th quadrotor drone and the i-1-th quadrotor drone.

4. The method for robust formation control of quadrotor drones under communication topology constraints according to claim 3 is characterized in that: The state information and control information of the η∈{φ,θ} channel are expressed as follows after the output of the guidance module: in, represents the second-order derivative of the global reference of the quadrotor drone in the η∈{φ,θ} channel, represents the expected input of the quadrotor drone in the η∈{φ,θ} channel.

5. The method for robust formation control of quadrotor drones under communication topology constraints according to claim 4 is characterized in that: The output of the disturbance observer for the ξ∈{ψ,x,y,z} channel is expressed as: Among them, T i ξ is the gain matrix; ξ i represents the state of the i-th quadrotor drone in the ξ∈{ψ,x,y,z} channel; Representative i The first derivative of ; Represents the trajectory tracking input, that is, the second calculation result of the ξ∈{ψ,x,y,z} channel.

6. The method for robust formation control of quadrotor drones under communication topology constraints according to claim 5 is characterized in that: The output of the disturbance observer of the η∈{φ,θ} channel is expressed as: Among them, T i η is the gain matrix; η i represents the state of the i-th quadrotor drone in the η∈{φ,θ} channel; Represents η i The first derivative of ; Represents the trajectory tracking input, that is, the second calculation result of the η∈{φ,θ} channel.

7. The method for robust formation control of quadrotor drones under communication topology constraints according to claim 6 is characterized in that: The control information is represented as 8. A controller, characterized in that: Based on the control information described in any one of claims 1 to 7, formation control is performed on the quadrotor drone.

9. A controller stability and robustness analysis method, characterized in that: include: A1. Construct the standard form of singular perturbation theory; including: A11 constructs the estimated error representation and tracking error representation of the disturbance observer of the ξ∈{ψ,x,y,z} channel; the estimated error representation of the disturbance observer of the ξ∈{ψ,x,y,z} channel is: The tracking error of the ξ∈{ψ,x,y,z} channel is expressed as: A12. Construct the estimation error representation and tracking error representation of the disturbance observer of the η∈{φ,θ} channel; The estimation error of the disturbance observer of the η∈{φ,θ} channel is expressed as A2. Define robustness indicators; The robustness index of the ξ∈{ψ,x,y,z} channel is expressed as: in Represents the tracking error, the upper bound of the error is a function that increases monotonically with the increase of ε and is always positive; the robustness index of the η∈{φ,θ} channel is expressed as: in Represents the tracking error, the upper bound of the error is a function that increases monotonically with the increase of ε and is always positive; A3, the controller stability analysis is performed using singular perturbation theory; Stability analysis of the ξ∈{ψ,x,y,z} channel: First, substitute the condition of ε = 0 into the estimated error representation of the disturbance observer of the ξ∈{ψ,x,y,z} channel, and we get Quasi-steady-state model: Then, the quasi-steady-state model is substituted into the tracking error representation of the ξ∈{ψ,x,y,z} channel, and the condition of ε=0 is applied to obtain the following simplified model: The boundary layer model of the estimation error representation of the disturbance observer of the ξ∈{ψ,x,y,z} channel is: When selecting the parameter T i ξ >0,ξ∈{ψ,x,y,z} and When ξ∈{ψ,x,y,z}, it can be proved that both the simplified model and the boundary layer model are stable; Stability analysis of η∈{φ,θ} channel: First, substitute the condition of ε = 0 into the estimated error representation of the disturbance observer of the η∈{φ,θ} channel, and we get Quasi-steady-state model: Then, the quasi-steady-state model is substituted into the tracking error representation of the η∈{φ,θ} channel, and the condition of ε=0 is applied to obtain the following simplified model: The boundary layer model of the estimation error representation of the disturbance observer of the η∈{φ,θ} channel is: When selecting the parameter T i η >0,η∈{φ,θ} and When η∈{φ,θ}, it can be proved that both the simplified model and the boundary layer model are stable; A4. Controller robustness analysis The robustness analysis process of ξ∈{ψ,x,y,z} channel is: The solution of the simplified model of ξ∈{ψ,x,y,z} channel is expressed as: According to Theorem 11.2 in "Nonlinear Systems", we can conclude that there exists a positive constant k ξ ,right and There are the following inequalities: Further conclusion: According to the stability analysis of the ξ∈{ψ,x,y,z} channel in step A3, we can get Then confirm that there is ε ** >0 and when ε→0 The positive boundary function And The following inequality is obtained: When ε is reduced, the controller obtains better robustness; The robustness analysis process of η∈{φ,θ} channel is: The solution of the simplified model of η∈{φ,θ} channel is expressed as: According to Theorem 11.2 in "Nonlinear Systems", we can conclude that there exists a positive constant k η ,right and There are the following inequalities: Further conclusion: According to the stability analysis of the η∈{φ,θ} channel in step A3, we can get η∈{φ,θ}, then it is certain that there exists ε ** >0 and when ε→0 The positive boundary function And The following inequality is obtained: When ε is reduced, the controller obtains better robustness.

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