Robust and Precise Formation Control Method for Quadrotor UAVs Based on Virtual Control Network and Active Disturbance Rejection Controller

Abstract

This invention discloses a robust and precise formation control method for quadrotor drones based on a virtual control network and an active disturbance rejection controller (ADRC). The method includes the following steps: Step S1: Estimating the state of the virtual leader quadrotor drone; Step S2: Establishing a virtual control network; Step S3: The trajectory of the virtual leader quadrotor drone is generated by trajectory planning, and each follower quadrotor drone tracks the trajectory of the virtual leader quadrotor drone and independently applies its own ADRC. The beneficial effect of this robust and precise formation control method for quadrotor drones based on a virtual control network and ADRC is that it develops a distributed observer for each follower to estimate the position coordinates of the virtual leader, significantly reducing communication costs.

Description

Technical Field

[0001] This invention belongs to the field of quadrotor UAV formation control, specifically relating to a robust and precise quadrotor UAV formation control method based on a virtual control network and an active disturbance rejection controller. Background Technology

[0002] The invention patent application, titled "A Method for Flight Control of Unmanned Aerial Vehicle (UAV) Swarms, UAVs, Systems, and Media," with publication number CN110703803A, discloses a "multiple UAVs performing missions, and a UAV ground command and control system." This system includes a formation control platform, a trajectory planning platform, a data communication platform, an auxiliary system control platform, and a control conversion platform. During mission execution, the UAV swarm coordinates all information to jointly complete various tasks. The system constructs a communication signal network of different frequencies for the UAV swarm, with UAVs operating at the same frequency forming a UAV group. A UAV swarm formation control algorithm based on MAS (Multi-Signal System) implements distributed control over multiple UAV groups to weaken the role of the navigator. The UAV ground command and control system... The system continuously monitors all communication signal networks of the drone swarm. Each drone can be dynamically and randomly designated as a new navigator when needed. It acquires real-time status information of all groups within the swarm, assigns different initial autonomy levels to different groups based on their communication network frequencies, and adjusts the autonomy levels of different drone groups based on their real-time status information. The drone ground command and control system acquires real-time environmental information of the drone groups and calculates the complexity information of the drone groups during mission execution based on the real-time environmental information and the final instructions from ground control. The complexity information includes mission route complexity, environmental complexity, and drone status information. If the complexity value is greater than or equal to a preset threshold, the drone swarm automatically selects an autonomy level to execute the mission.

[0003] Taking the technical solution disclosed in the aforementioned patent application as an example, in the prior art, leader-follower, virtual structures, and their combinations are common formation control strategies. However, when the physical leader is damaged, the entire formation will be unable to operate, and when drones in the swarm malfunction or new drones join the swarm, the virtual structure lacks fault tolerance and flexibility. Furthermore, centralized communication architectures are difficult to implement in engineering.

[0004] See attached diagram. Figure 1 The aerodynamic model of the quadcopter UAV is characterized by equations (1) and (2):

[0005]

[0006] Among them, F i(i = 1, 2, 3, 4) is the lift force of the i-th rotor, Q i (i = 1, 2, 3, 4) represents the horizontal tension of rotor i, ω i (i = 1, 2, 3, 4) is the angular velocity of rotor i, K L It is the overall lift coefficient of the rotor, K Q U1 is the rotor's overall drag coefficient, U2 is the control variable for roll angle ξ, U3 is the control variable for pitch angle θ, and ψ and U4 are the vertical accelerations. The control variables are (x, y, z), which are the three-dimensional position coordinates of the UAV in space. and Let f1(·), f2(·), and f3(·) represent the corresponding velocities and accelerations, m be the mass of the UAV, g be the gravitational acceleration, f1(·), f2(·), and f3(·) be the internal disturbances, and w1(t), w2(t), and w3(t) be the external disturbances. x I y I z Let l be the moment of inertia of the three axes, and l be the distance from the axis of rotation of the four rotors to the center of mass of the fuselage.

[0007] It is worth mentioning that, for precise formation flying with specific shapes, a relative kinematics model is used instead of a cluster kinematics mathematical model. Simultaneously, a virtual leader acts as the formation leader, using a real-time planned flight path to guide the formation flight.

[0008] XOY represents the Northeast Celestial Sphere coordinate system, X ri O ri Y ri This represents the heading coordinate system, with the origin located at the center of gravity of the following UAV i. ri The axis points in the direction of the horizontal velocity of follower i, Z ri The axis is perpendicular to the ground and points upwards, Y ri The axis is determined by referring to the right-hand rule. (X) ri Y ri Z ri The position of the virtual guide in the heading coordinate system of the drone i is indicated.

[0009] See attached diagram. Figure 2 The relative kinematic model is characterized by equation (3):

[0010]

[0011] Wherein, rotation angle ψ i ′=90°-ψ i , ψ i It is the heading angle following the drone i, (x i y i , z i ) and (xL y L , z L (x) represents the position of the drone i and the virtual leader in the northeast celestial coordinate system. ri y ri , z ri ) represents the position of the virtual lead aircraft in the heading coordinate system {W} of the wingman i.

[0012] It is worth mentioning that, as an example, for a group of N quadcopter drones, the information exchange between the drones can be modeled using a directed graph G = (V, E), where V = {v i |i = 1, 2, ..., n} is a set of vertices, and E is a set of directed edges describing the information exchange between drones. If there is a direct communication connection from drone i to drone j, then E... ij ∈E. The set of neighboring UAVs i of a UAV can be described in the communication topology as N i ={v j |e ji If ∈E, j≠i}, then the communication topology of the entire formation can be represented by the adjacency matrix A=(a ij ) n×n Description, in which

[0013] For any drone v i ,if drone v i This refers to the formation navigator. For any pair of different UAVs, if there exists a directed path for exchanging information, then graph G is said to be connected.

[0014] It is worth noting that due to security reasons or communication bandwidth limitations, information flow between drones is often severely restricted, and a drone may be unable to communicate with all other drones in a distributed formation. Unexpected events such as partial communication interruptions and damage to some drone platforms can degrade the controllability of the entire formation, leading to mission failure. Therefore, ensuring the controllability of the formation when a local communication link or some drone platforms are destroyed is an urgent issue. Generally, there are three methods: the first is to develop strategies to generate robust performance in the event of a temporary loss of communication links; the second is to reconfigure or adaptively configure when such a failure occurs; and the third method, namely the technical solution disclosed in this invention, designs a directed graph-based anti-communication and drone platform destruction topology to improve the topological robustness of drones performing missions in complex environments.

[0015] It is worth mentioning that in the active disturbance rejection control section, the second-order system is characterized by equation (4):

[0016]

[0017] Where, x, y represents the system state, u represents the control input, b represents the gain coefficient, and w(t) represents the external disturbance. It is a function of the system dynamics that includes internal uncertainties; let Where b0 is an estimate of the true value b. X3 is considered the total disturbance of the system and is called the extended state; let... The original second-order system can then be transformed into an integral chain system containing the total perturbation, characterized by equation (5):

[0018]

[0019] The structure of NLADRC / LADRC / ADRC is described below: ADRC typically includes a tracking differentiator (TD), a state observer (ESO), and a feedback control law. The tracking differentiator is used to arrange the conversion process and extract the difference of the input signal. A linear tracking differentiator is characterized by equation (6):

[0020]

[0021] Where V0 is the input, V i (i = 1, 2) is the output, r0 is an adjustable speed factor, and fh is a function that guarantees fast convergence from V1 to V0.

[0022] The state observer is used to estimate the system's state and total disturbance, which is the core and essence of ADRC. A third-order state observer is characterized by equation (7):

[0023]

[0024] The inputs to the state observer are the regulation output y and the control input u; the output of the state observer is z. i (i = 1, 2, 3), providing estimates of system states x1, x2 and total disturbance x3, respectively; β 0i (i = 1, 2, 3) is the observer gain, and e is the observer error "z1 - y". It is a nonlinear function, defined by equation (8):

[0025]

[0026] Where, α i And δ are important parameters that are predetermined. This nonlinear function, within the NLADRC framework, exhibits "small error and large gain; when α..." i When α < 1, the error is large and the gain is small, etc. i When α = 1, this nonlinear fal(e, α) iThe δ) function becomes a linear function, and the observer gain can be determined as β. 01 =3ω o , Where ω o For observer bandwidth.

[0027] In this process, a feedback control law is used to suppress the residual and achieve the desired control objective. The feedback control law is represented by equation (9):

[0028]

[0029] The form of U0 can be used in the following combinations. Where k i (i = 1, 2) is the control gain. When α i When α′ = 1, this nonlinear fal(e, α′) i The δ) function becomes a linear function, k p k d It can be determined to be k p =2ω c , Where ω c This refers to the controller bandwidth.

[0030] See attached diagram. Figure 3 This illustrates the framework of the ADRC algorithm.

[0031] The SADRC principle is described below: LADRC and NLADRRC each have their own advantages and disadvantages, and the goal of SADRC is to combine the advantages of both. This invention uses a linear control law, while SADRC represents the switching between LESO and NLESO based on the state error e. The SADRC scheme is as follows:

[0032] Initial operation phase: If there may be an initial state error between the device and the state observer, NLESO is used during the transition time T (manually set) to avoid the "peak phenomenon". Otherwise, the "initial operation phase" step is omitted and the normal operation phase is directly entered.

[0033] Normal operation phase: See attached diagram. Figure 4 After the initial operation phase, the controller automatically switches between LESO and NLESO based on the error e. A specific δ′ > δ is selected; when the error e < δ′, NLESO starts operating; otherwise, LESO starts operating. This δ′ is a general boundary for the performance of LESO and NLESO, i.e., when e < δ′, NLESO outperforms LESO, and LESO outperforms NLESO. The SADRC scheme combines the advantages of LADRC and NLADRC. Summary of the Invention

[0034] In view of the current situation of the prior art, this invention overcomes the above-mentioned defects and provides a robust and precise formation control method for quadrotor UAVs based on virtual control network and active disturbance rejection controller.

[0035] This invention discloses a robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller. Its main objective is to cleverly combine and fully utilize the leader-follower and virtual structure methods to propose a virtual control network with a virtual leader. To overcome the shortcomings of centralized communication architectures, a distributed observer is proposed. To enhance the robustness of the formation control method against internal uncertainties and external disturbances, active disturbance rejection control technology is employed, and an outer-loop position controller and an inner-loop attitude controller are designed.

[0036] This invention adopts the following technical solution: a robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller, comprising the following steps:

[0037] Step S1: Estimate the status of the virtual navigation quadcopter drone;

[0038] Step S2: Establish a virtual control network;

[0039] Step S3: The trajectory of the virtual lead quadcopter is generated by trajectory planning. Each follower quadcopter tracks the trajectory of the virtual lead quadcopter and independently applies its own active disturbance rejection controller, so that each follower quadcopter estimates the state of the virtual lead quadcopter, and finally obtains the trajectory of each follower quadcopter relative to the virtual lead quadcopter.

[0040] As a further preferred technical solution to the above technical solution, in step S1, let η be the northeast celestial coordinate. L =[x L y L , z L ] T The location coordinates of the virtual navigator in the system. For U A V i Estimated position coordinates of the virtual lead; in a distributed communication framework, U A V i The position coordinates of the virtual lead are represented by equation (10):

[0041]

[0042] Where the adjustable variable λ>0, N L This represents a group of drones that communicate directly with the virtual leader; the virtual leader's state η.L Only in v i ∈N L When directly obtaining information, drone j obtains information when communicating directly with drone i. ij =1, otherwise take a ij =0.

[0043] As a further preferred technical solution to the above technical solution, in step S1: the relative kinematic model of the quadcopter UAV is characterized by equation (16):

[0044]

[0045] Wherein, rotation angle ψ i ′=90°-ψ i , ψ i It is the heading angle following the drone i, (x i y i , z i )and Let x represent the position of the following drone i and the estimated position of the virtual leader in the northeast celestial coordinate system, respectively. ri y ri , z ri ) represents the position of the virtual lead aircraft in the heading coordinate system {W} of the wingman i; It is an estimated state under a distributed communication topology.

[0046] As a further preferred technical solution to the above technical solution, step S2 is specifically implemented as follows: virtual control points are set with different priorities. According to the priority order, the virtual control point with higher priority selects the nearest drone first, and then the virtual control point with lower priority is reconsidered and the nearest drone is selected by the virtual control point with lower priority.

[0047] As a further preferred technical solution to the above technical solution, step S2 is specifically implemented as follows: if the virtual control points are not set with different priorities, calculate the relative distance between each UAV and all virtual control points one by one, and take the minimum sum of distances to determine the correspondence between the UAV and the virtual control points.

[0048] As a further preferred technical solution to the above technical solutions, the "trajectory tracking" in step S3 is specifically implemented as follows: trajectory tracking adopts a cascaded control method, including outer loop position control and inner loop attitude control.

[0049] As a further preferred technical solution to the above technical solutions, "outer ring position control" is implemented in the following steps:

[0050] The aerodynamic model of the quadcopter UAV in step S7 is characterized by equations (17) and (18):

[0051]

[0052] Among them, U x U y U z It is a virtual control value, determined by U x U y U z Calculate the inner-loop attitude control command; f x f y f z Considered as the total disturbance, w x w y w z These are various internal and external disturbances; for outer loop position control, let [x c y c z c ] T The position command for the follower, [xyz] T It is the real-time feedback of the follower's position coordinates, and equation (16) is rewritten as equation (19);

[0053]

[0054] Among them, (x r y r , z r (x) represents the virtual lead aircraft's position in the wingman's heading coordinate system {W}, (x) L y L , z L The position coordinates of the virtual leader are estimated by the following drone; based on equation (19), equation (20) is obtained:

[0055]

[0056] in, It refers to the expected position coordinates of the virtual leader following the drone in the heading coordinate system;

[0057] Based on equations (17) to (20), a LADRC-based position controller is designed and obtained, characterized by equations (21) to (23):

[0058]

[0059]

[0060] Where, r x0 r y0 r z0 It is a parameter that affects the speed of tracking the input signal, β xi ,βyi ,β zi i = 1, 2, 3 are the ESO gains that need to be adjusted, k xi， k yi， k zi , i = 1, 2 are the gains of the control law that need to be adjusted;

[0061] "Inner loop attitude control" is implemented in the following steps:

[0062] Given ψ c The inner ring attitude angle control command (φ) is obtained from equation (24). c θ c , ψ c ):

[0063]

[0064] Inner ring attitude angle control command (φ) c θ c , ψ c The attitude loop controller is designed using the control quantity U4 and the control quantity U4, and is characterized by equation (25):

[0065]

[0066] Among them, V i (i = 1, 2, 3) are virtual control values, then we get equation (26):

[0067]

[0068] The SADRC controller is designed using equation (26), and characterized by equations (27) to (29):

[0069]

[0070] The robust and precise formation control method for quadrotor UAVs based on virtual control networks and active disturbance rejection controllers disclosed in this invention has the following advantages:

[0071] First, a distributed observer was developed for each follower to estimate the location coordinates of the virtual leader, which greatly reduced communication costs.

[0072] Secondly, the concept of virtual control network was proposed and applied, which is more flexible and more fault-tolerant than traditional virtual structure methods;

[0073] Third, an active disturbance rejection controller was adopted, and a distributed robust and precise formation controller was designed, which has high performance and is easy to implement in engineering. Attached Figure Description

[0074] Figure 1It is an aerodynamic model of a quadcopter drone.

[0075] Figure 2 It is a diagram showing the relative positions of leaders and followers.

[0076] Figure 3 This is a framework diagram of the ADRC algorithm.

[0077] Figure 4 This is a schematic diagram of the SADRC scheme.

[0078] Figure 5 This is a schematic diagram of the virtual control network for the expected formation.

[0079] Figure 6 This is the overall plan diagram. Detailed Implementation

[0080] This invention discloses a robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller. The specific implementation of this invention will be further described below with reference to a preferred embodiment (Example 1).

[0081] Those skilled in the art should note that the terms "follower" and "follower" that may be used in the various embodiments of the present invention are the same concept and will not be distinguished.

[0082] Those skilled in the art should note that the terms "virtual navigator," "virtual team leader," "virtual leader," "virtual leader," "virtual navigator quadcopter drone," "navigator drone," and "virtual navigator drone" that may be involved in the various embodiments of the present invention are all the same concept and will not be distinguished further.

[0083] Those skilled in the art should note that the various embodiments of the present invention may involve the same concept, such as "follower" or "follower quadcopter drone," and will not be distinguished further.

[0084] Those skilled in the art should note that the “NLADRC” that may be involved in the various embodiments of the present invention is defined as: nonlinear active disturbance rejection control.

[0085] Those skilled in the art should note that the “LADRC” that may be involved in the various embodiments of the present invention is defined as: Linear Active Disturbance Rejection Control.

[0086] Those skilled in the art should note that the “ADRC” that may be involved in the various embodiments of the present invention is defined as: Active Disturbance Rejection Control.

[0087] Those skilled in the art should note that the “ESO” that may be involved in various embodiments of the present invention is defined as: State Observer.

[0088] Those skilled in the art should note that the “SADRC” that may be involved in various embodiments of the present invention is defined as: the switching between LESO and NLESO based on the state error e.

[0089] Those skilled in the art should note that the “LESO” that may be involved in various embodiments of the present invention is defined by us as: State Observer.

[0090] Those skilled in the art should note that the “NLESO” that may be involved in various embodiments of the present invention is defined as: Nonlinear Extended State Observer.

[0091] Example 1.

[0092] Preferably, this embodiment discloses a robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller.

[0093] Specifically, this embodiment discloses a robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller, including the following steps:

[0094] Step S1: Estimate the status of the virtual navigation quadcopter drone;

[0095] Step S2: Establish a virtual control network;

[0096] Step S3: The trajectory of the virtual lead quadcopter is generated by trajectory planning. Each follower quadcopter tracks the trajectory of the virtual lead quadcopter and independently applies its own active disturbance rejection controller, so that each follower quadcopter estimates the state of the virtual lead quadcopter, and finally obtains the trajectory of each follower quadcopter relative to the virtual lead quadcopter.

[0097] The following describes the key technical points of step S1 (estimating the virtual navigator state).

[0098] Using a virtual leader instead of a physical leader effectively avoids the problem of the entire formation being unable to function when the physical leader is damaged. Each drone in the formation has difficulty communicating globally with other drones in the formation. Only a subset of drones in the formation can directly access the virtual leader's information; drones outside this subset can only access it from "neighboring" drones. A particular drone may receive the virtual leader's information from different "neighboring" drones; therefore, each drone needs to obtain consistent virtual leader status information based on local information fusion.

[0099] Let η L =[x L y L , zL ] T These are the position coordinates of the virtual navigator in the Northeast Celestial Sphere coordinate system. For U A V i Estimated position coordinates of the virtual lead; in a distributed communication framework, U A V i The position coordinates of the virtual lead are represented by equation (10):

[0100]

[0101] Where λ>0, N L This represents a group of drones that communicate directly with the virtual leader; the virtual leader's state η. L Only in v i ∈N L When directly obtaining information, drone j obtains information when communicating directly with drone i. ij =1, otherwise take a ij =0.

[0102] The asymptotic convergence condition of equation (10) is explained below.

[0103] If and only if from the virtual lead to v i When a reachable communication topology exists, equation (10) can make

[0104] View the virtual leader as an additional drone in the formation, i.e. The communication status between other (physical) drones and virtual leads is characterized by equation (11):

[0105]

[0106] The column vector σ = [σ1, ..., σ2] is formed. i , …, σ n ] T Combined formula (12):

[0107]

[0108] Rewrite equation (10) as equation (13):

[0109]

[0110] After transformation, formula (11) is rewritten as formula (14);

[0111]

[0112] Based on equation (14), we obtain equation (15):

[0113]

[0114] Where, when a ij When = 1, it means U A V j with U A V j There is direct communication between them; if there is an accessible communication topology from Virtual Navigator U A V i There must be a sequence [i, j, ..., k, n+1] such that a ij =…=a k(n+1) =1, then

[0115] It is worth mentioning that Equation (10) can estimate the state under a distributed communication topology. asymptotically converges to the actual state η L The rate of asymptotic convergence is determined by the variable λ. Therefore, by choosing a suitable λ, the estimated state can be used. As the actual state η L This guides the formation. Then, equation (3) of the relative kinematic model is rewritten as equation (16):

[0116]

[0117] Wherein, rotation angle ψ i ′=90°-ψ i , ψ i It is the heading angle following the drone i, (x i y i , z i )and Let x represent the position of the following drone i and the estimated position of the virtual leader in the northeast celestial coordinate system, respectively. ri y ri , z ri ) represents the position of the virtual lead aircraft in the heading coordinate system {W} of the wingman i; It is an estimated state under a distributed communication topology.

[0118] The following describes the key technical points of step S2 (establishing a virtual control network).

[0119] It should be noted that traditional virtual structure methods can easily set up the formation structure of UAV swarms, and due to the formation error feedback mechanism, high-precision formation maintenance can be achieved. However, traditional virtual structure methods map each UAV to a virtual control point. When a UAV in the swarm malfunctions or a new UAV joins the swarm, the virtual structure changes, lacking fault tolerance and flexibility. Therefore, this embodiment uses a virtual control network, eliminating the one-to-one correspondence between UAVs and virtual control points. Virtual control points are set with different priorities. According to the priority order, higher-priority virtual control points are selected based on the nearest UAV, and then lower-priority virtual control points are reconsidered and filled in sequentially.

[0120] Prioritizing virtual control points offers at least two advantages. First, when the number of virtual control points exceeds the number of drones, drones should be deployed to more important virtual points. For example, when using drones in a circular formation to dynamically acquire a target, priority should be given to the four directions of the "circle"; when flying in a V-formation, drones should be deployed near the apex. Second, it significantly reduces computational complexity. For instance, assuming ten virtual control points and ten drones, and the drones are deployed based on control priority, the required number of computations is significantly reduced. However, if no priority is set, the relative distance between each drone and all virtual control points is calculated one by one.

[0121] Then, the minimum sum of distances is used to determine the correspondence between the drone and the virtual control point. The calculation process is as follows: First, calculating the distance between each drone and each virtual control point requires 10 * 10 = 100 calculations; second, there are... There are schemes with different distance combinations between the drone and the control point. The total distance sum for each scheme needs to be calculated again 3,628,800 times; finally, the correspondence between the drone and the virtual control point is determined based on the minimum sum distance. The total number of calculations is 100 + 3,628,800 + 3,628,800 = 7,257,700, which shows that the amount of computation is enormous and undoubtedly a huge waste of computing resources for drones.

[0122] The method of establishing a virtual control network is illustrated using a V-formation as an example. Taking 9 virtual control points and 7 drones as an example, the expected virtual control network for the formation is as follows: Figure 5As shown in the diagram, the black triangle represents the virtual leader, and the other circles represent followers. The virtual control points are prioritized as p1, p2, p3, p4, p5, p6, p7, p8, and p9, in descending order. Virtual control point p1 is given priority, and the distance between control point p1 and the seven drones is calculated. The drone with the shortest distance is then selected to take over control point p1. Subsequently, virtual control points p2, p2, ..., p7 are considered based on the shortest distance principle. When a new drone joins the formation, the corresponding control point p8 can be selected; when two new drones join the formation, the corresponding control points p8 and p9 can be selected sequentially; if more new drones are added, the virtual control network can be expanded.

[0123] This demonstrates that the virtual control network method is highly flexible and possesses a certain degree of fault tolerance. In contrast, with traditional virtual structure methods, the virtual structure changes when a drone is damaged or a new drone joins the formation, making it difficult to continue performing the mission.

[0124] It is worth mentioning that there are no strict requirements on the positions of multi-rotor drones, but aerodynamic coupling effects need to be considered for fixed-wing drones. The communication topology between each virtual control point is designed as a sabotage-resistant topology, which can be redesigned according to the "formation reconstruction strategy" if one or more drones are damaged.

[0125] The following describes the key technical points of step S3 (the trajectory of the virtual lead quadcopter is generated by trajectory planning, each follower quadcopter tracks the trajectory of the virtual lead quadcopter, and independently applies the active disturbance rejection controller of the follower quadcopter, so that each follower quadcopter estimates the state of the virtual lead quadcopter, so as to finally obtain the trajectory of each follower quadcopter relative to the virtual lead quadcopter).

[0126] The essence of leader-follower swarm control is that followers track the leader's trajectory. The virtual leader's trajectory is generated through trajectory planning, and each follower independently designs its own estimated virtual leader state based on its trajectory. This approach simplifies the multi-UAV swarm control problem into a two-UAV trajectory tracking problem, thus giving the UAV swarm a distributed characteristic.

[0127] Based on the dynamic model of a quadcopter UAV, trajectory tracking (control) employs a cascaded control method, including outer-loop position control and inner-loop attitude control. The overall scheme of the control system (the entire multi-loop control system for the UAV close-range formation model) is as follows: Figure 6As shown, the outer loop position controller employs LADRC, reducing the difficulty of parameter tuning. A linear tracking differentiator (TD) is used to schedule the transient process to track the trajectory of the virtual leader, and a linear state observer (ESO) is used to estimate and compensate for wind disturbances and other uncertainties (such as load changes). Due to the strong coupling of the attitude inner loop and its sensitivity to disturbances, attitude angle control requires fast response, high tracking accuracy, and strong anti-interference capability; therefore, SADRC is adopted. Simultaneously, since the outer loop position controller handles angle control commands, there are no jumps, thus eliminating the transition process to reduce response delay. The controller design and stability analysis are described below.

[0128] 1) Outer Ring Position Controller / Formation Controller: The aerodynamic model of the quadcopter UAV characterized by equations (1) and (2) in the background technology is an ideal model. In reality, there are various internal and external disturbances, such as wind disturbances and parameter disturbances. The new aerodynamic model of the quadcopter UAV is characterized by equations (17) and (18):

[0129]

[0130] Among them, U x U y U z It is a virtual control value, determined by U x U y U z Calculate the inner-loop attitude control command; f x f y f z Considered as the total disturbance, w x w y w z These are various internal and external disturbances; for outer loop position control, let [x c y c z c ] T The position command for the follower, [xyz] T It is the real-time feedback of the follower's position coordinates, and equation (16) is rewritten as equation (19);

[0131]

[0132] Among them, (x r y r , z r (x) represents the actual position coordinates of the virtual leader in the heading coordinate system following the drone. L y L , z L The position coordinates of the virtual leader are estimated by the following drone; based on equation (19), equation (20) is obtained:

[0133]

[0134] in, It refers to the expected position coordinates of the virtual leader following the drone in the heading coordinate system.

[0135] Based on equations (17) to (20), a LADRC-based position controller is designed and obtained, characterized by equations (21) to (23).

[0136]

[0137] Where, r x0 r y0 r z0 It is a parameter that affects the speed of tracking the input signal, β xi ,β yi ,β zi i = 1, 2, 3 are the ESO gains that need to be adjusted, k xi k yi k zi , i = 1, 2 is the gain of the control law that needs to be adjusted.

[0138] 2) Internal Attitude Loop Controller Design: First, the inner loop attitude angle control command (φ) needs to be calculated from the outer loop position controller. c θ c , ψ c ) and control quantity U4. However, through these three equations (U x U y U z It is clearly impossible to solve for a set of boundary values ​​using this method. Because there is a significant coupling between the x-axis motion and the pitch angle, and between the y-axis motion and the roll angle, and because the control variable U4 is a necessary command, it is impossible to solve for a set of boundary values ​​using this method. c In this case, the inner ring attitude angle control command (φ) is obtained from equation (24). c θ c , ψ c ):

[0139]

[0140] Inner ring attitude angle control command (φ) c θ c , ψ c The attitude loop controller is designed using the control quantity U4 and the control quantity U4, and is characterized by equation (25):

[0141]

[0142] Among them, V i(i = 1, 2, 3) is the virtual control value, and then the formula (26) is obtained:

[0143]

[0144] Design the SADRC controller from formula (26), which is characterized by formulas (27) to (29):

[0145]

[0146]

[0147] To simply describe the switching mechanism between the nonlinear state observer (ESO) and the linear state observer (ESO), it is characterized by formula (30):

[0148]

[0149] Among them, α i , δ i and γ i are important parameters that need to be determined in advance. The determination rules of α i , δ i and γ i are described as follows respectively.

[0150] Specifically, delta_i is the linear interval, and its value cannot be too small, otherwise the nonlinear gain will be too large; nor can it be too large, otherwise the advantage of the nonlinear gain cannot be reflected.

[0151] gama_i is obtained by experiment or theoretical derivation. Its essence is the critical point of the performance of LESO and NLeso: when the error e_i < gama_i, take NLESO; when the error e_i > gama_i, take LESO. This can give full play to the advantages of LESO and NLeso and make the overall performance optimal.

[0152] Specifically, the physical meaning and determination rule of α i are as follows:

[0153] Physical meaning: α i is the power parameter in the fal function (nonlinear function), which determines the nonlinear degree of the fal function. By adjusting the value of α i , the gain of the fal function at different error magnitudes can be changed, so as to achieve the control effect of "small error, large gain; large error, small gain".

[0154] Determination rule: The value of α i is usually determined according to the actual application scenario and the expected control performance. Generally speaking, a smaller α iA specific value will result in a smaller gain for the fal function when the error is large, and a larger gain when the error is small. This helps to speed up convergence and reduce overshoot. In practical applications, a suitable α can be determined through simulation or experimentation. i value.

[0155] Specifically, β i The physical meaning and determining rules:

[0156] Physical meaning: β i It is the gain parameter in ESO (Extended State Observer) or NLESO (Nonlinear Extended State Observer), which is used to adjust the observer's estimation speed of system state and disturbances.

[0157] Determine the rule: β i The value of β is usually determined based on the system's dynamic characteristics and noise level. A larger β... i A higher β value can speed up the observer's response, but it can also lead to excessive sensitivity to noise. Therefore, in practical applications, a suitable β value needs to be found through debugging and experimentation. i The value is adjusted to achieve a balance between fast response and noise suppression.

[0158] When the virtual control value V i When (i = 1, 2, 3) is determined, the actual control value U i (i = 1, 2, 3) are determined by equation (31):

[0159]

[0160] 3) Control System Stability Analysis: To ensure the stability of the multi-loop control system, it is necessary to analyze the stability of the entire error feedback closed-loop control subsystem. Before proceeding with the formal analysis, two existing technologies are described: LADRC for single-input single-output (SISO) systems and SADRC for multiple-input multiple-output (MIMO) systems.

[0161] Consider a general second-order SISO nonlinear time-varying dynamic system, such as equations (17) and (18), and apply LADRC to control the object. Those skilled in the art will know that: assuming f is differentiable and assuming... If h is bounded, then there exists a constant σ > 0, a finite T > 0, and ω o >0, ω c >0, so for some positive integer j and

[0162] Considering a general second-order MIMO nonlinear time-varying dynamic system like equation (26), and applying SADRC to control the object, those skilled in the art will know that: assuming f is differentiable, and The gain vector and the observer gain vector are bounded. If we choose the gain vector K and the observer gain vector L such that A c l is Hurwitz, then δ cl The exponential (t) converges to the bounded sphere. Where λ m ax(P cl ) is P cl The largest eigenvalue, P cl It is equation A cl TP cl +P cl A cl =-I (mn+m(n+1))×(mn+m(n+1)) The solution, h max It is the absolute maximum value of h(t).

[0163] Based on this, the stability analysis of the entire error feedback closed-loop subsystem is described below. A Lyapunov function is constructed for the multi-loop control system of the quadcopter UAV, characterized by equation (32):

[0164]

[0165] Here, x represents the state variable of the multi-loop control system, and e1 and e2 are the tracking errors of the position loop and attitude loop, respectively. Therefore, the entire multi-loop control system is asymptotically stable, provided that... Next, we will demonstrate this by incrementally adding each loop from the inner loop to the outer loop.

[0166] Attitude loop stability analysis. The tracking error of the attitude loop is... in It is a control command, ξ2=[φ θ ψ] T This is the actual attitude angle. For this error, the Lyapunov function V(ξ2) is constructed as follows, and characterized by equation (33):

[0167]

[0168] Those skilled in the art will understand that by adjusting the appropriate gain vector K and observer gain vector L, it can be guaranteed that V(ξ2) < 0. This means that the tracking error e2 asymptotically converges to zero and ξ2 asymptotically converges to...

[0169] Position loop stability analysis. Similarly, the tracking error of the position loop is... in It's a control command, ξ1 = [xyz] T These are the actual position coordinates. For this error, the Lyapunov function V(ξ1) is constructed as follows, and characterized by equation (34):

[0170]

[0171] According to the position control model (17) and equation (18), the stability of the outer position loop is not directly related to the attitude angle. Those skilled in the art will know that by adjusting appropriate values ​​of the gain vector K′ and the observer gain vector L′, the stability of the outer position loop can be guaranteed. Therefore, we can draw a similar conclusion: by adjusting the appropriate values ​​K, K′, L, L′, we can ensure This means that the derivative of the Lyapunov function of the multi-loop control system of a quadcopter drone is

[0172] In summary, the entire multi-loop control system of the close-range UAV formation model is asymptotically stable.

[0173] It is worth mentioning that the specific selection and other technical features of the quadcopter drone involved in this patent application should be regarded as prior art. The specific structure, working principle, and possible control methods and spatial arrangement of these technical features can be adopted using conventional choices in the field, and should not be regarded as the inventive point of this patent. This patent will not be further elaborated in detail.

[0174] For those skilled in the art, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the protection scope of this invention.

Claims

1. A robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller, characterized in that, Includes the following steps: Step S1: Estimate the status of the virtual navigation quadcopter drone; Step S2: Establish a virtual control network; Step S3: The trajectory of the virtual lead quadcopter drone is generated by trajectory planning. Each follower quadcopter drone tracks the trajectory of the virtual lead quadcopter drone and independently applies the active disturbance rejection controller of the follower quadcopter drone, so that each follower quadcopter drone estimates the state of the virtual lead quadcopter drone on its own, so as to finally obtain the trajectory of each follower quadcopter drone relative to the virtual lead quadcopter drone. Step S3, "trajectory tracking", is specifically implemented in the following steps: trajectory tracking adopts a cascaded control method, including outer loop position control and inner loop attitude control; "Outer ring position control" is implemented in the following steps: The aerodynamic model of the quadcopter UAV in step S7 is characterized by equations (17) and (18): Among them, U x U y U z It is a virtual control value, determined by U x U y U z Calculate the inner-loop attitude control command; f x ,f y ,f z Considered as the total disturbance, w x ,w y ,w z These are various internal and external disturbances; for outer loop position control, let [x] c y c z c ] T The position command for the follower, [xyz] T It is the real-time feedback of the position coordinates of the follower, and equation (16) is rewritten as equation (19); Among them, (x r ,y r ,z r (x) represents the virtual lead aircraft's position in the wingman's heading coordinate system {W}, (x) L y L , z L The position coordinates of the virtual leader are estimated by the slave drone; based on equation (19), equation (20) is obtained: in, It is the expected position coordinate of the virtual leader in the heading coordinate system of the slave UAV; Based on equations (17) to (20), a LADRC-based position controller is designed and obtained, characterized by equations (21) to (23): Where, r x0 r y0 r z0 It is a parameter that affects the speed of tracking the input signal, β xi ,β yi ,β zi i = 1, 2, 3 are the ESO gains that need to be adjusted, k xi k yi k zi , i = 1, 2 are the gains of the control law that need to be adjusted; "Inner loop attitude control" is implemented through the following steps: Given ψ c The inner ring attitude angle control command (φ) is obtained from equation (24). c ,θ c ,ψ c ): Inner ring attitude angle control command (φ) c θ c , ψ c The attitude loop controller is designed using the control quantity U4 and the control quantity U4, and is characterized by equation (25): Among them, V i (i = 1, 2, 3) are virtual control values, then we get equation (26): The SADRC controller is designed using equation (26), and characterized by equations (27) to (29): In equation (18), φ is the roll angle; φ is the pitch angle; ψ is the yaw angle; K1 is the drag coefficient of the x-axis; K2 is the drag coefficient of the y-axis; and K3 is the drag coefficient of the z-axis. In equation (27), fal φ (e φ This is represented by formula (30): In equation (30), α i It is a linear interval; δ i It is the critical point for the performance of LESO and NLeso; γ i It is the exponential parameter in the fal function.

2. The robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller as described in claim 1, characterized in that, In step S1, let η L =[x L y L , z L ] T These are the position coordinates of the virtual navigator in the Northeast Celestial Sphere coordinate system. For U A V i Estimated position coordinates of the virtual lead; in a distributed communication framework, U A V i The position coordinates of the virtual lead are represented by equation (10): Where λ>0,N L This represents a group of drones that communicate directly with the virtual leader; the virtual leader's state η. L Only in v i ∈N L When directly obtained, drone j obtains a when communicating directly with drone i. ij =1, otherwise take a ij =0.

3. The robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller according to claim 1, characterized in that, Step S2 is implemented as follows: Virtual control points are set with different priorities. According to the priority order, the virtual control point with higher priority selects the nearest drone first. Then, the virtual control point with lower priority is reconsidered and selects the nearest drone.

4. The robust and precise formation control method for quadrotor UAVs based on a virtual control network and an active disturbance rejection controller as described in claim 1, characterized in that, Step S2 is implemented as follows: If the virtual control points are not set with different priorities, calculate the relative distance between each UAV and all virtual control points one by one, and take the minimum sum of distances to determine the correspondence between the UAV and the virtual control points.

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