Full-distributed unmanned aerial vehicle robust formation control method based on minimum information amount

Abstract

The invention provides a fully-distributed unmanned aerial vehicle robust formation control method based on minimum information amount, and the method comprises the following steps: employing a second-order system as a kinematic model of an unmanned aerial vehicle, and building a state space model of an unmanned aerial vehicle system; establishing a state space model of the virtual leader system to describe a global flight path vector of the unmanned aerial vehicle; describing a communication network of the unmanned aerial vehicle group by using a directed graph; designing an output-based adaptive distributed observer to estimate virtual leader system information required by each unmanned aerial vehicle; based on the output information of the observer, constructing an asymptotic internal model to process uncertain parameters in the virtual leader system; an asymptotic internal model is combined with a dynamic state feedback controller, an unmanned aerial vehicle robust formation flight controller is constructed, and the unmanned aerial vehicle robust formation flight controller and an output-based adaptive distributed observer jointly control robust formation flight of a full-distributed unmanned aerial vehicle group. And the robustness and the distributed performance of the formation flight of the unmanned aerial vehicles are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of control systems and unmanned aerial vehicles, and in particular to a fully distributed unmanned aerial vehicle robust formation control method based on minimum information amount. Background Art

[0002] Drones have the advantages of strong maneuverability, small size, and low cost. Formation control of various types of drone swarm systems has been widely used in various fields, such as collaborative load transportation, regional detection and surveillance, and collaborative hunting. Autonomous formation control is the basis for drone swarm systems to achieve practical tasks.

[0003] In the process of formation control, the drone swarm needs to communicate uninterruptedly. When the actual task is complex and there are a large number of drones in the swarm, the data that needs to be transmitted in the communication network will increase significantly, and the communication burden will become the main factor limiting the formation. At the same time, drone swarms often encounter certain harsh environments, such as mines and tunnels. In these environments, the drone system will be affected by various uncertain factors, resulting in certain changes in the system's model parameters, and thus unable to maintain the stability of the overall performance of the drone swarm.

[0004] At present, there are few studies on the formation control of UAV swarms that aim at both minimum communication and system robustness. As for the formation control problem under the requirement of minimum communication, some literature focuses on the problem of multi-AUV cooperative formation in complex underwater environments (Multi-AUV formation control based on blind spot concept to reduce communication volume Zhou Tian, ​​Kang Fengju, School of Navigation, Northwestern Polytechnical University, National Laboratory for Underwater Information Processing and Control, Northwestern Polytechnical University), and designed a multi-AUV distributed cooperative control method combining artificial potential field, virtual navigator and blind spot, which reduces the communication volume of AUV formation coordination and control process in an obstacle-free environment. However, this technology still has local extreme points, the design of potential field function is difficult, and the robustness of the entire system cannot be guaranteed. Summary of the invention

[0005] Based on the minimum virtual leader system information, the present invention proposes a fully distributed UAV robust formation flight control method, which solves the problem of robust formation flight of UAV swarms. The present invention effectively improves the robustness and distributed performance of UAV formation flight, ensuring that the UAV swarm can safely and stably complete the desired formation mission.

[0006] The present invention is achieved by at least one of the following technical solutions.

[0007] A fully distributed UAV robust formation control method based on minimum information volume comprises the following steps:

[0008] Step 1: Use the second-order system as the kinematic model of the UAV and establish the state space model of the UAV system;

[0009] Step 2: Establish a state space model of the virtual leader system to describe the global flight path vector of the UAV;

[0010] Step 3: Use a directed graph to describe the communication network of the drone swarm;

[0011] Step 4: Design an output-based adaptive distributed observer to estimate the virtual leader system information required by each UAV;

[0012] Step 5: Based on the output information of the observer, construct an asymptotic internal model to deal with the uncertain parameters in the UAV system;

[0013] Step 6: Combine the asymptotic internal model with the dynamic state feedback controller to construct a UAV robust formation flight controller, which is used together with the output-based adaptive distributed observer to control the fully distributed UAV swarm robust formation flight.

[0014] Furthermore, in step 1, a second-order system is used to describe the motion state of the UAV. Suppose there are N UAVs, and the kinematic model of the i-th UAV is described as:

[0015]

[0016] Among them, v i (t),u i (t)∈R 3 represents the speed and control input of the i-th UAV, t is the time, represents the position p of the i-th drone i (t) and the differential of velocity, R 3 represents a 3D column vector; ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i represent the nominal part and uncertain part of the uncertain control gain matrix respectively.

[0017] Furthermore, in step 2, a state space model of the virtual leader system is established to generate the global flight path vector p of the UAV 0(t)∈R 3 , the state space model of the virtual leader system is described as:

[0018]

[0019] p 0 (t) = W 0 r 0 (t)(2b);

[0020] Among them, r 0 (t)∈R q represents the q-dimensional internal state of the virtual leader, t is the time, represents the differential of the internal state of the virtual leader; S 0 ∈R q×q is the system matrix of the virtual leader system, R represents the real number field, W 0 ∈R 3×q is the output matrix of the virtual leader system.

[0021] Furthermore, the UAV formation vector and formation flight tracking error are described as:

[0022] p ri (t) = p 0 (t)+p fi (3a);

[0023] e i (t) = p i (t)-p 0 (t)-p fi (3b); where p ri (t)∈R 3 is the formation vector of UAV i; p 0 (t)∈R 3 is the global flight path vector of the UAV, which represents the reference flight path of the entire UAV swarm and is regarded as a virtual leader; i (t) is the position of the i-th UAV; p fi ∈R 3 is the local formation vector, indicating the relative position between the i-th UAV and the virtual leader; e i (t)∈R 3 is the formation flight tracking error of the i-th UAV.

[0024] Furthermore, in step 1, a state space model of the UAV system is established. The state space model of the UAV system is described as:

[0025]

[0026] p i (t) = Ci x i (t)(4b); where x f (t) = [p i (t) T v i (t) T ] T is the state variable of the i-th UAV, v i (t), p i (t),u i (t) represents the speed, position and control input of the i-th UAV, is the differential of the state variable of the i-th UAV, A i , B i , C i They are the system matrix, input matrix, and output matrix of the state space model of the UAV system, satisfying: C i =[I 3 0],I 3 represents a 3D identity matrix, ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let Δε i , and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i Represent the nominal part and uncertain part of the uncertain control gain matrix respectively, and the matrix A i , B i All by nominal part and the uncertain part ΔA i , ΔB i Superimposed,

[0027] Furthermore, in step 3, a directed graph G = (V, E) is used to describe the communication network of the drone swarm, where V = {0, 1, ..., N} is a node set, E = {(i, j), i, j∈V, i≠j} is an edge set, node 0 is associated with the virtual leader system, node i = 1, ..., N is associated with the i-th drone, N is the number of drones, and the weighted adjacency matrix of the directed graph G is a ijrepresents the communication weight coefficient between UAV i and UAV j. The directed graph G contains a directed spanning tree with the virtual leader system as the root node.

[0028] Furthermore, considering that the virtual leader system is not known in advance by each UAV, an output-based adaptive distributed observer is designed to estimate the virtual leader system information required by each UAV; let the virtual leader system matrix S 0 The minimum polynomial of is: φ +α 0,1 λ φ-1 +...+α 0,φ-1 λ+α 0,φ , λ is the main variable of the minimal polynomial, φ is the order of the minimal polynomial, α 0,1 ,…,α 0,φ-1 ,α 0,φ is the coefficient of the minimum polynomial, take α 0 =[α 0,1 …α 0,φ ] 1 Represented by the virtual leader system matrix S 0 The column vector of the minimum polynomial coefficients, based on the output of the adaptive distributed observer:

[0029]

[0030] Among them, μ α >0 and μ ζ >0 is the gain of the distributed observer, N is the number of drones, α i (t) = [α i,1 (t),…,α i,φ (t)] T is the i-th UAV’s pair α 0 The estimated value of , t is the time, α i,1 (t),…,α i,φ (t) is the i-th UAV’s response to α 0,1 …α 0,φ The estimated value of α j (t) is the jth UAV observer information received by the i-th UAV from the communication network, ζ i (t) is the state of the observer, is the global flight path vector p of the i-th UAV 0 (t) is estimated, the system matrix of the observer is α i The differential of (t), For i The differential of (t), R φ×φ is a φ×φ dimensional matrix, a ijis the communication weight coefficient between UAV i and UAV j, a i0 is the communication weight coefficient between UAV i and the virtual leader system, I 3 is a 3×3 dimensional identity matrix, is the output matrix of the observer, Σ i (t) is the only positive solution of the algebraic Riccati equation, which is:

[0031]

[0032] Among them, I φ is the φ×φ-dimensional identity matrix.

[0033] Furthermore, in step 5, according to the estimated virtual leader information, an asymptotic internal model (G i1 (t),G 02 ) to handle the uncertain system parameters in the UAV system, G i1 (t) is the dynamic model related to the virtual leader system, G 02 To ensure that the i-th UAV constructs an asymptotic internal model (G i1 (t),G 02 ) Additional model for stabilization, G i1 (t) and G 02 satisfy:

[0034]

[0035] Among them, I 3 is a 3×3 dimensional unit diagonal matrix, α i,φ (t) is the system matrix S of the observer i The minimum polynomial coefficient, R 3(φ+1)×3(φ+1) represents a 3(φ+1)×3(φ+1) dimensional matrix, R 3(φ+1)×3 represents a 3(φ+1)×3 dimensional matrix, where φ is the virtual leader system matrix S 0 Minimum polynomial order.

[0036] Furthermore, in step 6, the asymptotic internal model is combined with the dynamic state feedback control law to define the matrix:

[0037]

[0038] in represents the nominal part of the system matrix of the UAV state space model, represents the nominal part of the control matrix, C i is the output matrix of the UAV system state space model, is the parameter matrix that combines the asymptotic internal model with the nominal part of the UAV state space model system matrix, is the parameter matrix that combines the asymptotic internal model with the nominal part of the control matrix of the UAV state space model, 0 6×3(φ+1) represents a 6×3(φ+1)-dimensional zero matrix, φ is the virtual leader system matrix S 0 Minimum polynomial order, 0 3(φ+1)×3 represents a 3(φ+1)×3 dimensional zero matrix, R (6+3(φ+1))×(6+3(φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, R (6+3(φ+1))×3 represents a (6+3(φ+1))×3-dimensional matrix;

[0039] According to the following algebraic Riccati equation, the controller feedback gain matrix K for the robust formation flight of UAVs is designed: i (t):

[0040]

[0041] where Λ i is a positive solution, Λ i ∈R (6+3(φ+1))×(6+3(φ+1)) , K i (t) is the controller feedback gain matrix; in order to is the Hurwitz matrix, let the feedback gain coefficient R (6+3(φ+1))×(6+3(Φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, I 6+3(φ+1) represents the (6+3(φ+1))×(6+3(φ+1))-dimensional identity matrix, R 3 ×(6+(3φ+1)0 It is a 3×(6+3(φ+1)) dimensional matrix.

[0042] Furthermore, in step 6, let the controller feedback gain matrix K i (t) = [K i1 (t)K i2 (t)], design a robust formation flight controller for UAVs:

[0043] u i (t) = K i1 (t)x i (t)+K i2 (t)z i (t)(6a);

[0044]

[0045]

[0046] Where K i1 (t)∈R3×6 ,K i2 (t)∈R 3×3(φ+1) ,u i (t) is the control input of the i-th UAV, x i (t) is the state variable of the i-th UAV, z i (t) represents the state of the dynamic compensator, For z i The differential of (t), (G i1 (t),G 02 ) is the asymptotic inner membrane, represents the equivalent formation flight tracking error of the i-th UAV, p i (t) is the drone position of the i-th drone, is the estimated value of the global flight path vector of UAV i, p fi Represents the relative position between the i-th UAV and the virtual navigator.

[0047] In summary, the present invention has the following advantages and beneficial effects over the prior art:

[0048] (1) An output-based adaptive distributed observer is designed to reduce the necessary communication information required for the UAV to estimate the global flight path vector, greatly reducing the communication load of the system.

[0049] (2) For the second-order UAV system, the case where the velocity damping matrix and the control gain matrix have uncertain parameters is considered. Based on the estimation of the minimum polynomial coefficients of the virtual leader system matrix, an asymptotic internal model for handling the uncertain system parameters is constructed, which can ensure the stability of the system even if the system parameters change around their nominal values. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a communication directed graph in an embodiment of the present invention;

[0051] Figure 2 A position change diagram of a UAV formation in an embodiment of the present invention;

[0052] Figure 3 A graph showing a change in the flight tracking error of a UAV in an embodiment of the present invention;

[0053] Figure 4 A graph showing a change in the estimation error of a drone observer in a drone formation according to an embodiment of the present invention;

[0054] Figure 5 The present invention is a flowchart of a fully distributed UAV robust formation control method based on minimal information according to an embodiment of the present invention. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical scheme and advantages of the embodiments of the present invention clearer, the specific implementation of the present invention will be clearly and completely described below in combination with the embodiments and drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0056] like Figure 5 As shown, a fully distributed UAV robust formation control method based on minimum information volume in this embodiment includes the following steps:

[0057] Step 1: Use the second-order system as the kinematic model of the UAV and establish the state space model of the UAV system. Suppose there are N UAVs, and the kinematic model of the i-th UAV is described as:

[0058]

[0059] Among them, v i (t),u i (t)∈R 3 represents the speed and control input of the i-th UAV, t is the time, represents the position p of the i-th drone i (t) and the differential of velocity, R 3 represents a 3D column vector; ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i They represent the nominal part and the uncertain part of the uncertain control gain matrix respectively. The state space model of the UAV system is described as:

[0060]

[0061] p i (t) = C i x i (t) (2b);

[0062] Among them, x i(t) = [p i (t) T v i (t) T ] T is the state variable of the i-th UAV, v i (t), p i (t),u i (t) represents the speed, position and control input of the i-th UAV, is the differential of the state variable of the i-th UAV, A i , B i , C i They are the system matrix, input matrix, and output matrix of the state space model of the UAV system, satisfying: C i =[I 3 0],I 3 represents a 3D identity matrix, ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let ε i = and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i Represent the nominal part and uncertain part of the uncertain control gain matrix respectively, and the matrix A i , B i All by nominal part and the uncertain part ΔA i , ΔB i Superimposed,

[0063] Step 2: Establish a state space model of the virtual leader system to describe the global flight path vector of the UAV; the state space model of the virtual leader system is described as:

[0064]

[0065] p 0 (t) = W 0 r 0 (t)(3b);

[0066] where p 0(t)∈R 3 represents the global flight path vector of the UAV, r 0 (t)∈R q represents the q-dimensional internal state of the virtual leader, t is the time, represents the differential of the internal state of the virtual leader; S 0 ∈R q×q is the system matrix of the virtual leader system, R represents the real number field, W 0 ∈R 3×q is the output matrix of the virtual leader system.

[0067] The UAV formation vector and formation flight tracking error are described as:

[0068] p ri (t) = p 0 (t)+p fi (4a);

[0069] e i (r) = p i (t)-p 0 (t)-p fi (4b); where p ri (t)∈R 3 is the formation vector of UAV i; p 0 (t)∈R 3 is the global flight path vector of the UAV, which represents the reference flight path of the entire UAV swarm and is regarded as a virtual leader; i (t) is the position of the i-th UAV; p fi ∈R 3 is the local formation vector, indicating the relative position between the i-th UAV and the virtual leader; e i (t)∈R 3 is the formation flight tracking error of the i-th UAV.

[0070] Step 3: Use a directed graph to describe the communication network of the drone swarm;

[0071] The communication network of the drone swarm is described by a directed graph G = (V, E), where V = {0, 1, ..., N} is a node set, E = {(i, j), i, j∈V, i≠j} is an edge set, node 0 is associated with the virtual leader system, node i = 1, ..., N is associated with the i-th drone, N is the number of drones, and the weighted adjacency matrix of the directed graph G is a ij represents the communication weight coefficient between UAV i and UAV j. The directed graph G contains a directed spanning tree with the virtual leader system as the root node.

[0072] Step 4: Design an output-based adaptive distributed observer to estimate the virtual leader system information required by each UAV;

[0073] Considering that the virtual leader system is not known in advance by each UAV, an output-based adaptive distributed observer is designed to estimate the virtual leader system information required by each UAV. Let the virtual leader system matrix S 0 The minimum polynomial of is: φ +α 0,1 λ φ-1 +...+α 0,φ-1 λ+α 0,φ , λ is the main variable of the minimal polynomial, φ is the order of the minimal polynomial, α 0,1 ,…,α 0,φ-1 ,α 0,φ is the coefficient of the minimum polynomial, take α 0 =[α 0,1 …α 0,φ ] T Represented by the virtual leader system matrix S 0 The column vector of the minimum polynomial coefficients, φ is the virtual leader system matrix S 0 The highest order of the minimal polynomial, under the output-based adaptive distributed observer:

[0074]

[0075] Among them, μ α >0 and μ ζ >0 is the gain of the distributed observer, N is the number of drones, α i (t) = [α i,1 (t),…,α i,φ (t)] 0 is the i-th UAV’s pair α 0 The estimated value of , t is the time, α i,1 (t),…,α i,φ (t) is the i-th UAV’s response to α 0,1 …α 0,φ The estimated value of α j (t) is the jth UAV observer information received by the i-th UAV from the communication network, ζ i (t) is the state of the observer, is the global flight path vector p of the i-th UAV 0 (t), the observer's system matrix S i (t)= is α i The differential of (t), For i The differential of (t), Rφ×φ is a φ×φ dimensional matrix, a ij is the communication weight coefficient between UAV i and UAV j, a i0 is the communication weight coefficient between UAV i and the virtual leader system, I 3 is a 3×3 dimensional identity matrix, w 0 =[1 0…0]∈R 1×φ is the output matrix of the observer, Σ i (t) is the only positive solution of the algebraic Riccati equation, which is:

[0076]

[0077] Among them, I φ is the φ×φ-dimensional identity matrix.

[0078] Step 5: Based on the output information of the observer, construct an asymptotic internal model to deal with the uncertain parameters in the UAV system;

[0079] According to the estimated virtual leader information, construct an asymptotic internal model (G i1 (t),G 02 ) to handle the uncertain system parameters in the UAV system, G i1 (t) is the dynamic model related to the virtual leader system, G 02 To ensure (G i1 (t),G 02 ) Additional model for stabilization, G i1 (t) and G 02 satisfy:

[0080]

[0081] Among them, I 3 is a 3×3 dimensional unit diagonal matrix, α i,φ (t) is the system matrix S of the observer i The minimum polynomial coefficient, R 3(φ+1)×3(φ+1) represents a 3(φ+1)×3(φ+1) dimensional matrix, R 3(φ+1)×3 represents a 3(φ+1)×3 dimensional matrix, where φ is the virtual leader system matrix S 0 Minimum polynomial order.

[0082] Step 6: Combine the asymptotic internal model with the dynamic state feedback controller to construct a UAV robust formation flight controller, which is used together with the output-based adaptive distributed observer to control the fully distributed UAV swarm robust formation flight.

[0083] Combine the asymptotic internal model with the dynamic state feedback control law and define the matrix:

[0084]

[0085] in represents the nominal part of the system matrix of the UAV state space model, represents the nominal part of the control matrix, C i is the output matrix of the UAV system state space model, is the parameter matrix that combines the asymptotic internal model with the nominal part of the UAV state space model system matrix, is the parameter matrix that combines the asymptotic internal model with the nominal part of the control matrix of the UAV state space model, 0 6×3(φ+1) represents a 6×3(φ+1)-dimensional zero matrix, φ is the virtual leader system matrix S 0 Minimum polynomial order, 0 3(φ+1)×3 represents a 3(φ+1)×3 dimensional zero matrix, R (6+3(φ+1))×(6+3(φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, R (6+3(φ+1))×3 represents a (6+3(φ+1))×3-dimensional matrix;

[0086] According to the following algebraic Riccati equation, the controller feedback gain matrix K for the robust formation flight of UAVs is designed: i (t):

[0087]

[0088] where Λ i is a positive solution, Λ i ∈R (6+3(φ+1))×(6+3(φ+1)) , K i (t) is the controller feedback gain matrix; in order to is the Hurwitz matrix, let the feedback gain coefficient R (6+3(φ+1))×(6+3(φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, I 6+3(φ+1) represents the (6+3(φ+1))×(6+3(φ+1))-dimensional identity matrix, K 3 ×(6+(3φ+1)) It is a 3×(6+3(φ+1)) dimensional matrix.

[0089] Assume the controller feedback gain matrix K i (t) = [K i1 (t)K i2 (t)], design a robust formation flight controller for UAVs:

[0090] u i (t) = K i1 (t)x i (t)+K i2 (t)zi (t)(6a);

[0091]

[0092] Where K i1 (t)∈R 3×6 ,K i2 (t)∈R 3×3(φ+1) ,u i (t) is the control input of the i-th UAV, x i (t) is the state variable of the i-th UAV, z i (t) represents the state of the dynamic compensator, For z i The differential of (t), (G i1 (t),G 02 ) is the asymptotic inner membrane, represents the equivalent formation flight tracking error of the i-th UAV, p i (t) is the drone position of the i-th drone, is the estimated value of the global flight path vector of UAV i, p fi Represents the relative position between the i-th UAV and the virtual navigator.

[0093] As a specific embodiment, in this embodiment, Matlab is used to simulate and verify 5 drones. Figure 1 In the communication directed graph shown, number 0 is the virtual leader, and numbers 1,…,5 correspond to 5 drones respectively. It is expected that the 5 drones can be formed into a wedge shape, and while the whole drone moves at a uniform speed along the y-axis, its height changes in the form of a sine function.

[0094] In the kinematic model of the i-th (i=1,...,5) UAV, the nominal part of the velocity damping matrix is ​​known to be The nominal part of the control gain matrix is ​​Γ i o =I 3 The uncertain parts of the velocity damping matrix and the control gain matrix satisfy Δε i =Δω i =i·I 3 .

[0095] According to the formation requirements, as an embodiment, let the angular velocity ω = 0.3 rad / s, and the global flight path vector p 0 (t) = [0 t 15 sin (ωt)] T , the system matrix S of the virtual leader system 0 , the output matrix W 0 And the initial value of the state satisfies:

[0096]

[0097] The local formation vector satisfies:

[0098]

[0099] The initial position of each drone is set to:

[0100]

[0101] The gain μ of the distributed observer a =1,μ ζ =10, feedback gain coefficient κ i =2.

[0102] like Figure 1 As shown in FIG. 1 , it is a communication directed graph in this embodiment, where number 0 is a virtual leader, and 1, …, 5 correspond to 5 drones respectively. Then the adjacency matrix a of the communication directed graph can be obtained: ij , where i = 0, 1, 2, 3, 4, 5, j = 0, 1, 2, 3, 4, 5:

[0103]

[0104] The motion trajectory of each drone is as follows: Figure 2 As shown in Figure 2, the five drones can quickly achieve the desired formation. In the x, y, and z directions, the flight tracking errors of each drone change as shown in Figure 2. Figure 3 (a) Figure 3 (b) Figure 3 As shown in (c), the error curves converge quickly to 0. In the x, y, and z directions, the estimated errors of each drone observer are as follows: Figure 4 (a) Figure 4 (b) Figure 4 As shown in (c), the error curves converge quickly to 0. It can be found that the formation control method proposed in the present invention can effectively solve the low communication volume and high robustness requirements in the formation control process of the drone group. So far, the digital simulation of the present invention has been completed, and its effectiveness has been verified.

[0105] The present invention can be applied to the problem of robust formation control of drone swarms under low communication load requirements. The constructed fully distributed drone swarm robust formation flight control method based on minimal virtual leader information includes an output-based adaptive distributed observer and a drone robust formation flight controller, which effectively improves the robustness of the system while ensuring the efficient completion of the formation mission.

[0106] The above examples are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above examples. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A fully distributed UAV robust formation control method based on minimum information, characterized in that: The following steps are involved: Step 1: Use the second-order system as the kinematic model of the UAV and establish the state space model of the UAV system; Step 2: Establish a state space model of the virtual leader system to describe the global flight path vector of the UAV; Step 3: Use a directed graph to describe the communication network of the drone swarm; Step 4: Design an output-based adaptive distributed observer to estimate the virtual leader system information required by each UAV; Step 5: Based on the output information of the observer, construct an asymptotic internal model to deal with the uncertain parameters in the UAV system; Step 6: Combine the asymptotic internal model with the dynamic state feedback controller to construct a UAV robust formation flight controller, which is used together with the output-based adaptive distributed observer to control the fully distributed UAV swarm robust formation flight.

2. A fully distributed UAV robust formation control method based on minimum information according to claim 1, characterized in that: In step 1, a second-order system is used to describe the motion state of the UAV. Suppose there are N UAVs, and the kinematic model of the i-th UAV is described as: Among them, v i (t),u i (t)∈R 3 represents the speed and control input of the i-th UAV, t is the time, represents the position p of the i-th drone i (t) and the differential of velocity, R 3 represents a 3D column vector; ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i represent the nominal part and uncertain part of the uncertain control gain matrix respectively.

3. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 2, the state space model of the virtual leader system is established to generate the global flight path vector p0(t)∈R of the UAV 3 , the state space model of the virtual leader system is described as: p0(t)=W0r0(t)(2b); Where r0(t)∈R q represents the q-dimensional internal state of the virtual leader, t is the time, represents the differential of the internal state of the virtual leader; S0∈R q×q is the system matrix of the virtual leader system, R represents the real number field, W0∈R 3×q is the output matrix of the virtual leader system.

4. A fully distributed UAV robust formation control method based on minimum information according to claim 3, characterized in that: The UAV formation vector and formation flight tracking error are described as: p ri (t)=p0(t)+p fi (3a); e i (t)=p i (t)-p0(t)-p fi (3b); Among them, p ri (t)∈R 3 is the formation vector of UAV i; p0(t)∈R 3 is the global flight path vector of the UAV, which represents the reference flight path of the entire UAV swarm and is regarded as a virtual leader; i (t) is the position of the i-th UAV; p fi ∈R 3 is the local formation vector, indicating the relative position between the i-th UAV and the virtual leader; e i (t)∈R 3 is the formation flight tracking error of the i-th UAV.

5. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 1, a state space model of the UAV system is established. The state space model of the UAV system is described as: p i (t)=C i x i (t) (4b)? Among them, x i (t) = [p i (t) T v i (t) T ] T is the state variable of the i-th UAV, v i (t), p i (t),u i (t) represents the speed, position and control input of the i-th UAV, is the differential of the state variable of the i-th UAV, A i , B i , C i They are the system matrix, input matrix, and output matrix of the state space model of the UAV system, satisfying: C i =[I30], I3 represents a 3D identity matrix, ε i ∈R 3×3 represents the uncertain velocity damping matrix, and let and Δε i denote the nominal part and the uncertain part of the uncertain velocity damping matrix respectively; Γ i ∈R 3×3 Denotes the uncertain control gain matrix, and let Γ i =Γ i 0 +ΔΓ i , Γ i 0 and ΔΓ i Represent the nominal part and uncertain part of the uncertain control gain matrix respectively, and the matrix A i , B i All by nominal part and the uncertain part ΔA i , ΔB i Superimposed, 6. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 3, a directed graph G = (V, E) is used to describe the communication network of the drone swarm, where V = {0, 1, ..., N} is a node set, E = {(i, j), i, j∈V, i≠j} is an edge set, node 0 is associated with the virtual leader system, node i = 1, ..., N is associated with the i-th drone, N is the number of drones, and the weighted adjacency matrix of the directed graph G is a ij represents the communication weight coefficient between UAV i and UAV j. The directed graph G contains a directed spanning tree with the virtual leader system as the root node.

7. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 4, considering that the virtual leader system is not known in advance by each UAV, an output-based adaptive distributed observer is designed to estimate the virtual leader system information required by each UAV; Let the minimum polynomial of the virtual leader system matrix S0 be: φ +α 0,1 λ φ-1 +...+α 0,φ-1 λ+α 0,φ , λ is the main variable of the minimal polynomial, φ is the order of the minimal polynomial, α 0,1 ,…,α 0,φ-1 ,α 0,φ is the coefficient of the minimum polynomial, and α0=[α 0,1 …α 0,φ ] T represents the column vector consisting of the minimum polynomial coefficients of the virtual leader system matrix S0, based on the output of the adaptive distributed observer: Among them, μ α >0 and is the gain of the distributed observer, N is the number of drones, α i (t) = [α i,1 (t),…,α i,φ (t)] T is the estimated value of α0 by the i-th UAV, t is the time, α i,1 (t),…,α i,φ (t) is the i-th UAV’s response to α 0,1 …α 0,φ The estimated value of α j (t) is the jth UAV observer information received by the i-th UAV from the communication network, is the state of the observer, is the estimate of the global flight path vector p0(t) by the i-th UAV, and the system matrix of the observer is α i The differential of (t), for The differential, R φ×φ is a φ×φ dimensional matrix, a ij is the communication weight coefficient between UAV i and UAV j, a i0 is the communication weight coefficient between UAV i and the virtual leader system, I3 is a 3×3 dimensional unit matrix, is the output matrix of the observer, Σ i (t) is the only positive solution of the algebraic Riccati equation, which is: Among them, I φ is the φ×φ-dimensional identity matrix.

8. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 5, based on the estimated virtual leader information, an asymptotic internal model (G i1 (t),G 02 ) to handle the uncertain system parameters in the UAV system, G i1 (t) is the dynamic model related to the virtual leader system, G 02 To ensure that the i-th UAV constructs an asymptotic internal model (G i1 (t),G 02 ) Additional model for stabilization, G i1 (t) and G 02 satisfy: Among them, I3 is a 3×3 dimensional unit diagonal matrix, α i,φ (t) is the system matrix C of the observer i The minimum polynomial coefficient, R 3 (φ+1)×3(φ+1) represents a 3(φ+1)×3(φ+1) dimensional matrix, R 3(φ+1)×3 represents a 3(φ+1)×3 dimensional matrix, where φ is the order of the minimal polynomial of the virtual leader system matrix S0.

9. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 6, characterized in that: In step 6, the asymptotic internal model is combined with the dynamic state feedback control law to define the matrix: in represents the nominal part of the system matrix of the UAV state space model, represents the nominal part of the control matrix, C i is the output matrix of the UAV system state space model, is the parameter matrix that combines the asymptotic internal model with the nominal part of the UAV state space model system matrix, is the parameter matrix that combines the asymptotic internal model with the nominal part of the control matrix of the UAV state space model, 0 6×2(φ+1) represents a 6×3(φ+1)-dimensional zero matrix, φ is the order of the minimum polynomial of the virtual leader system matrix S0, 0 3(φ+1)×3 represents a 3(φ+1)×3 dimensional zero matrix, R (6+3(φ+1))×(6+3(φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, R (6+3(φ+1))×3 represents a (6+3(φ+1))×3-dimensional matrix; According to the following algebraic Riccati equation, the controller feedback gain matrix K for the robust formation flight of UAVs is designed: i (t): where Λ i is a positive solution, Λ i ∈R (6+3(φ+1))×(6+3(φ+1)) , K i (t) is the controller feedback gain matrix; in order to is the Hurwitz matrix, let the feedback gain coefficient R (6+3(φ+1))×(6+3(φ+1)) represents a (6+3(φ+1))×(6+3(φ+1))-dimensional matrix, I 6+3(φ+1) represents the (6+3(φ+1))×(6+3(φ+1))-dimensional identity matrix, R 3 ×(6+(3φ+1)) It is a 3×(6+3(φ+1)) dimensional matrix.

10. The method for robust formation control of fully distributed UAVs based on minimum information according to claim 1, characterized in that: In step 6, let the controller feedback gain matrix K i (t) = [K i1 (t)K i2 (t)], design a robust formation flight controller for UAVs: Where K i1 (t)∈R 3×6 ,K i2 (t)∈R 3×3(φ+1) ,u i (t) is the control input of the i-th UAV, x i (t) is the state variable of the i-th UAV, z i (t) represents the state of the dynamic compensator, For z i The differential of (t), (G i1 (t),G 02 ) is the asymptotic inner membrane, represents the equivalent formation flight tracking error of the i-th UAV, p i (t) is the drone position of the i-th drone, is the estimated value of the global flight path vector of UAV i, p fi Represents the relative position between the i-th UAV and the virtual navigator.

Images