An Elastic Formation Control Method for Unmanned Aerial Vehicles Considering Input Constraints and Speed Constraints

Abstract

The present invention discloses an elastic formation control method for unmanned aerial vehicles (UAVs) considering input constraints and speed constraints. First, based on the double-mass spring system and considering the elastic constraint relationship between UAV formations, a dynamic model of UAV elastic formation is established. Then, considering the input and speed constraints, a consensus control method using local velocity information and relative velocity information is designed. Finally, a leader-follower model is introduced, and a distributed formation control strategy is adopted to design a leader-follower controller under input and speed constraints, enabling the follower UAVs to quickly track the flight path of the leader under input and speed constraints, and the position tracking error and speed tracking error finally converge to 0 consistently. By establishing a dynamic model of the UAV elastic formation model affected by inter-aircraft collisions and limited communication data volume, and considering the input saturation and UAV speed limitation problems in the consensus control, the present invention effectively improves the anti-saturation ability of the UAV formation.

Description

Technical Field

[0001] The present invention relates to an elastic formation control method for unmanned aerial vehicles (UAVs) considering input constraints and speed constraints, and belongs to the technical field of UAV formation control. Background Technique

[0002] In recent years, the cooperative control of multi-UAV systems has been increasingly widely applied in military and civilian fields, attracting great attention. At present, the design of many control algorithms is based on simplified models. In actual engineering, in addition to considering the anti-collision problem between UAVs and the limited communication data volume problem, it is also necessary to consider the input saturation problem caused by the limited driving power of physical devices, and the speed constraint problem caused by the hovering of fixed-wing UAVs and the limited motor speed. In these cases, it is very necessary to have a consistency controller that simultaneously considers speed and input saturation. However, few current studies have considered this problem.

[0003] Currently, most control methods for multi-UAV system formations mainly include the leader-following method, the virtual structure method, and the behavior-based method. Only a few studies have considered the anti-collision problem between UAVs. Fortunately, the elastic formation model can effectively solve the anti-collision problem between UAVs. However, the unimproved elastic formation model requires a large amount of communication resources, and when the number of UAV clusters increases significantly, the force relationship of each UAV becomes particularly complex, which may lead to a decline in the dynamic performance and flexibility of the UAV formation. Regarding the research on input constraints and speed constraints, there are relatively many studies on the anti-saturation problem of second-order systems in the existing literature, and there are very few studies on the second-order system simultaneously affected by input constraints and speed constraints. Therefore, it is of great significance and value to design a control strategy considering input constraints and speed constraints based on the improved elastic formation model to ensure the safe and stable operation of the UAV formation system. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an elastic formation control method for UAVs considering input constraints and speed constraints, by establishing a dynamic model problem of the UAV elastic formation model affected by inter-aircraft collisions and limited communication data volume, and considering the input saturation problem and the UAV speed constraint problem in the consistency control method, effectively improving the anti-saturation ability of the UAV formation.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] An elastic formation control method for UAVs considering input constraints and speed constraints includes the following steps:

[0007] Step 1: Based on the dual-mass spring system, considering the elastic constraint relationship between UAV formations, establish the dynamic model of UAV elastic formations.

[0008] Step 2: Simplify the dynamic model of UAV elastic formations established in Step 1 into a second-order system equation.

[0009] Step 3: For the second-order system equation of UAV formations, design a distributed consensus controller using local velocity information and relative velocity information to achieve the consistency of velocity and input constraints.

[0010] Step 4: Introduce a virtual leader UAV, regard all UAVs in the UAV formation as follower UAVs, and design a leader-follower controller under input and velocity constraints, so that the follower UAVs can follow the flight path of the given virtual leader UAV under input and velocity constraints.

[0011] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects:

[0012] 1. The UAV elastic formation model established by the present invention defines an elastic constraint between each UAV and its neighbor UAVs. When the distance between UAVs is too close, the elastic constraint repulsive force is greater, which can effectively avoid the problem of mutual collision between UAVs.

[0013] 2. The present invention uses a directed graph communication topology structure and a leader-follower system model. It does not require all UAVs to communicate with each other, and can perform selective communication according to task requirements, thereby reducing communication burden and resource consumption and optimizing bandwidth usage. In addition, through the directed graph communication structure, task allocation can be more effectively achieved.

[0014] 3. The present invention considers a consensus controller based on input constraints and velocity constraints, which does not require global graph information such as the Laplacian matrix of a general directed communication graph, improving the robustness of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flowchart of the UAV elastic formation control method considering input constraints and velocity constraints of the present invention;

[0016] Figure 2 is the communication topology diagram of the UAV formation system in the embodiment of the present invention;

[0017] Figure 3 is a schematic diagram of the three-dimensional flight trajectory of the UAV formation in the embodiment of the present invention;

[0018] Figure 4 is the follower UAV of the UAV formation in the embodiment of the present invention position tracking error curve of the channel;

[0019] Figure 5 is the follower UAV in the UAV formation of the embodiment of the present invention The position tracking error curve of the channel;

[0020] Figure 6 is the follower UAV in the UAV formation of the embodiment of the present invention The position tracking error curve of the channel;

[0021] Figure 7 is the follower UAV in the UAV formation of the embodiment of the present invention The speed tracking error curve of the channel;

[0022] Figure 8 is the follower UAV in the UAV formation of the embodiment of the present invention The speed tracking error curve of the channel;

[0023] Figure 9 is the follower UAV in the UAV formation of the embodiment of the present invention The speed tracking error curve of the channel;

[0024] Figure 10 is the follower UAV in the UAV formation of the embodiment of the present invention The speed response curves of three channels;

[0025] Figure 11 is the follower UAV in the UAV formation of the embodiment of the present invention The control input response curves of three channels. Detailed implementation manners

[0026] The following details the implementation manners of the present invention. Examples of the implementation manners are shown in the drawings. The implementation manners described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0027] As Figure 1 shown, the present invention proposes a UAV elastic formation control method considering input constraints and speed constraints, including the following steps:

[0028] Step 1: Based on the double-mass spring system, considering the elastic constraint relationship between UAV formations, establish the dynamic model of the UAV elastic formation.

[0029] Assume that the studied multi-UAV system consists of UAVs. Its communication network is abstracted into a directed graph to represent, where represents the set of nodes; The set of edges connecting to the node ; The edge represents the information flow from node to node . The adjacency matrix of the graph , , and when , if , then . The neighbor set of node is defined as . The degree of node is the number of neighbors , denoted by , then the degree matrix is defined as: . .

[0030] Considering the elastic constraint relationship between UAV formations, the intangible constraint of the relative position between two UAVs in the formation is defined as the formation elastic constraint, also known as the formation spring. Each end of the UAV formation elastic constraint is connected to a UAV. The formation elastic constraint force is related to the relative distance between the two UAVs. When the distance exceeds the formation distance, the elastic constraint exhibits gravitational force; when it is less than the formation distance, the elastic constraint exhibits repulsive force. Using to represent the stiffness of the UAV formation spring, with the unit of , it also represents the strength of the UAV elastic constraint. Establish the dynamic model of the UAV elastic formation:

[0031] ,

[0032] where, represents the mass of the -th UAV, represents the position information of the -th UAV, , represents the stiffness matrix of the elastic constraint of the -th UAV, and respectively represent the adjacency matrix and degree matrix of the UAV formation communication network, is the expected formation distance between UAVs, is the control input.

[0033] Step 2: Based on Step 1, further simplify the dynamic model of the UAV elastic formation into the form of a second-order system equation.

[0034] Based on Step 1, by combining the and terms in the dynamic model of the UAV elastic formation, we can obtain:

[0035] ,

[0036] wherein, represents the formation position error of the th unmanned aerial vehicle (UAV) relative to the th UAV.

[0037] Further simplify the dynamic model of the elastic formation of UAVs to obtain the following model:

[0038] ,

[0039] Based on Step 1 and the above description, decompose the dynamic model of each UAV in the elastic formation of UAVs into second-order system equations:

[0040] ,

[0041] wherein, represents the velocity information of the th UAV.

[0042] Step 3: Considering the input constraint and velocity constraint conditions, design a consensus control method using local velocity information and relative velocity information.

[0043] For the second-order system equations of the UAV formation described in Step 2, propose a distributed consensus controller using local velocity information and relative velocity information to achieve the consensus of velocity and input constraints. Assign a constant formation vector to each UAV , and let represent the expected relative position of UAV and UAV in the formation. When , is satisfied, the formation control is achieved.

[0044] Design the original control input of the UAV formation system as:

[0045] ,

[0046] wherein, , , , , , is the sign function, so can be obtained.

[0047] Based on Step 1 and the above description, the control input can be rewritten as:

[0048] ,

[0049] Among them, .

[0050] To limit the range of the control input and restrict the elastic force in step 1, the second-order system equation is rewritten as:

[0051] ,

[0052] Let the elastic coefficient matrix , then the actual control input of the UAV is:

[0053] ,

[0054] Among them, .

[0055] Step 4: Introduce a leader-follower model and design a leader-follower controller under input and speed constraints, so that the follower UAV can still follow the flight path of the given leader UAV under input and speed constraints, and the position tracking error and speed tracking error finally converge to 0 uniformly.

[0056] For the second-order system equation of the UAV formation in step 3, the position and speed of the UAV cannot be directly controlled, so a leader UAV needs to be introduced to guide the UAV to the desired trajectory. The leader UAV only needs to interact with a limited number of UAVs in the communication network. Define all other UAVs except the leader as followers, and the leader UAV is represented as node 0.

[0057] The leader also needs to satisfy speed constraints and input constraints. Define the leader dynamics model as follows:

[0058] ,

[0059] Among them, , can be freely designed to specify the desired trajectory. Under the conditions and , it can be seen that both the speed constraints and input constraints of the leader are satisfied.

[0060] According to the leader dynamics model and the second-order system equation of the UAV formation in step 2, design the leader-follower controller as follows:

[0061] ,

[0062] Among them, , .

[0063] In practical applications, the discontinuous term It will cause the chattering phenomenon. To reduce the chattering of the control input, the sign function in the leader-follower controller can be replaced by the following continuous saturation function :

[0064] ,

[0065] where .

[0066] To test the cooperative control performance of the elastic formation of the unmanned aerial vehicles designed in the present invention, a simulation experiment was designed according to the model and controller algorithm of the present invention. On a computer with a configuration of CPU: Intel(R) Core(TM) i5 10500 and on-board RAM of 16 GB, a simulation environment was built using MATLAB R2023a / Simulink for simulation.

[0067] The leader-follower model consists of 1 leader unmanned aerial vehicle and 5 follower unmanned aerial vehicles. 0 is the leader, and 1, 2, 3, 4, 5 are the followers. The leader 0 only communicates with the follower 1, and assuming that the communication graph is directed, the communication topology of the unmanned aerial vehicle elastic formation system is as Figure 2 shown. According to Figure 2 the information, some related matrices can be obtained:

[0068] Adjacency matrix , degree matrix , Laplacian matrix ;

[0069] The positions of the followers relative to the leader are set as , , , , , and the desired trajectory of the leader is set as: . The model parameters of the unmanned aerial vehicle elastic formation are shown in Table 1, and the simulation parameters of the controller are shown in Table 2.

[0070] Table 1 Unmanned Aerial Vehicle Formation Model Parameters

[0071]

[0072] Table 2 Controller Parameters

[0073]

[0074] The present invention provides a method for elastic formation control of unmanned aerial vehicles considering input constraints and speed constraints, Figure 3 which is the three-dimensional flight trajectory effect diagram of the unmanned aerial vehicle formation. It can be seen that the flight trajectory of the control method proposed by the present invention can converge quickly and has high tracking accuracy. Figures 4 to 6This is the follower UAV in the UAV formation of the present invention The trajectory tracking error curves of three channels can be seen The trajectory tracking error of the channel converges to within 0.2 at 5.27 s The trajectory tracking error of the channel converges to within 0.2 at 8.45 s The trajectory tracking error of the channel converges to within 0.2 at 0.91 s Figures 7 to 9 This is the follower UAV in the UAV formation of the present invention The speed tracking error curves of three channels can be seen The speed tracking error of the channel converges to within 0.2 at 6.30 s The speed tracking error of the channel converges to within 0.2 at 9.40 s The speed tracking error of the channel converges to within 0.2 at 0.58 s Figure 10 This is the follower UAV in the UAV formation of the present invention The speed response curves of three channels can be seen that the speeds of the follower UAVs are all within the allowable amplitude constraints Figure 11 This is the follower UAV in the UAV formation of the present invention The control input response curves of three channels can be seen that the amplitudes of the control input signals are within the allowable constraints

[0075] Based on the same inventive concept, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the foregoing UAV elastic formation control method considering input limitation and speed limitation are implemented

[0076] Based on the same inventive concept, an embodiment of the present application provides a computer-readable storage medium. The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the foregoing UAV elastic formation control method considering input limitation and speed limitation are implemented

[0077] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code

[0078] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions executed by the processor of the computer or other programmable data processing device generate a means for implementing the functions specified in one flow Figure 1 one flow or more flows and / or blocks Figure 1 one block or more blocks.

[0079] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction means that implements the functions specified in one flow Figure 1 one flow or more flows and / or blocks Figure 1 one block or more blocks.

[0080] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in one flow Figure 1 one flow or more flows and / or blocks Figure 1 one block or more blocks.

[0081] The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention.

Claims

1. An elastic formation control method for unmanned aerial vehicles considering input constraints and speed constraints, characterized in that It includes the following steps: Step 1: Based on the dual-mass spring system, considering the elastic constraint relationship between UAV formations, establish the dynamic model of UAV elastic formations; Step 2: Simplify the dynamic model of UAV elastic formations established in Step 1 into a second-order system equation; Step 3: For the second-order system equation of UAV formations, design a distributed consensus controller using local velocity information and relative velocity information to achieve the consistency of velocity and input constraints; In Step 3, the formula of the distributed consensus controller using local velocity information and relative velocity information is as follows: Among them, K fi = KB, K = diag{k1, k2, k3}, v min and v max are the minimum speed and the maximum speed of the UAV respectively. k1, k2, k3 are all constants greater than 0, b1, b2, b3 are all constants greater than 0. v i and v j represent the speed information of the i-th and j-th UAVs respectively. m i represents the mass of the i-th UAV, represents the formation position error of the i-th UAV relative to the j-th UAV. a ij represents the element in the adjacency matrix A of the directed graph G of the UAV formation communication network. u i ' represents the distributed consensus controller of the i-th UAV; Step 4: Introduce a virtual leader UAV, regard all UAVs in the UAV formation as follower UAVs, and design a leader-follower controller under input and velocity constraints, so that the follower UAVs can follow the flight path of the given virtual leader UAV under input and velocity constraints.

2. The elastic formation control method for an unmanned aerial vehicle considering input constraints and speed constraints according to claim 1, wherein The specific process of Step 1 is as follows: It is assumed that the UAV formation consists of n UAVs, and the communication network of the UAV formation is represented by a directed graph G = {V, E}, where V = {r i , i = 1, 2, …, n} represents a set of n nodes, represents the set of edges connecting node r i and node r j ; the adjacency matrix of graph G is A = [a ij , a ii = 0, and when i ≠ j, if (r j , r i ) ∈ E, then a ij > 0. The edge (r j , r i ) represents the information flow from node r j to node r i ; the degree matrix of graph G is D = diag{deg(r1), deg(r2), …, deg(r n ), deg(r i ) represents the degree of node r i . Considering the elastic constraint relationship between UAV formations, the elastic binding force of the formation is related to the relative distance between two UAVs. When the distance exceeds the formation distance, the elastic constraint shows gravitational force, and when it is less than the formation distance, the elastic constraint shows repulsive force. Establish the dynamic model of UAV elastic formations as follows: where, m i represents the mass of the i-th UAV, I is the identity matrix, p i = [x i , y i , z i T represents the position information of the i-th UAV, K f = diag{K f1 , K f2 ,..., K fn}, K fi represents the stiffness matrix of the elastic constraint of the i-th UAV, A and D respectively represent the adjacency matrix and degree matrix of the UAV formation communication network, is the expected formation distance between UAVs, are the expected position information of the i-th and j-th UAVs respectively, F ci is the control input, i = 1,..., n.​ 3. The method for elastic formation control of drones considering input limitation and speed limitation according to claim 2, characterized in that, The specific process of Step 2 is as follows: Combine the p i and terms in the dynamic model of the elastic formation of UAVs to obtain: Among them, p j represents the position information of the j-th unmanned aerial vehicle; Simplify the combined model to obtain the dynamic model of each UAV in the UAV elastic formation: Decompose the dynamic model of each UAV in the UAV elastic formation into a second-order system equation: where v i = [v xi , v yi , v yi T .​ 4. The elastic formation control method for drones considering input limitation and speed limitation according to claim 3, characterized in that, In Step 4, the formula of the leader-follower controller under input and velocity constraints is as follows: Among them, u i represents the leader-follower controller of the i-th UAV, and the subscript 0 represents the virtual leader UAV; Let There is where sat ε (ω) is a saturation function, 0 < ε < 1, and sgn is a sign function.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, When the processor executes the computer program, it realizes the steps of the UAV elastic formation control method considering input constraints and velocity constraints as described in any one of claims 1 to 4.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it realizes the steps of the UAV elastic formation control method considering input constraints and velocity constraints as described in any one of claims 1 to 4.

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