A formation control method for a heterogeneous multi-agent system considering input constraints

Abstract

The application discloses a kind of heterogeneous multi-agent system formation control method considering input limited, belong to the field of aviation and navigation technology.The method includes the following steps: first, according to Newton-Euler principle, establish quadrotor unmanned aerial vehicle and unmanned surface ship mathematical model;Then, quadrotor unmanned aerial vehicle and unmanned surface ship mathematical model are simplified, introduce controller saturation function, obtain quadrotor unmanned aerial vehicle and unmanned surface ship XOY plane position mathematical model;Second, establish heterogeneous multi-agent system communication topology graph, based on virtual leader, obtain each quadrotor unmanned aerial vehicle and unmanned surface ship tracking error, establish each agent sliding mode function;Finally, combined with sliding mode control and auxiliary system design anti-saturation controller, realize the formation control of heterogeneous multi-agent system.The method of the application considers the formation control of heterogeneous multi-agent system under input limited, realizes the anti-saturation control of heterogeneous multi-agent system, improves the stability and robustness of formation system.

Description

Technical Field

[0001] This invention relates to unmanned aerial vehicle (UAV) system formation control technology, and in particular to a formation control method for heterogeneous multi-agent systems that takes into account input constraints. Background Technology

[0002] In recent years, due to the limitations of individual quadcopter drones or unmanned surface vessels (USVs) in performing monitoring tasks, heterogeneous multi-agent systems composed of quadcopter drones and USVs have been developed to improve monitoring efficiency. This system fully utilizes the wide operating range and broad field of view of quadcopter drones, as well as the high speed of USVs. By integrating these two different types of agents, this heterogeneous multi-agent system can simultaneously monitor relevant dynamics in the air and at sea, improving the comprehensiveness and efficiency of monitoring.

[0003] In heterogeneous multi-agent systems, different agents exhibit individual differences, possessing mathematical models and state variables with varying structures, which increases the complexity of controller design. Furthermore, during air-sea coordinated formation operations, actuators are typically set to optimal execution ranges for safety reasons. However, during high-maneuver missions, these ranges may be exceeded, leading to limited controller inputs. These input limitations can range from affecting the dynamic and steady-state performance of the control system to causing system instability and significant economic losses.

[0004] Traditional formation control often considers a single intelligent agent system, making it difficult to meet the needs of diverse tasks. To improve the speed and convergence of formation systems while simultaneously meeting the requirements of collaborative control for air and sea unmanned systems, researching the formation control problem of heterogeneous multi-agent systems under input constraints is of great significance. Summary of the Invention

[0005] Purpose of the invention: The purpose of this invention is to provide a formation control method for heterogeneous multi-agent systems that considers input constraints. This method can solve the formation control problem of heterogeneous multi-agent systems while addressing the controller input saturation problem, thereby enhancing the speed and robustness of the control system and improving the cooperative control performance of the formation system.

[0006] Technical solution: The present invention provides a method for formation control of heterogeneous multi-agent systems considering input constraints, comprising the following steps:

[0007] S1. Establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle;

[0008] S2. When considering only the XOY plane position system in the heterogeneous multi-agent system, the mathematical models of the quadrotor UAV and unmanned surface vessel are simplified to obtain the XOY plane mathematical models of the quadrotor UAV and unmanned surface vessel, and then the mathematical model of the heterogeneous multi-agent system is obtained by introducing the controller saturation function.

[0009] S3. Establish a communication topology diagram for a heterogeneous multi-agent system, obtain the tracking error of each agent based on the virtual leader, and establish the sliding mode function for each agent; wherein, the communication topology diagram of the heterogeneous multi-agent system is described by a directed graph;

[0010] S4. Design the input of the compensation controller for the anti-saturation auxiliary system;

[0011] S5. Combine sliding mode control and auxiliary system to design an anti-saturation controller to realize the formation control of heterogeneous multi-agent system.

[0012] Furthermore, the mathematical model of the quadcopter UAV established in step S1 is as follows:

[0013]

[0014]

[0015] Where i1 represents the i1th quadcopter drone, They are respectively The first derivative, They are respectively The second derivative, This provides the position information of the center of gravity of the i1th quadcopter UAV in the ground coordinate system. This represents the roll angle, pitch angle, and attitude angle of the i1th quadcopter UAV in the body coordinate system. for The first derivative, for The second derivative, where m is the mass of the quadcopter drone, and K x ,K y ,K z K represents the air drag coefficient of the quadcopter UAV in the x, y, and z directions in the ground coordinate system. φ ,K θ ,K ψ Let I be the coefficient of air friction in the directions φ, θ, ψ of the quadcopter UAV in the body coordinate system. x ,I y ,I z Let x, y, and z represent the moments of inertia of the quadcopter UAV about the x, y, and z axes, respectively. I x ,I y ,I z The reciprocal of g, where g is the acceleration due to gravity. This is the control input for the position information of the i1th quadcopter UAV. This is the control input for the roll angle of the i1th quadcopter UAV. This is the control input for the pitch angle of the i1th quadcopter UAV. This is the control input for the yaw angle of the i1th quadcopter UAV.

[0016] Furthermore, the mathematical model of the unmanned surface vessel established in step S1 is as follows:

[0017]

[0018]

[0019] Where i2 represents the i2th unmanned surface vessel; They are respectively The first derivative, This represents the position information of the i2th unmanned surface vessel in the ground coordinate system; Let x and y be the linear velocities of the i2th unmanned surface vessel in the ground coordinate system, respectively. They are respectively The first derivative; and Let represent the heading angle and bow roll rate of the i2th unmanned surface vessel, respectively. They are respectively First derivative; m 11 ,m 22 ,m .. d represents the inertial mass of the unmanned surface vessel along the x-axis, y-axis, and bow direction, respectively; 11 ,d 22 ,d .. These are the water flow damping coefficients of the unmanned surface vessel along the x-direction, y-direction, and bow direction, respectively. For the thrust of the i2th unmanned surface vessel, The bow-turning moment of the i2th unmanned surface vessel;

[0020] make As the reference point for the i2th unmanned surface vessel, the reference point satisfies the integrity constraint; therefore, the control problem of the reference point is considered:

[0021]

[0022] in, This represents the position information of the i2th unmanned surface vessel reference point in the ground coordinate system. Let be the distance from the reference point of the i2th unmanned surface vessel to the center of mass of the unmanned surface vessel.

[0023] Furthermore, in step S2, when the heterogeneous multi-agent system only considers the XOY plane position system, the mathematical model of the quadcopter UAV is further simplified to:

[0024]

[0025] in, They are respectively The second derivative, This provides the position information of the center of gravity of the i1th quadrotor UAV in the ground coordinate system. For virtual control variables, These are dummy variables; they are represented as follows:

[0026]

[0027]

[0028]

[0029] These represent the roll angle, pitch angle, and attitude angle of the i1th quadcopter UAV in the body coordinate system, respectively. The control input for the quadcopter's position information is given by K, where m is the mass of the quadcopter; x ,K y These represent the air drag coefficients of the quadcopter UAV in the x and y directions in the ground coordinate system. They are respectively The first derivative;

[0030] The mathematical model of the unmanned surface vessel is simplified as follows:

[0031]

[0032] in, They represent The second derivative; This represents the position information of the i2th unmanned surface vessel reference point in the ground coordinate system; For virtual control variables, These are dummy variables; they are represented as follows: and Let represent the heading angle and bow roll rate of the i2th unmanned surface vessel, respectively. They are respectively The first derivative; Let x and y be the linear velocities of the i2th unmanned surface vessel in the ground coordinate system, respectively. They are respectively The first derivative; Let be the distance from the reference point of the i2th unmanned surface vessel to the center of mass of the unmanned surface vessel;

[0033] Since the formation control of heterogeneous multi-agent systems only considers the XOY plane, the simplified mathematical models of the quadcopter UAV and the unmanned surface vessel are combined as follows:

[0034]

[0035] Where i represents the i-th agent, p i =[x i ,y i ] T For the XOY plane position information of the i-th agent, For p i The first derivative, correspondingly, This represents the speed information of the i-th agent. For v i The first derivative, u i This serves as the control input for the i-th agent.

[0036] Define dummy variable ξ i =[p i ,v i ] T The heterogeneous multi-agent system is transformed into the following state equation:

[0037]

[0038] in, For ξ i The first derivative of , where A and B are constant matrices;

[0039] Define a dummy variable Ξ = [ξ1, ξ2, ..., ξ] N ] T U = [u1, u2, ..., u N ] T The following mathematical model of the heterogeneous multi-agent system is obtained:

[0040]

[0041] in, I is the first derivative of Ξ. N It is an N-dimensional identity matrix.

[0042] Furthermore, the controller saturation function introduced in step S2 is:

[0043]

[0044] Δu=sat(u)-u

[0045] Where u represents the control input of the quadcopter UAV and unmanned surface vessel, and sat(u) represents the control input with saturation characteristics. max ,-u max These represent the upper and lower bounds of the corresponding controller inputs for the quadcopter UAV and the unmanned surface vessel, respectively, and Δu is the difference between the control input with saturation characteristics and the desired control input.

[0046] Furthermore, the establishment of the communication topology diagram of the heterogeneous multi-agent system in step S3 is specifically as follows:

[0047] Consider N agents, i∈V, j∈V, where V is a set of N agents. The communication topology is a directed graph. describe, Represents a set of nodes. The set of edges is represented by the adjacency matrix Γ = [Γi] of the graph. ij ] N×N ,Γi ij Let Γ be the adjacency weight between the i-th node and the j-th node; Γ is true if and only if (j,i)∈ε. ij >0, otherwise Γ ij =0, (j,i)∈ε indicates that there exists an edge from the i-th node to the j-th node; definition Let D be the in-degree of the i-th node, and let D = diag{d1, d2, ..., d...} N Let} be the in-degree matrix of the system; then the Laplace matrix of the graph is expressed as L = D - Γ; if the graph A graph is a collection of nodes that have directed communication with every other node. It contains a spanning tree with that node as the root node; if the graph There exists a node p0 that provides signals to other nodes. If other nodes p i If reference information for node p0 can be obtained, then g i =1, otherwise g i =0, g i Let the adjacency weight between the i-th node and the virtual leader be represented, and define the virtual matrix G = diag{g1, g2, ..., g...}. N}, L G =L+G,L G It is a Laplace matrix based on a virtual leader.

[0048] Furthermore, in step S3, the tracking errors of each quadcopter drone and unmanned surface vessel are obtained based on the virtual leader, and a sliding mode function is established for each agent, specifically as follows:

[0049] Consider a heterogeneous multi-agent system comprising a directed graph of spanning trees with a virtual leader as the root node. The virtual leader is set as the desired trajectory to be followed, and the virtual leader model is defined as follows:

[0050]

[0051] Where p0 = [x0, y0] T This indicates that the agent expects to track a trajectory. For the agent's desired tracking speed, Let p0 and v0 be the first derivatives, respectively, and x0 and y0 be the position information of the desired tracking trajectory. Let x0 and y0 be the first derivatives of x0 and y0, and u0 be the desired control input.

[0052] Define h ip For the positional formation configuration of the i-th agent, h iv For the velocity formation configuration of the i-th agent, define a virtual variable H. p =[h 1p ,h 2p ,...,h Np ] T H v =[h 1v ,h 2v ,...,h Nv ] T h i =[h ip ,h iv ] T H = [H p H v ] T For each agent, if the following conditions are met:

[0053]

[0054] Where, ξ i Let ξ0 be a dummy variable, where ξ0 = [p0, v0] T Then, the heterogeneous multi-agent system can achieve tracking control;

[0055] Define the tracking error e of the i-th agent. i for:

[0056]

[0057]

[0058] in, For e i The first derivative; N is the number of agents, Γ ij ,Γ i0 Let Γ be an element in the adjacency matrix of a directed graph, representing the adjacency weight between the i-th node and the j-th node. i0 p represents the adjacency weight between the i-th node and the virtual leader. i p j These are the XOY plane position information of the i-th and j-th agents, respectively, v i v j h represents the velocity information of the i-th and j-th agents, respectively; jp For the positional formation configuration of the j-th agent, hjv For the velocity formation configuration of the j-th agent;

[0059] Introducing sliding mode function:

[0060]

[0061] Among them, s i Let c1, c2 > 0 represent the sliding mode variables of the i-th agent, and c1, c2 > 0 are the control parameters to be designed.

[0062] Define a virtual variable P = [p1, p2, ..., p N ] T V = [v1, v2, ..., v N ] T Based on the tracking error of the i-th agent and its first derivative formula, the error terms of virtual variables P and V are obtained. and

[0063]

[0064]

[0065] The sliding mode function becomes:

[0066]

[0067] Where S is a dummy variable, represented as S = [s1(t), s2(t), ..., s N (t)] T L G It is a Laplace matrix based on a virtual leader.

[0068] Furthermore, the anti-saturation auxiliary system designed in step S4 is as follows:

[0069]

[0070] in, As auxiliary variables, C = [c1, c2], where c1, c2, γ > 0 are the control parameters to be designed, B is a constant matrix, and Δu i Let Δu be the difference between the control input with saturation characteristics and the desired control input for the i-th agent. j Let Γ be the difference between the control input with saturation characteristics and the desired control input for the j-th agent. ij Let be an element in the adjacency matrix of the directed graph, representing the adjacency weight between the i-th node and the j-th node; d i Let g be the in-degree of the i-th node in the directed graph. i Let s represent the adjacency weight between the i-th node and the virtual leader in a directed graph.i Let N represent the sliding mode variable of the i-th agent, and N be the number of agents.

[0071] Furthermore, step S5 specifically involves:

[0072] Based on sliding mode variable structure control theory and combined with anti-saturation auxiliary system, a control law for heterogeneous multi-agent system under input constraints is designed:

[0073]

[0074] Among them, L G It is a Laplace matrix based on a virtual leader, C = [c1, c2], where c1, c2 > 0 are the control parameters to be designed, A and B are constant matrices, and S = [s1(t), s2(t), ..., s...]. N (t)] T s i Let η,k represent the sliding mode variable of the i-th agent. " , The parameters of the controller to be designed must meet the following requirements. Let H be the first derivative of H, and H = [H p H v ] T H p H v For dummy variables, For auxiliary variables, i = 1, ..., N, u0 is the desired control input;

[0075] The control input of the i-th agent is represented as:

[0076]

[0077] Where, d i Let g be the in-degree of the i-th node in the directed graph. i Let s represent the adjacency weight between the i-th node and the virtual leader in a directed graph. i Let ξ represent the sliding mode variable of the i-th agent. i For dummy variables, for h i The first derivative, for h j The first derivative, h i =[h ip ,h iv ] T h ip For the positional formation configuration of the i-th agent, h iv For the velocity formation configuration of the i-th agent; Γ ij Let be an element in the adjacency matrix of the directed graph, representing the adjacency weight between the i-th node and the j-th node.

[0078] Based on the same inventive concept, the present invention provides a formation control system for heterogeneous multi-agent systems considering input constraints, comprising:

[0079] Mathematical model building unit, used to establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle;

[0080] The position model construction unit is used to simplify the mathematical models of quadrotor UAVs and unmanned surface vessels when only considering the XOY plane position system in heterogeneous multi-agent systems. It obtains the XOY plane mathematical models of quadrotor UAVs and unmanned surface vessels, and further obtains the mathematical model of heterogeneous multi-agent systems, introducing the controller saturation function.

[0081] The sliding mode function establishment unit establishes a communication topology graph of the heterogeneous multi-agent system, obtains the tracking error of each agent based on the virtual leader, and establishes the sliding mode function of each agent; wherein, the communication topology graph of the heterogeneous multi-agent system is described by a directed graph;

[0082] The auxiliary system design unit designs the input of the anti-saturation auxiliary system compensation controller.

[0083] The anti-saturation controller design unit combines sliding mode control and auxiliary system to design an anti-saturation controller, realizing formation control of heterogeneous multi-agent systems.

[0084] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0085] This invention designs a formation tracking controller for heterogeneous multi-agent systems based on graph theory, sliding mode control, virtual leader, and auxiliary systems. Mathematical models of a quadrotor UAV and an unmanned surface vessel are obtained based on Newton-Euler principles. These models are simplified to obtain XOY plane formation information. A directed communication topology is established, and a virtual leader is introduced to obtain the final control objective of the heterogeneous multi-agent system. An improved auxiliary system reduces the controller's computational complexity. The auxiliary system is directly integrated with the sliding mode method, satisfying actuator saturation constraints while ensuring asymptotic stability of the formation tracking error, thus improving the system's dynamic tracking performance. The controller design is theoretically simple and can be better applied to practical heterogeneous system formation control. Attached Figure Description

[0086] Figure 1 This is a flowchart of the method of the present invention;

[0087] Figure 2 This is a schematic diagram of the controller saturation function of the present invention;

[0088] Figure 3 This invention is based on a virtual leader communication topology diagram. Detailed Implementation

[0089] The invention will now be further explained with reference to the accompanying drawings.

[0090] Figure 1-3 As shown, this invention provides a formation control method for heterogeneous multi-agent systems considering input constraints. This method is applicable to the formation control of heterogeneous multi-agent systems under input constraints. The specific process is as follows:

[0091] S1. Establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle;

[0092] Consider N (N = N1 + N2) heterogeneous multi-agents, including N1 quadcopter drones and N2 unmanned surface vessels. Define the multi-agent sets V1 = {1, 2, ..., N1}, V2 = {N1 + 1, N1 + 2, ..., N} and V = {1, 2, ..., N}.

[0093] Based on the Newton-Euler principle, the following mathematical model of a quadcopter drone can be obtained:

[0094]

[0095]

[0096] Where i1∈V1 represents the i1th quadcopter drone, This provides the position information of the center of gravity of the i1th quadcopter UAV in the ground coordinate system. They are respectively The first derivative, They are respectively The second derivative, These represent the roll angle, pitch angle, and attitude angle of the i1th quadcopter UAV in the body coordinate system, respectively. They are respectively The first derivative, They are respectively The second derivative, where m is the mass of the quadcopter drone, and K x ,K y ,K z K represents the air drag coefficient of the quadcopter UAV in the x, y, and z directions in the ground coordinate system. φ ,K θ ,K ψ Let I be the coefficient of air friction in the directions φ, θ, ψ of the quadcopter UAV in the body coordinate system. x ,I y ,I z Let x, y, and z represent the moments of inertia of the quadcopter UAV about the x, y, and z axes, respectively. I x ,Iy ,I z The reciprocal of g, where g is the acceleration due to gravity. For the i1th quadcopter UAV control input, The control input for the position information of the quadcopter drone. For the control input of the roll angle of the quadcopter drone, This is the control input for the pitch angle of the quadcopter drone. This is the control input for the yaw angle of the quadcopter drone.

[0097] Similarly, based on the Newton-Euler principle, a mathematical model for unmanned surface vessels can be obtained:

[0098]

[0099]

[0100] Where i2∈V2 represents the i2th unmanned surface vessel; This represents the position information of the i2th unmanned surface vessel in the ground coordinate system. They are respectively The first derivative; Let x and y be the linear velocities of the i2th unmanned surface vessel in the ground coordinate system, respectively. They are respectively The first derivative; and Let represent the heading angle and bow roll rate of the i2th unmanned surface vessel, respectively. They are respectively First derivative; m 11 ,m 22 ,m .. d represents the inertial mass of the unmanned surface vessel along the x-axis, y-axis, and bow direction, respectively; 11 ,d 22 ,d .. The damping coefficients for the unmanned surface vessel along the x-direction, y-direction, and bow direction are given. For the control input of the i2th unmanned surface vessel, For thrust, This is the bow-turning torque.

[0101] Because the mathematical model of unmanned surface vessels is a non-holonomic constraint model, the definition is... As the reference point for the i2th unmanned surface vessel, the reference point satisfies integrity constraints. Therefore, consider the control problem of the reference point:

[0102]

[0103] In the formula, This represents the position information of the i2th unmanned surface vessel reference point in the ground coordinate system. Let be the distance from the reference point of the i2th unmanned surface vessel to the center of mass of the unmanned surface vessel.

[0104] S2. Simplify the mathematical models of the quadrotor UAV and the unmanned surface vessel to obtain the XOY plane position models of the quadrotor UAV and the unmanned surface vessel, and introduce the controller saturation function.

[0105] Since the formation control problem of heterogeneous multi-agent systems only involves position and velocity, the heterogeneous multi-agent system can be considered only as an XOY plane position system. The mathematical model of the quadcopter UAV can be further simplified to:

[0106]

[0107] in, For virtual control variables, These are dummy variables, represented as follows:

[0108]

[0109]

[0110]

[0111] For unmanned surface vessels, by differentiating equation (5), the mathematical model of unmanned surface vessels can be simplified to:

[0112]

[0113] In the formula, For virtual control variables, These are dummy variables, represented as follows:

[0114]

[0115]

[0116]

[0117]

[0118] Since the formation control of heterogeneous multi-agent systems only considers the XOY plane, equations (6) and (7) can be synthesized as follows:

[0119]

[0120] Where i∈V represents the i-th agent, p i =[x i ,y i ]T For the XOY plane position information of the i-th agent, For p i The first derivative, correspondingly, This represents the speed information of the i-th agent. For v i The first derivative, u i This is the control input for the i-th agent. This invention primarily considers formation control of heterogeneous multi-agent systems. Since the quadcopter UAV and the unmanned surface vessel are not on the same plane, formation control mainly considers the XOY plane. The quadcopter UAV's z-channel can be autonomously designed with a controller, ensuring all UAVs maintain the same altitude.

[0121] Define dummy variable ξ i =[p i ,v i ] T Heterogeneous multi-agent systems can be transformed into the following state equations:

[0122]

[0123] in, For ξ i The first derivative of , where A and B are constant matrices, is expressed as .

[0124] Define a dummy variable Ξ = [ξ1, ξ2, ..., ξ] N ] T U = [u1, u2, ..., u N ] T The following mathematical model of the heterogeneous multi-agent system can be obtained:

[0125]

[0126] in, I is the first derivative of Ξ. N It is an N-dimensional identity matrix.

[0127] Introducing the controller saturation function, its expression is as follows:

[0128]

[0129] Δu=sat(u)-u (12)

[0130] Where u represents the control input of the quadcopter UAV and unmanned surface vessel, and sat(u) represents the control input with saturation characteristics. m]x ,-u m]xThese represent the upper and lower bounds of the corresponding controller inputs for the quadcopter UAV and the unmanned surface vessel, respectively, where Δu is the difference between the control input with saturation characteristics and the desired control input. For example... Figure 2 As shown.

[0131] S3. Establish a communication topology diagram for a heterogeneous multi-agent system, obtain the tracking error of each agent based on the virtual leader, and establish the sliding mode function for each agent.

[0132] Consider N agents, i∈V, j∈V, the communication topology can be a directed graph. describe, Represents a set of nodes. The set of edges is represented by the adjacency matrix Γ = [Γ] of the graph. ij ] N×N , Γ ij Let Γ be the adjacency weight between the i-th node and the j-th node. Γ is true if and only if (j,i)∈ε. ij >0, otherwise Γ ij =0, (j,i)∈ε indicates that there exists an edge from the i-th node to the j-th node. Definition Let D be the in-degree of the i-th node, and let D = diag{d1, d2, ..., d...} N Let} be the in-degree matrix of the system. Then the Laplace matrix of the graph can be expressed as L = D - Γ. If the graph A graph is a collection of nodes that have directed communication with every other node. It contains a spanning tree with that node as the root node. If the graph... There exists a node p0 that provides signals to other nodes. If other nodes p i (i = 1, 2, ..., N) can obtain reference information for node p0, then g i =1, otherwise g i =0, g i Let the adjacency weight between the i-th node and the virtual leader be represented, and define the virtual matrix G = diag{g1, g2, ..., g...}. N}, L G =L+G,L G It is a Laplace matrix based on a virtual leader.

[0133] Consider a heterogeneous multi-agent system comprising a directed graph of spanning trees with a virtual leader as the root node. The virtual leader can be defined as the desired tracking trajectory. Let's define the virtual leader model as follows:

[0134]

[0135] In the formula, p0 = [x0, y0] T This indicates that the agent expects to track a trajectory. For the agent's desired tracking speed, Let p0 and v0 be the first derivatives, respectively, and x0 and y0 be the position information of the desired tracking trajectory. Let x0 and y0 be the first derivatives of x0 and y0 respectively, and u0 be the desired control input.

[0136] Define h ip For the positional formation configuration of the i-th agent, h iv For the velocity formation configuration of the i-th agent, define a virtual variable H. p =[h 1p ,h 2p ,...,h Np ] T H v =[h 1v ,h 2v ,...,h Nv ] T h i =[h ip ,h iv ] T H = [H p H v ] T For each agent, if the following conditions are met...

[0137]

[0138] Where ξ0 = [p0, v0] T Then the heterogeneous multi-agent system (10) achieves tracking control.

[0139] Define the tracking error e of the i-th agent. i for:

[0140]

[0141]

[0142] in, For e i The first derivative, Γ i0 This represents the adjacency weight between the i-th node and the virtual leader.

[0143] Introducing sliding mode function:

[0144]

[0145] Among them, s i Let c1, c2>0 represent the sliding mode variables of the i-th agent, and c1, c2>0 are the control parameters to be designed.

[0146] Define a virtual variable P = [p1, p2, ..., p N ] T V = [v1, v2, ..., v N ] T Similarly, the error terms of dummy variables P and V can be obtained according to equations (15) and (16). and

[0147]

[0148]

[0149] The sliding mode function can be transformed into:

[0150]

[0151] Where S is a dummy variable, representing the transpose of the matrix composed of sliding mode variables of N agents, denoted as S=[s1(t),s2(t),...,s N (t)] T .

[0152] S4. Design the input of the compensation controller for the anti-saturation auxiliary system;

[0153] To address the controller saturation problem, the following anti-saturation auxiliary system is defined:

[0154]

[0155] in, As auxiliary variables, C = [c1, c2], γ > 0 represents the controller parameters to be designed, and Δu i Let Δu be the difference between the control input with saturation characteristics and the desired control input for the i-th agent. j Let be the difference between the control input with saturation characteristics and the desired control input for the j-th agent.

[0156] S5. Combine sliding mode control and auxiliary system to design an anti-saturation controller to realize formation tracking control of heterogeneous multi-agent system.

[0157] Based on sliding mode variable structure control theory and combined with anti-saturation auxiliary system, a control law for heterogeneous multi-agent system under input constraints is designed:

[0158]

[0159] Where η,k " , The parameters of the controller to be designed must meet the following requirements. The first derivative of H,

[0160] The control input of the i-th agent can be represented as:

[0161]

[0162] in, for h i The first derivative, for h j The first derivative.

[0163] Figure 3 Given an example topology, define a virtual leader 0. A heterogeneous multi-agent system comprises two unmanned aerial vehicles (i = 1, 2) and an unmanned surface vessel (i = 3, 4). The virtual leader is expected to autonomously design its trajectory based on… Figure 3 Establishing topological information, the desired formation of the heterogeneous multi-agent system relative to the virtual leader in the XOY plane can be set as h1 = [-1, -1]; h2 = [1, -1]; h . = [1, -2]; h4 = [-2, -2].

[0164] Based on the same inventive concept, the present invention provides a formation control system for heterogeneous multi-agent systems considering input constraints, comprising:

[0165] Mathematical model building unit, used to establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle;

[0166] The position model construction unit is used to simplify the mathematical models of quadrotor UAVs and unmanned surface vessels when only considering the XOY plane position system in heterogeneous multi-agent systems. It obtains the XOY plane mathematical models of quadrotor UAVs and unmanned surface vessels, and further obtains the mathematical model of heterogeneous multi-agent systems, introducing the controller saturation function.

[0167] The sliding mode function establishment unit establishes a communication topology graph of the heterogeneous multi-agent system, obtains the tracking error of each agent based on the virtual leader, and establishes the sliding mode function of each agent; wherein, the communication topology graph of the heterogeneous multi-agent system is described by a directed graph;

[0168] The auxiliary system design unit designs the input of the anti-saturation auxiliary system compensation controller.

[0169] The anti-saturation controller design unit combines sliding mode control and auxiliary system to design an anti-saturation controller, realizing formation control of heterogeneous multi-agent systems.

[0170] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for formation control of heterogeneous multi-agent systems considering input constraints, characterized in that, Includes the following steps: S1. Establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle; S2, heterogeneous multi-agent systems only consider When using a planar positioning system, the mathematical models of the quadcopter UAV and unmanned surface vessel are simplified to obtain the quadcopter UAV and unmanned surface vessel. The planar mathematical model is used to further obtain the mathematical model of the heterogeneous multi-agent system, and the controller saturation function is introduced. S3. Establish a communication topology graph for the heterogeneous multi-agent system, obtain the tracking error of each agent based on the virtual leader, and establish the sliding mode function for each agent; wherein, the communication topology graph of the heterogeneous multi-agent system is described by a directed graph; S4. Design the input of the compensation controller for the anti-saturation auxiliary system; the designed anti-saturation auxiliary system is as follows: ； in, As an auxiliary variable, , For the control parameters to be designed, It is a constant matrix. For the first The difference between the control input and the desired control input for an agent with saturation characteristics. For the first The difference between the control input and the desired control input for an agent with saturation characteristics. Let be an element in the adjacency matrix of a directed graph, representing the th element. The node and the first The adjacency weights between nodes; For the directed graph of the th The in-degree of each node. Represents the directed graph's first... The adjacency weights between each node and the virtual leader. Indicates the first Sliding mode variables of an agent The number of agents; S5. A saturation-resistant controller is designed by combining sliding mode control and auxiliary systems to achieve formation control of heterogeneous multi-agent systems; specifically: Based on sliding mode variable structure control theory and combined with anti-saturation auxiliary system, a control law for heterogeneous multi-agent system under input constraints is designed: ； in, It is based on the Laplace matrix of a virtual leader. It is a constant matrix. , Indicates the first Sliding mode variables of an agent The parameters of the controller to be designed must meet the following requirements. ; for The first derivative, , , For dummy variables, , As an auxiliary variable, , To control the input as desired; No. The control input of an intelligent agent is represented as follows: ； in, For dummy variables, for The first derivative, for The first derivative, , For the first Positional formation configuration of individual agents For the first Speed ​​formation configuration of individual agents.

2. The method for formation control of heterogeneous multi-agent systems considering input constraints according to claim 1, characterized in that, The mathematical model of the quadcopter UAV established in step S1 is as follows: ； ； in, Indicates the first A quadcopter drone, They are respectively The first derivative, They are respectively The second derivative, For the first Information on the position of the center of gravity of a quadcopter drone in a ground coordinate system. Indicates the first The roll angle, pitch angle, and attitude angle of a quadcopter UAV in the body coordinate system. for The first derivative, for The second derivative, For the mass of quadcopter drones, The quadcopter UAV in the ground coordinate system Air drag coefficient in the direction, For quadcopter UAVs in body coordinate system The coefficient of air friction in the direction, These represent the quadcopter drones orbiting... Moment of inertia of the shaft, They are respectively The reciprocal, It is the acceleration due to gravity. For the first The control input for the position information of a quadcopter drone. For the first The control input for the roll angle of a quadcopter drone. For the first The control input for the pitch angle of a quadcopter drone. For the first The control input for the yaw angle of a quadcopter drone.

3. The method for formation control of heterogeneous multi-agent systems considering input constraints according to claim 2, characterized in that, The mathematical model of the unmanned surface vessel established in step S1 is as follows: ； ； in, Indicates the first An unmanned surface vessel; They are respectively The first derivative, Represents the first in the ground coordinate system Location information of an unmanned surface vessel; They are respectively the first in the ground coordinate system An unmanned surface vessel linear velocity in the direction, They are respectively The first derivative; and They represent the first The bow angle and bow roll rate of an unmanned surface vessel. They are respectively The first derivative; They are unmanned surface vessels direction, Orientational and heading inertial mass; They are unmanned surface vessels direction, The damping coefficients of the flow in the direction and heading; For the first The thrust of an unmanned surface vessel For the first Bow-turning torque of an unmanned surface vessel; make As the first A reference point for an unmanned surface vessel, satisfying integrity constraints; therefore, the control problem of the reference point is considered: ； in, Represents the first in the ground coordinate system Location information of reference points for unmanned surface vessels For the first The distance from the reference point of the unmanned surface vessel to its center of mass.

4. The formation control method for heterogeneous multi-agent systems considering input constraints according to claim 3, characterized in that, In step S2, the heterogeneous multi-agent system only considers When considering a planar position system, the mathematical model of a quadcopter UAV is further simplified to: ； in, They are respectively The second derivative, For the first Position information of the center of gravity of a quadcopter drone in the ground coordinate system; For virtual control variables, These are dummy variables; they are represented as follows: ； ； ； ； They represent the first The roll angle, pitch angle, and attitude angle of a quadcopter UAV in the body coordinate system. The control input for the position information of the quadcopter drone. For the mass of a quadcopter drone; The quadcopter UAV in the ground coordinate system Air drag coefficient in the direction, They are respectively The first derivative; The mathematical model of the unmanned surface vessel is simplified as follows: ； in, , They represent The second derivative; Represents the first in the ground coordinate system Location information of reference points for unmanned surface vessels; For virtual control variables, These are dummy variables; they are represented as follows: ; ; ; ; and They represent the first The bow angle and bow roll rate of an unmanned surface vessel. They are respectively The first derivative; They are respectively the first in the ground coordinate system An unmanned surface vessel linear velocity in the direction, They are respectively The first derivative; For the first The distance from the reference point of the unmanned surface vessel to the center of mass of the unmanned surface vessel; Since the formation control of heterogeneous multi-agent systems only considers Since it is planar, the simplified mathematical models of the quadcopter UAV and the unmanned surface vessel are combined as follows: ； in, Indicates the first An intelligent agent. For the first A smart agent Planar position information, for The first derivative, correspondingly, Indicates the first Speed ​​information of each agent for The first derivative, For the first An intelligent agent controls the input; Define virtual variables The heterogeneous multi-agent system is transformed into the following state equation: ； in, for The first derivative, It is a constant matrix; Define virtual variables , The following mathematical model of the heterogeneous multi-agent system is obtained: ； in, for The first derivative, for 3D identity matrix.

5. The method for formation control of heterogeneous multi-agent systems considering input constraints according to claim 4, characterized in that, The controller saturation function introduced in step S2 is: ； ； in, This indicates the control input for quadcopter drones and unmanned surface vessels. This indicates a control input with saturation characteristics. These represent the upper and lower bounds of the corresponding controller inputs for the quadcopter UAV and the unmanned surface vessel, respectively. It is the difference between the control input with saturation characteristics and the desired control input.

6. The method for formation control of heterogeneous multi-agent systems considering input constraints according to claim 5, characterized in that, The specific steps in step S3 to establish the communication topology of the heterogeneous multi-agent system are as follows: consider An intelligent agent. , , for A collection of intelligent agents, with a communication topology represented by a directed graph. describe, Represents a set of nodes. The set of edges, the adjacency matrix of a graph , For the first The node and the first The adjacency weights between nodes; if and only if , ,otherwise , This indicates the existence of a line from the first... The node to the first Edges of nodes; definition For the first The in-degree of each node. Let be the in-degree matrix of the system; then the Laplace matrix of the graph is expressed as: If the diagram A graph is a collection of nodes that have directed communication with every other node. It contains a spanning tree with that node as the root node; if the graph There exists a node that provides signals to other nodes. If other nodes Able to obtain nodes The reference information is as follows. ,otherwise , Indicates the first The adjacency weights between each node and the virtual leader define the virtual matrix. , , It is a Laplace matrix based on a virtual leader.

7. The method for formation control of heterogeneous multi-agent systems considering input constraints according to claim 6, characterized in that, In step S3, the tracking errors of each quadcopter drone and unmanned surface vessel are obtained based on the virtual leader, and the sliding mode function of each agent is established, specifically as follows: Consider a heterogeneous multi-agent system comprising a directed graph of spanning trees with a virtual leader as the root node. The virtual leader is set as the desired trajectory to be followed, and the virtual leader model is defined as follows: ； in, This indicates that the agent expects to track a trajectory. For the agent's desired tracking speed, They are respectively The first derivative, For the location information of the trajectory to be tracked, for The first derivative, To control the input as desired; definition For the first Positional formation configuration of individual agents For the first Speed ​​formation configuration of individual agents, defining virtual variables. , , , For each agent, if the following conditions are met: ； in, For dummy variables, Then, the heterogeneous multi-agent system can achieve tracking control; Definition of the first Individual agent tracking error for: ； in, for The first derivative; For the number of agents, The elements in the adjacency matrix of the directed graph. Indicates the first The node and the first The adjacency weights between nodes; Indicates the first The adjacency weights between each node and the virtual leader; , The first The and the first A smart agent Planar position information, , They represent the first The and the first Speed ​​information of each agent; For the first Positional formation configuration of individual agents For the first Speed ​​formation configuration of individual agents; Introducing sliding mode function: ； in, Indicates the first Sliding mode variables of an agent The control parameters to be designed; Define virtual variables , According to the The tracking error of an agent and its first derivative formula are used to obtain the virtual variable. and Error term and : ； The sliding mode function becomes: ； in, For dummy variables, represented as ; It is a Laplace matrix based on a virtual leader.

8. A system for use in the formation control method for heterogeneous multi-agent systems considering input constraints as described in claim 1, characterized in that, include: Mathematical model building unit, used to establish mathematical models of quadcopter drones and unmanned surface vessels based on the Newton-Euler principle; Location model building blocks, used in heterogeneous multi-agent systems, only consider When using a planar positioning system, the mathematical models of the quadcopter UAV and unmanned surface vessel are simplified to obtain the quadcopter UAV and unmanned surface vessel. The planar mathematical model is used to further obtain the mathematical model of the heterogeneous multi-agent system, and the controller saturation function is introduced. The sliding mode function establishment unit establishes a communication topology graph of the heterogeneous multi-agent system, obtains the tracking error of each agent based on the virtual leader, and establishes the sliding mode function of each agent; wherein, the communication topology graph of the heterogeneous multi-agent system is described by a directed graph; The auxiliary system design unit designs the input of the anti-saturation auxiliary system compensation controller. The anti-saturation controller design unit combines sliding mode control and auxiliary system to design an anti-saturation controller, realizing formation control of heterogeneous multi-agent systems.

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