Unmanned aerial vehicle-unmanned vehicle system two-part formation control method under switching topology

Abstract

The application discloses a UAV-unmanned vehicle system two-part formation control method under a switching topology, relates to the field of flight control, and is based on an established nonlinear dynamic model, constructs a heterogeneous unified model through a UAV fixed-height assumption, introduces a structure balance two-part topology and a corresponding symbolic graph Laplacian matrix, distinguishes information interaction relations of in-group cooperation and cross-group competition, and defines a switching communication topology on the heterogeneous unified model, designs a time-varying formation offset vector, fuses neighbor communication constraints and a virtual leader traction term, deduces two-part formation distributed tracking errors, and constructs two-part tracking errors, designs ADP distributed optimal control, constructs an infinite time domain coupled quadratic performance index through the two-part tracking errors, deduces a multi-agent coupled HJB partial differential equation, adopts a heuristic dynamic programming HDP double network architecture, designs an evaluation network and an execution network to online approximate solve the HJB equation, and iteratively updates network weights to obtain an approximate optimal control strategy.

Description

Technical Field

[0001] This invention belongs to the field of flight control technology, specifically relating to a two-part formation control method for a UAV-unmanned vehicle system under a switching topology. Background Technology

[0002] As a typical heterogeneous unmanned system, the UAV-RV system combines the advantages of UAVs (fast response, wide detection range, and strong communication capabilities) with RVs (high payload capacity and high ground target reconnaissance accuracy), enabling effective resource complementarity. Therefore, its cooperative control has attracted attention. It's important to note that UAVs and RVs exhibit significant dynamic differences at the individual level. How to fully consider these differences, establish a reasonable system model, and achieve cooperative control objectives is a problem worthy of in-depth exploration. In certain practical applications, introducing a competitive interaction mechanism can effectively improve the cooperative operation capability of the UAV-RV system. In this case, the underlying information interaction topology is often modeled as a symbolic graph. Within this framework, binary formation control is an important research direction in the field of UAV-RV system formation control under symbolic graphs.

[0003] Traditional UAV-autonomous vehicle (UAV) system collaborative formation control focuses on ideal environments with fixed topologies. However, real-world factors such as environmental changes, signal interference, and network failures can all lead to communication link interruptions between UAVs and unmanned vehicles. Introducing dynamic switching of communication topologies is an effective way to adapt to this challenge.

[0004] Furthermore, traditional control methods, by not explicitly incorporating energy loss into performance metrics, lead to unnecessary energy consumption during long-term collaborative tasks, impacting endurance and operational efficiency. Optimal control theory provides an effective approach to address this problem. The Hamilton-Jacobi-Bellman (HJB) equation aims to minimize the structured cost index while balancing expected performance and available control resources to meet system performance requirements. Since the HJB equation is a complex nonlinear equation, traditional analytical methods are insufficient for solving it; therefore, adaptive dynamic programming (ADP) has become an important approach. The ADP algorithm employs an evaluation-execution network structure, where the evaluation network focuses on assessing and analyzing environmental feedback information, and the execution network obtains the optimal control strategy. However, the update rules for the reinforcement learning-based evaluation and execution networks are extremely complex. These factors make directly applying existing optimal control methods to engineering practice challenging.

[0005] Therefore, this invention proposes an optimal control strategy based on adaptive dynamic programming to solve the binary formation control problem of UAV-unmanned vehicle systems under switching topologies. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a binary formation control method for UAV-unmanned vehicle systems under switching topology.

[0007] To achieve the objectives of this invention, the following technical solutions will be adopted.

[0008] A binary formation control method for a UAV-Vehicle system under switching topology includes the following steps:

[0009] S1: Establish a nonlinear dynamics model of a drone-unmanned vehicle system based on a virtual leader-follower model;

[0010] S2: Based on the nonlinear dynamics model, by using the UAV altitude-fixed assumption, the three-dimensional UAV is reduced to two dimensions, and a heterogeneous unified model suitable for the cooperative control of UAV-unmanned vehicle systems is constructed.

[0011] S3: Symbolic graphs are used to describe cluster communication. A structurally balanced bipartite topology and a corresponding symbolic graph Laplace matrix are introduced to distinguish the information interaction relationships of intra-group cooperation and cross-group competition, so as to define the switching communication topology acting on the heterogeneous unified model.

[0012] S4: Design a time-varying formation offset vector, integrate neighbor communication constraints and virtual leader traction terms, derive the binary formation distributed tracking error, and construct the binary tracking error.

[0013] S5: Design ADP distributed optimal control, construct an infinite time-domain coupled quadratic performance index by binary tracking error, derive multi-agent coupled HJB partial differential equations; adopt heuristic dynamic programming HDP dual network architecture, design evaluation network and execution network to approximate the solution of HJB equations online, and iteratively update network weights to obtain an approximate optimal control strategy.

[0014] The drone is a quadcopter drone, and its nonlinear dynamic model is expressed as follows:

[0015] ;

[0016] in, , and The three-axis positions of the UAV in the ground inertial coordinate system. , , These represent the linear velocities at the three axes of the drone. , and The acceleration of the drone in its three-axis position. , and These are roll angle, pitch angle, and yaw angle, respectively. , and These are the roll rate, pitch rate, and yaw rate of the UAV, respectively. , and These are the roll acceleration, pitch acceleration, and yaw acceleration of the UAV, respectively. , and They are respectively about , , Moment of inertia of the shaft For the rotor's moment of inertia, It is the acceleration due to gravity. For the quality of drones, , and They are respectively , , Drag coefficient in the direction, , and These are the attitude aerodynamic damping coefficients of the airframe about the roll / pitch / yaw axes, respectively;

[0017] The control input for the drone is the total lift. Roll control torque Pitch control torque Yaw control torque Specifically, it is expressed as:

[0018] ;

[0019] in, , , and These are the rotational speeds of the four rotors. This refers to the combined angular velocity of the motor rotor. The distance between the center of mass and the rotor axis of rotation. The tensile coefficient, This is the reverse control torque coefficient;

[0020] The unmanned vehicle is a two-wheel drive unmanned vehicle, and its kinematic model is expressed as follows:

[0021] ;

[0022] in, and The location of the driverless car The linear velocity of the autonomous vehicle. The steering angle of the driverless car. Let be the angular velocity of the autonomous vehicle. Since the kinematic model of the autonomous vehicle contains a nonholonomic constraint system, it is an underactuated problem. We can choose to build the model around the front node of the autonomous vehicle, and the new coordinates can be represented as:

[0023] ;

[0024] in, Let be the distance from the midpoint of the two wheels to the front node of the autonomous vehicle. Then the nonlinear dynamics model of the autonomous vehicle is:

[0025] ;

[0026] in, , , For the power of driverless cars, For the quality of driverless cars, For the torque of the driverless car, The moment of inertia of the unmanned vehicle.

[0027] Furthermore, based on the nonlinear dynamics model, a heterogeneous unified model suitable for the cooperative control of UAV-unmanned vehicle systems is constructed.

[0028] Unmanned aerial vehicle (UAV) systems include drones and Driverless cars, driverless cars only Moving on a two-dimensional plane, while the drone is... Moving on a three-dimensional plane, when the drone is only flying at a fixed altitude, the drone-unmanned vehicle system is... Formation tracking motion on a two-dimensional plane. To facilitate the description and analysis of the binary formation tracking problem, the first... drones and the first The unified representation of the autonomous vehicle model is as follows:

[0029] ;

[0030] in, For state variables, For control input; where, , , , They represent the first The X-axis plane position of each individual, the first The position of each individual in the Y-axis plane, the first The velocity of the X-axis of each individual, the first Individual Y-axis velocity; Indicates matrix transpose; This indicates the X-axis control acceleration input; This indicates the Y-axis control acceleration input; and These are the system matrix and the input matrix, respectively; where, It is a second-order identity matrix; Indicates the Kronecker product;

[0031] The virtual leader model is as follows:

[0032] ;

[0033] in, For the virtual leader's state variables, For the leader system matrix; where, and Represents the expected plane coordinates of the virtual leader; and This indicates the virtual leader's desired planar velocity.

[0034] Furthermore, a symbolic diagram is used to describe the cluster's handover communication topology, introducing a structurally balanced bipartite topology and its corresponding Laplace matrix. First, a symbolic diagram is used to describe the cluster's handover communication topology:

[0035] Consider by drones, A network system consisting of autonomous vehicles and a virtual leader, whose communication graph is characterized by switching topologies. Indicates the switching signal It is a piecewise constant function, where , Represents the number of topological structures; the vertex set is Each vertex Represents drones / unmanned vehicles , Represents a virtual leader; edge set And the adjacency matrix is When drones / unmanned vehicles Able to time With drones / unmanned vehicles During communication, there are edges The corresponding weight ,otherwise ;

[0036] Secondly, we introduce a structurally balanced bipartite topology and its corresponding Laplace matrix:

[0037] For communication diagram If the vertex set Two sets , satisfy , , , and , , , Then it is called It is a structural equilibrium diagram; otherwise, it is called a structural non-equilibrium diagram; communication diagram. The Laplace matrix is ​​defined as , Denotes the first Laplace matrix Line 1 Column elements, Represents the matrix dimension. One follower and one virtual leader, represented as follows:

[0038] ;

[0039] Assuming the virtual leader only sends messages and does not receive messages from other drones / autonomous vehicles; when the first When a drone / unmanned vehicle receives information directly from the virtual leader ,otherwise ;

[0040] definition Let be a diagonal matrix, where, hour, ; hour, .

[0041] Furthermore, the time-varying formation offset vector is designed as follows: Overall expected formation vector This indicates that the drone-unmanned vehicle system is in Desired formation on a plane; let augmented formation reference state , To obtain the desired relative offset velocity, the binary formation tracking error of the UAV-Vehicle system is obtained by fusing neighbor communication constraints and a virtual leader traction term, as shown in the following expression:

[0042] ;

[0043] in, Indicates the weight of communication connection strength; Indicates the first The actual state of each individual, including its actual planar position and actual planar velocity; Indicates the first Each individual entity expects a formation reference state, including its expected relative offset position and expected relative offset velocity; when hour, Indicates collaboration within a group; when hour, Indicates cross-group checks and balances; when hour, This indicates no communication. Indicates the first Communication gain from individual to virtual leader; The adjustment coefficient before the leader's state is used to match the binary tracking target. This indicates the global reference state of the virtual leader.

[0044] Furthermore, define the first The local performance metrics of a drone / autonomous vehicle are represented by an infinite time-domain quadratic cost performance metric constructed from the binary tracking error:

[0045] ;

[0046] Among them, the error weighted positive semi-definite matrix Self-controlled input weighted positive definite / semi-positive definite matrix Coupled control input weighting matrix , For instantaneous utility function, Indicates the first Each individual controls the input themselves. Indicates except All other individuals besides; Indicates the remaining number Individual cluster control inputs; Indicates the first Individual local infinite time-domain performance cost index;

[0047] The ultimate goal is to find the optimal set of control strategies. The optimal value function is defined as:

[0048] ;

[0049] in, Indicates the optimal performance index; To allow control domains;

[0050] The coupled HJB equations are derived as follows:

[0051] ;

[0052] in, This represents the first derivative of the tracking error with respect to time.

[0053] The optimal control strategy is:

[0054] ;

[0055] A distributed optimal control algorithm based on adaptive dynamic programming is designed. A heuristic dynamic programming structure is employed to approximate the solution of the HJB equations online. An evaluation network and an execution network are constructed to approximate the optimal control strategy. The approximate value of the value function output by the evaluation network is:

[0056] ;

[0057] in, The approximate weights for the current evaluation network are an approximation of the ideal weights. The output of the hidden layer after passing through a non-linear activation function. To evaluate the input vector of the network, the approximate Hamiltonian residual equation is obtained:

[0058] ;

[0059] in, This indicates the residual error in the evaluation network approximation.

[0060] The weight estimation error of the evaluation network is defined as:

[0061] ;

[0062] in, To evaluate the ideal weights of the network;

[0063] To approximate the weights as close to the ideal value function, according to the gradient descent method, the goal is to select... To minimize the average residual error; the average residual error is defined as:

[0064] ;

[0065] The approximate control strategy for implementing the network output is as follows:

[0066] ;

[0067] in, To ideally implement network weights The current estimate;

[0068] Define the weight estimation error of the execution network as:

[0069] ;

[0070] The evaluation network update law is as follows:

[0071] ;

[0072] in, To evaluate the differential of the real-time weights of the network over time; To evaluate the network learning rate, Represents the residual loss function; This indicates the evaluation network Hamiltonian approximation residual; This represents an approximate estimate of the real-time weights of the evaluation network; To adjust the parameters, , , This represents the derivative vector of the evaluation network basis functions along the error trajectory; , Indicates the total gain of topological coupling; , The dynamics-energy coupling matrix of the machine is represented by the input matrix. Control weights Construction of basis function gradients; , Indicates the cluster number Individual coupling dynamics matrices are used for multi-machine coupling cost terms;

[0073] The update law for the execution network is:

[0074] ;

[0075] in, To implement the network's learning rate, and To adjust the parameters.

[0076] The beneficial effects of this invention are:

[0077] 1. This invention simultaneously considers the cooperative and competitive relationship between drones and unmanned vehicles. Under the structural balance diagram, the followers of the drone-unmanned vehicle system can accurately track the virtual leader, achieving binary formation, with the final positions being the same size but facing opposite directions;

[0078] 2. This invention introduces a dynamic switching communication topology mechanism, enabling the UAV-Vehicle system to adapt to topology changes in real time and adaptively adjust the control strategy, significantly improving the system's robustness and formation stability under switching interference.

[0079] 3. This invention designs a distributed optimal control algorithm based on adaptive dynamic programming. It employs a heuristic dynamic programming structure to approximate the HJB equations online, obtaining a near-optimal control strategy. This reduces unnecessary energy consumption in long-term cooperative tasks while ensuring adaptive optimal cooperative tracking performance. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of the control structure of the present invention;

[0081] Figure 2 This is a diagram showing all communication topologies under the control method of this invention;

[0082] Figure 3 This is a topology switching diagram under the control method of the present invention;

[0083] Figure 4 This is a three-dimensional trajectory curve obtained using the control method of the present invention;

[0084] Figure 5 The image shows the position tracking curve obtained using the control method of this invention.

[0085] Figure 6 This is a position tracking error curve obtained using the control method of the present invention;

[0086] Figure 7 The image shows the evaluation network weight update curve obtained using the control method of this invention.

[0087] Figure 8 This is a control input curve obtained using the control method of the present invention. Detailed Implementation

[0088] To make the objectives, technical solutions, and effects of this invention clearer, the technical solutions of this invention are described in detail below with reference to specific examples. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of this invention.

[0089] The present invention provides a binary formation control method for a UAV-Vehicle system under a switching topology, the method comprising:

[0090] Establish a nonlinear dynamic model of a drone-unmanned vehicle system based on a virtual leader-follower architecture;

[0091] Based on a nonlinear dynamics model, and by assuming a fixed altitude for the UAV, the three-dimensional UAV is reduced to two dimensions, thus constructing a heterogeneous unified model suitable for the cooperative control of UAV-unmanned vehicle systems.

[0092] Symbolic graphs are used to describe cluster communication. A structurally balanced bipartite topology and a corresponding symbolic graph Laplace matrix are introduced to distinguish the information interaction relationships of intra-group cooperation and cross-group competition, so as to define the switching communication topology acting on the heterogeneous unified model.

[0093] Design a time-varying formation offset vector, integrate neighbor communication constraints and virtual leader traction terms, derive the binary formation distributed tracking error, and construct the binary tracking error.

[0094] The ADP distributed optimal control is designed, which constructs an infinite time-domain coupled quadratic performance index by bisection tracking error and derives multi-agent coupled HJB partial differential equations. The heuristic dynamic programming HDP dual-network architecture is adopted to design an evaluation network and an execution network to approximate the solution of the HJB equations online, and iteratively updates the network weights to obtain an approximate optimal control strategy.

[0095] Furthermore, the drone is a quadcopter drone, and its nonlinear dynamic model is expressed as follows:

[0096] ;

[0097] in, , and The three-axis positions of the UAV in the ground inertial coordinate system. , , These represent the linear velocities at the three axes of the drone. , and The acceleration of the drone in its three-axis position. , and These are roll angle, pitch angle, and yaw angle, respectively. , and These are the roll rate, pitch rate, and yaw rate of the UAV, respectively. , and These are the roll acceleration, pitch acceleration, and yaw acceleration of the UAV, respectively. , and They are respectively about , , Moment of inertia of the shaft For the rotor's moment of inertia, It is the acceleration due to gravity. For the quality of drones, , and They are respectively , , Drag coefficient in the direction, , and These are the attitude aerodynamic damping coefficients of the airframe about the roll / pitch / yaw axes, respectively;

[0098] The control input for the drone is the total lift. Roll control torque Pitch control torque Yaw control torque Specifically, it is expressed as:

[0099] ;

[0100] in, , , and These are the rotational speeds of the four rotors. This refers to the combined angular velocity of the motor rotor. The distance between the center of mass and the rotor axis of rotation. The tensile coefficient, This is the reverse control torque coefficient;

[0101] The unmanned vehicle is a two-wheel drive unmanned vehicle, and its kinematic model is expressed as follows:

[0102] ;

[0103] in, and The location of the driverless car The linear velocity of the autonomous vehicle. The steering angle of the driverless car. Let be the angular velocity of the autonomous vehicle. Since the kinematic model of the autonomous vehicle contains a nonholonomic constraint system, it is an underactuated problem. We can choose to build the model around the front node of the autonomous vehicle, and the new coordinates can be represented as:

[0104] ;

[0105] in, Let be the distance from the midpoint of the two wheels to the front node of the autonomous vehicle. Then the nonlinear dynamics model of the autonomous vehicle is:

[0106] ;

[0107] in, , , For the power of driverless cars, For the quality of driverless cars, For the torque of the driverless car, The moment of inertia of the unmanned vehicle.

[0108] Furthermore, based on the nonlinear dynamics model, a heterogeneous unified model suitable for the cooperative control of UAV-unmanned vehicle systems is constructed.

[0109] Unmanned aerial vehicle (UAV) systems include drones and Driverless cars, driverless cars only Moving on a two-dimensional plane, while the drone is... Moving on a three-dimensional plane, when the drone is only flying at a fixed altitude, the drone-unmanned vehicle system is... Formation tracking motion on a two-dimensional plane. To facilitate the description and analysis of the binary formation tracking problem, the first... drones and the first The unified representation of the autonomous vehicle model is as follows:

[0110] ;

[0111] in, For state variables, For control input; where, , , , They represent the first The X-axis plane position of each individual, the first The position of each individual in the Y-axis plane, the first The velocity of the X-axis of each individual, the first Individual Y-axis velocity; Indicates matrix transpose; This indicates the X-axis control acceleration input; This indicates the Y-axis control acceleration input; and These are the system matrix and the input matrix, respectively; where, It is a second-order identity matrix; Indicates the Kronecker product;

[0112] The virtual leader model is as follows:

[0113] ;

[0114] in, For the virtual leader's state variables, For the leader system matrix; where, and Represents the expected plane coordinates of the virtual leader; and This indicates the virtual leader's desired planar velocity.

[0115] Furthermore, a symbolic diagram is used to describe the cluster's handover communication topology, introducing a structurally balanced bipartite topology and its corresponding Laplace matrix. First, a symbolic diagram is used to describe the cluster's handover communication topology:

[0116] Consider by drones, A network system consisting of autonomous vehicles and a virtual leader, whose communication graph is characterized by switching topologies. Indicates the switching signal It is a piecewise constant function, where , Represents the number of topological structures; the vertex set is Each vertex Represents drones / unmanned vehicles , Represents a virtual leader; edge set And the adjacency matrix is When drones / unmanned vehicles Able to time With drones / unmanned vehicles During communication, there are edges The corresponding weight ,otherwise ;

[0117] Secondly, we introduce a structurally balanced bipartite topology and its corresponding Laplace matrix:

[0118] For communication diagram If the vertex set Two sets , satisfy , , , and , , , Then it is called It is a structural equilibrium diagram; otherwise, it is called a structural non-equilibrium diagram; communication diagram. The Laplace matrix is ​​defined as , Denotes the first Laplace matrix Line 1 Column elements, Represents the matrix dimension. One follower and one virtual leader, represented as follows:

[0119] ;

[0120] Assuming the virtual leader only sends messages and does not receive messages from other drones / autonomous vehicles; when the first When a drone / unmanned vehicle receives information directly from the virtual leader ,otherwise ;

[0121] definition Let be a diagonal matrix, where, hour, ; hour, .

[0122] Furthermore, the time-varying formation offset vector is designed as follows: Overall expected formation vector This indicates that the drone-unmanned vehicle system is in Desired formation on a plane; let augmented formation reference state , To obtain the desired relative offset velocity, the binary formation tracking error of the UAV-Vehicle system is obtained by fusing neighbor communication constraints and a virtual leader traction term, as shown in the following expression:

[0123] ;

[0124] in, Indicates the weight of communication connection strength; Indicates the first The actual state of each individual, including its actual planar position and actual planar velocity; Indicates the first Each individual entity expects a formation reference state, including its expected relative offset position and expected relative offset velocity; when hour, Indicates collaboration within a group; when hour, Indicates cross-group checks and balances; when hour, This indicates no communication. Indicates the first Communication gain from individual to virtual leader; The adjustment coefficient before the leader's state is used to match the binary tracking target. This indicates the global reference state of the virtual leader.

[0125] Furthermore, define the first The local performance metrics of a drone / autonomous vehicle are represented by an infinite time-domain quadratic cost performance metric constructed from the binary tracking error:

[0126] ;

[0127] Among them, the error weighted positive semi-definite matrix Self-controlled input weighted positive definite / semi-positive definite matrix Coupled control input weighting matrix , For instantaneous utility function, Indicates the first Each individual controls the input themselves. Indicates except All other individuals besides; Indicates the remaining number Individual cluster control inputs; Indicates the first Individual local infinite time-domain performance cost index;

[0128] The ultimate goal is to find the optimal set of control strategies. The optimal value function is defined as:

[0129] ;

[0130] in, Indicates the optimal performance index; To allow control domains;

[0131] The coupled HJB equations are derived as follows:

[0132] ;

[0133] in, This represents the first derivative of the tracking error with respect to time.

[0134] The optimal control strategy is:

[0135] ;

[0136] A distributed optimal control algorithm based on adaptive dynamic programming is designed. A heuristic dynamic programming structure is employed to approximate the solution of the HJB equations online. An evaluation network and an execution network are constructed to approximate the optimal control strategy. The approximate value of the value function output by the evaluation network is:

[0137] ;

[0138] in, The approximate weights for the current evaluation network are an approximation of the ideal weights. The output of the hidden layer after passing through a non-linear activation function. To evaluate the input vector of the network, the approximate Hamiltonian residual equation is obtained:

[0139] ;

[0140] in, This indicates the residual error in the evaluation network approximation.

[0141] The weight estimation error of the evaluation network is defined as:

[0142] ;

[0143] in, To evaluate the ideal weights of the network;

[0144] To approximate the weights as close to the ideal value function, according to the gradient descent method, the goal is to select... To minimize the average residual error; the average residual error is defined as:

[0145] ;

[0146] The approximate control strategy for implementing the network output is as follows:

[0147] ;

[0148] in, To ideally implement network weights The current estimate;

[0149] Define the weight estimation error of the execution network as:

[0150] ;

[0151] The evaluation network update law is as follows:

[0152] ;

[0153] in, To evaluate the differential of the real-time weights of the network over time; To evaluate the network learning rate, Represents the residual loss function; This indicates the evaluation network Hamiltonian approximation residual; This represents an approximate estimate of the real-time weights of the evaluation network; To adjust the parameters, , , This represents the derivative vector of the evaluation network basis functions along the error trajectory; , Indicates the total gain of topological coupling; , The dynamics-energy coupling matrix of the machine is represented by the input matrix. Control weights Construction of basis function gradients; , Indicates the cluster number Individual coupling dynamics matrices are used for multi-machine coupling cost terms;

[0154] The update law for the execution network is:

[0155] ;

[0156] in, To implement the network's learning rate, and To adjust the parameters.

[0157] To verify the effectiveness of the binary formation control method for UAV-Vehicle systems under topology switching, the following simulation experiment was conducted.

[0158] Consider using 4 driverless cars ( ) and 2 drones ( A drone-vehicle system composed of ) Figure 2 All communication topologies are displayed, where 0 represents the virtual leader. System topology switching is shown below. Figure 3 As shown in the figure. Among them, drones and unmanned vehicles are divided into two subsets. , The corresponding matrix All The trajectory of the virtual leader is...

[0159] ;

[0160] The initial position is , , , , , , .

[0161] The weight matrix is , , , , , , , .

[0162] Learning rate , Adjusting parameters , .

[0163] The network activation function is set to evaluate

[0164] ;

[0165] Time-varying expected formation

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] ;

[0171] ;

[0172] like Figure 1 As shown, the overall structure diagram of the control method implemented in this example is constructed. The simulation time for the control process is set to 40 seconds, and the three-dimensional trajectory curve obtained using the control method of this invention is shown below. Figure 4 As shown, the position tracking curve and the position tracking error curve are as follows: Figure 5 and 6 As shown, the results demonstrate that by applying the control method proposed in this invention, the UAV-unmanned vehicle system can quickly and accurately track the virtual leader to achieve bi-formation. Figure 7 The evaluation network weight update curve is shown, from Figure 7 It can be seen from this that the evaluation network weights can converge; the control input curve is as follows: Figure 8 As shown, the control input can tend towards the optimal value. Therefore, the control method of this invention enables the UAV-Vehicle system to possess adaptive optimal cooperative tracking performance and robustness to topology switching.

[0173] The above description is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be covered within the protection scope of the present invention.

Claims

1. A binary formation control method for an unmanned aerial vehicle (UAV)-unmanned vehicle (UAV) system under a switching topology, characterized in that, Includes the following steps: S1: Establish a nonlinear dynamics model of a drone-unmanned vehicle system based on a virtual leader-follower model; S2: Based on the nonlinear dynamics model, by using the UAV altitude-fixed assumption, the three-dimensional UAV is reduced to two dimensions, and a heterogeneous unified model suitable for the cooperative control of UAV-unmanned vehicle systems is constructed. S3: Symbolic graphs are used to describe cluster communication. A structurally balanced bipartite topology and a corresponding symbolic graph Laplace matrix are introduced to distinguish the information interaction relationships of intra-group cooperation and cross-group competition, so as to define the switching communication topology acting on the heterogeneous unified model. S4: Design a time-varying formation offset vector, integrate neighbor communication constraints and virtual leader traction terms, derive the binary formation distributed tracking error, and construct the binary tracking error. S5: Design ADP distributed optimal control, construct an infinite time-domain coupled quadratic performance index by binary tracking error, and derive multi-agent coupled HJB partial differential equations. A heuristic dynamic programming (HDP) dual-network architecture is adopted. An evaluation network and an execution network are designed to approximate the solution of the HJB equation online. The network weights are iteratively updated to obtain an approximate optimal control strategy.

2. The binary formation control method for a UAV-Vehicle system under a switching topology according to claim 1, characterized in that: The drone is a quadcopter drone, and its nonlinear dynamic model is expressed as follows: ； in, , and The three-axis positions of the UAV in the ground inertial coordinate system. , and These represent the linear velocities at the three axes of the drone. , and The acceleration of the drone in its three-axis position. , and These are roll angle, pitch angle, and yaw angle, respectively. , and These are the roll rate, pitch rate, and yaw rate of the UAV, respectively. , and These are the roll acceleration, pitch acceleration, and yaw acceleration of the UAV, respectively. , and They are respectively about , , Moment of inertia of the shaft, For the rotor's moment of inertia, It is the acceleration due to gravity. For the quality of drones, , and They are respectively , , Drag coefficient in the direction, , and These are the attitude aerodynamic damping coefficients of the airframe about the roll / pitch / yaw axes, respectively; The control input for the drone is the total lift. Roll control torque Pitch control torque Yaw control torque Specifically, it is expressed as: ； in, , , and The four rotor speeds are respectively. This refers to the combined angular velocity of the motor rotor. The distance between the center of mass and the rotor axis of rotation. The tensile coefficient, This is the reverse control torque coefficient; The unmanned vehicle is a two-wheel drive unmanned vehicle, and its kinematic model is expressed as follows: ； in, and The location of the driverless car The linear velocity of the autonomous vehicle. The steering angle of the driverless car. Let be the angular velocity of the autonomous vehicle. Since the kinematic model of the autonomous vehicle includes a nonholonomic constraint system, it is an underactuated problem. We can choose to build the model around the front node of the autonomous vehicle, and the new coordinates can be represented as: ； in, Let be the distance from the midpoint of the two wheels to the front node of the autonomous vehicle. Then the nonlinear dynamics model of the autonomous vehicle is: ； in, , , For the power of driverless cars, For the quality of driverless cars, For the torque of the driverless car, The moment of inertia of the unmanned vehicle.

3. The binary formation control method for a UAV-Vehicle system under a switching topology according to claim 2, characterized in that: Based on a nonlinear dynamics model, a heterogeneous unified model suitable for cooperative control of UAV-unmanned vehicle systems is constructed. Unmanned aerial vehicle (UAV) systems include drones and Driverless cars, driverless cars only Moving on a two-dimensional plane, while the drone is... Moving in a three-dimensional plane, when the drone is only flying at a fixed altitude, the drone-unmanned vehicle system is... Formation tracking motion on a two-dimensional plane. To facilitate the description and analysis of the binary formation tracking problem, the first... drones and the first The unified representation of each driverless car model is as follows: ； in, For state variables, For control input; where, , , , They represent the first The X-axis plane position of each individual, the first The position of each individual in the Y-axis plane, the first The velocity of the X-axis of each individual, the first Individual Y-axis velocity; Indicates matrix transpose; This indicates the X-axis control acceleration input; This indicates the Y-axis control acceleration input; and These are the system matrix and the input matrix, respectively; where, It is a second-order identity matrix; Indicates the Kronecker product; The virtual leader model is as follows: ； in, For the virtual leader's state variables, For the leader system matrix; where, and Represents the expected plane coordinates of the virtual leader; and This indicates the virtual leader's desired planar velocity.

4. The binary formation control method for a UAV-Vehicle system under a switching topology according to claim 3, characterized in that: Symbolic diagrams are used to describe the cluster's handover communication topology, introducing a structurally balanced bipartite topology and its corresponding Laplace matrix. First, a symbolic diagram is used to describe the cluster's handover communication topology: Consider by drones, A network system consisting of autonomous vehicles and a virtual leader, whose communication graph is characterized by switching topologies. Indicates the switching signal It is a piecewise constant function, where , Represents the number of topological structures; the vertex set is Each vertex Represents drones / unmanned vehicles , Represents a virtual leader; edge set And the adjacency matrix is When drones / unmanned vehicles Able to time With drones / unmanned vehicles During communication, there are edges The corresponding weight ,otherwise ; Secondly, we introduce a structurally balanced bipartite topology and its corresponding Laplace matrix: For communication diagram If the vertex set Two sets , satisfy , , , and , , , Then it is called It is a structural equilibrium diagram; otherwise, it is called a structural non-equilibrium diagram; communication diagram. The Laplace matrix is ​​defined as , Denotes the first Laplace matrix Line 1 Column elements, Represents the matrix dimension. One follower and one virtual leader, represented as follows: ； Assuming the virtual leader only sends messages and does not receive messages from other drones / autonomous vehicles; when the first When a drone / unmanned vehicle receives information directly from the virtual leader ,otherwise ; definition Let be a diagonal matrix, where, hour, ; hour, .

5. The binary formation control method for a UAV-Vehicle system under a switching topology according to claim 4, characterized in that: The time-varying formation offset vector is designed as follows: Overall expected formation vector This indicates that the drone-unmanned vehicle system is in Desired formation on a plane; Command the expanded formation to refer to its status. , To obtain the desired relative offset velocity, the binary formation tracking error of the UAV-Vehicle system is obtained by fusing neighbor communication constraints and a virtual leader traction term, as shown in the following expression: ； in, Indicates the weight of communication connection strength; Indicates the first The actual state of each individual, including its actual planar position and actual planar velocity; Indicates the first Each individual entity expects a formation reference state, including its expected relative offset position and expected relative offset velocity; when hour, Indicates collaboration within a group; when hour, Indicates cross-group checks and balances; when hour, This indicates no communication. Indicates the first Communication gain from individual to virtual leader; The adjustment coefficient before the leader's state is used to match the binary tracking target. This indicates the global reference state of the virtual leader.

6. The binary formation control method for a UAV-Vehicle system under a switching topology according to claim 5, characterized in that: Definition of the first The local performance metrics of a drone / autonomous vehicle are represented by an infinite time-domain quadratic cost performance metric constructed from the binary tracking error: ； Among them, the error weighted positive semi-definite matrix Self-controlled input weighted positive definite / semi-positive definite matrix Coupled control input weighting matrix , For instantaneous utility function, Indicates the first Each individual controls the input themselves. Indicates except All other individuals besides; Indicates the remaining number Individual cluster control inputs; Indicates the first Individual local infinite time-domain performance cost index; The ultimate goal is to find the optimal set of control strategies. The optimal value function is defined as: ； in, Indicates the optimal performance index; To allow control domains; The coupled HJB equations are derived as follows: ； in, This represents the first derivative of the tracking error with respect to time. The optimal control strategy is: ； A distributed optimal control algorithm based on adaptive dynamic programming is designed. A heuristic dynamic programming structure is employed to approximate the solution of the HJB equations online. An evaluation network and an execution network are constructed to approximate the optimal control strategy. The approximate value of the value function output by the evaluation network is: ； in, The approximate weights for the current evaluation network are an approximation of the ideal weights. The output of the hidden layer after passing through a non-linear activation function. To evaluate the input vector of the network, the approximate Hamiltonian residual equation is obtained: ； in, This indicates the residual error in the evaluation network approximation. The weight estimation error of the evaluation network is defined as: ； in, To evaluate the ideal weights of the network; To approximate the weights as close to the ideal value function, according to the gradient descent method, the goal is to select... To minimize the average residual error; the average residual error is defined as: ； The approximate control strategy for implementing the network output is as follows: ； in, To ideally implement network weights The current estimate; Define the weight estimation error of the execution network as: ； The evaluation network update law is as follows: ； in, To evaluate the differential of the real-time weights of the network over time; To evaluate the network learning rate, Represents the residual loss function; This indicates that the residual of the Hamiltonian approximation network is being evaluated. This represents an approximate estimate of the real-time weights of the evaluation network; To adjust the parameters, , , This represents the derivative vector of the evaluation network basis functions along the error trajectory; , Indicates the total gain of topological coupling; , The dynamics-energy coupling matrix of the machine is represented by the input matrix. Control weights Construction of basis function gradients; , Indicates the cluster number Individual coupling dynamics matrices are used for multi-machine coupling cost terms; The update law for the execution network is: ； in, To implement the network's learning rate, and To adjust the parameters.

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