A method for controlling a target by a drone formation based on distance constraints

Abstract

The application relates to a kind of unmanned aerial vehicle formation target tracking control methods based on distance constraint, which can realize the formation tracking of unmanned aerial vehicle cluster only by relying on position information under the condition that target state is unknown, without target speed or prior parameter support, and reduces the information dependence.Through the modeling method based on distance constraint, the stability and flexibility of formation geometry are guaranteed.Sliding mode control combined with adaptive gain adjustment is adopted to effectively suppress unknown disturbance and alleviate the chattering problem, so as to realize rapid and stable target tracking and formation maintenance in a limited time.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, and more specifically to a method for controlling UAV formation tracking targets based on distance constraints. Background Technology

[0002] Unmanned aerial vehicle (UAV) swarm tracking technology is a core research direction for the cooperative control of intelligent unmanned systems.

[0003] Formation tracking problems assume that the trackers do not know the target's speed, and only some trackers can directly observe the target's movement; others can only calculate the required speed for tracking by observing the movement of their neighbors and exchanging information. Therefore, how to handle the uncertainty of the target's motion is a key research focus for this type of problem. It is usually assumed that the target's speed has an upper bound. Existing literature has proposed many methods for UAV formation tracking control. One common approach uses distributed observers to collaboratively estimate the target speed; therefore, this type of method requires UAVs to exchange their internal estimation information and relies on communication between UAVs. Another approach introduces an adaptive term driven by formation error into the control law to compensate for the unknown target speed. A typical approach is to use a sign function term, which has the advantage of accelerating the convergence speed of formation error. However, the discrete switching characteristics of the sign function can lead to chattering, i.e., high-frequency oscillations in the control input; furthermore, this type of method usually still requires knowledge of the upper bound of the target speed. Summary of the Invention

[0004] The purpose of this invention is to provide a distance-constrained UAV formation tracking target control method that does not require knowledge of the upper bound of the parameters of the tracked target, thereby achieving a balance between convergence performance and practical feasibility.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A distance-constrained UAV formation tracking target control method includes the following steps:

[0007] Step 1: Initialize the drone system;

[0008] Configure drone system parameters; parameters include drone formation implementation. Number of drones Number of followers Minimum number of edges in a rigid formation Distance constraint vector Controller gain parameters and desired error tolerance ;

[0009] Construct a UAV topology matrix based on system parameters and store the system correlation matrix. ;

[0010] Step 2: Real-time sensing and data collection;

[0011] In each control cycle, each tracking drone obtains its own position through onboard sensors. Location of neighboring drones and the location of the tracked target. ;

[0012] Step 3: Calculate the current stiffness matrix and formation error vector ;

[0013] Calculate the side vectors of the unmanned aerial vehicle system Then calculate the current stiffness matrix. ; Calculate the first Squared distance error of the strip ,in, This forms the formation error vector. ;

[0014] Step 4: The controller dynamically adjusts the diagonal gain matrix based on the current error magnitude and stage. , ,in, For the first The gain coefficient corresponding to the edge. For the current moment, To meet The smallest root, when Gain coefficient The integral increases over time; when Gain coefficient According to error components The size is adaptively adjusted;

[0015] Step 5: Synthesize control commands;

[0016] Based on the current stiffness matrix Formation error vector and diagonal gain matrix Calculate control commands ;

[0017] Step 6: Instruction Execution and Looping;

[0018] Calculated control commands The command is sent to the drone's actuators, and the drone moves according to the new speed command.

[0019] Continue repeating steps 2 through 6 until the task is completed.

[0020] The drone formation achieves Represented as:

[0021] ,in, The navigator's position vector;

[0022] The number of trackers Minimum number of edges in a rigid formation .

[0023] The correlation matrix The construction method is as follows:

[0024]

[0025] If there is an edge Reaching the node but If there is a border From node Departure All other elements are 0;

[0026] Divide the edge into two parts with opposite directions. Then the correlation matrix ,in, for The corresponding correlation matrix.

[0027] The current stiffness matrix The calculation is as follows:

[0028] First, according to the formula Calculate the side vectors of the unmanned aerial vehicle system ,in, , It is a 3×3 identity matrix;

[0029] Then, according to the formula Calculate the current stiffness matrix ,in, It is a diagonal matrix spanned by the edge vectors.

[0030] The formation error vector The The elements are:

[0031]

[0032] Indicates adjacent nodes , The difference between the square of the actual distance and the square of the expected distance;

[0033] in, Represented as a distance constraint vector The Middle element .

[0034] The first Gain coefficient corresponding to the strip edge Segmentation is defined as:

[0035]

[0036] in, For controller gain parameters, To meet The smallest root, for The derivative of .

[0037] The control command The calculation is as follows:

[0038]

[0039] in, It is about controlling the gain. It is the stiffness matrix Divided into blocks The right half, i.e., the stiffness matrix The To the List; It is a diagonal gain matrix. It is a symbolic function.

[0040] By adopting the above solution, the present invention can produce the following beneficial effects:

[0041] 1. Formation tracking capability under unknown target state: This invention addresses the situation where the state of the tracked target is unknown. Formation control can be achieved solely by observing the target position and the positions of neighboring UAVs. There is no need to obtain target speed, acceleration or other prior parameters, which reduces information dependence and communication requirements.

[0042] 2. Distance-constrained formation maintenance mechanism: This invention describes formation error by constructing distance constraints between UAVs. Compared with the displacement-constrained method, it has a higher modeling difficulty, but it can avoid the problem of local coordinate system drift, thus having better flexibility and stability in maintaining the formation geometry.

[0043] 3. Robust Sliding Mode Control Framework: This invention equates the uncertainty of the target state to an external disturbance and compensates for it using a sliding mode control method, achieving effective tracking of unknown moving targets. Simultaneously, an adaptive gain adjustment mechanism is introduced to effectively alleviate chattering, a common phenomenon in traditional sliding mode control, improving the system's stability and feasibility.

[0044] 4. Finite-time convergence performance: The control law designed in this invention can ensure that the formation error converges to the desired range quickly within a finite time, thereby improving the dynamic response performance of the control system and meeting the requirements of speed and stability of multi-UAV systems in complex environments. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of the information interaction topology among drone groups according to an embodiment of the present invention;

[0046] Figure 2 This is a diagram showing the movement trajectory of a drone formation according to an embodiment of the present invention;

[0047] Figure 3 This refers to the drone formation error in this embodiment of the invention.

[0048] Figure 4 The adaptive gain coefficient of the sliding mode controller in this embodiment of the invention. Detailed Implementation

[0049] This invention discloses a distance-constrained UAV formation tracking target control method. It innovatively constructs a sliding mode controller and introduces an adaptive mechanism to effectively suppress chattering and eliminate dependence on target parameters. Simultaneously, by combining distance constraints, it achieves flexible construction and stable maintenance of the formation topology.

[0050] Drone swarms can be viewed as spatially distributed network systems where members share information through interaction or measurement, thus achieving collaboration within the drone cluster. When individual drones in the swarm are considered nodes, and the information-sharing links between drones are considered edges, the information-sharing network of the swarm can be viewed as a graph, which can be analyzed using graph theory.

[0051] Using undirected graphs To describe a containing A system of drones, in which the node set express A drone, edge collection Includes nodes With nodes The edge between, undirected edge Indicates drone Information can be obtained from each other through sensing or communication; the system has [a certain number of resources / capabilities]. There is an edge connecting the drones. Neighbors, drones The neighborhood of can be represented as .

[0052] A drone formation was recorded as ,in This is referred to as a formation implementation. Indicates the first The position coordinates of the drone in space. For both implementations... and If the distance between any two adjacent drones is equal, that is... If the distances between any two drones are equal, then the two implementations are said to be equivalent; that is, if the distances between any two drones are equal. If the two implementations are identical, then they are said to be congruent, meaning their formation shapes are exactly the same. For a given formation implementation... If any with Equivalent implementation All equal to If the formation is infinitesimally rigid, then this implementation is infinitesimally rigid. If the formation is infinitesimally rigid, it means that any tiny perturbation cannot change the shape of the formation, and only the formation as a whole is allowed to translate or rotate. This actually places requirements on the formation topology.

[0053] Define the correlation matrix If there is an edge Reaching the node but If there is a border From node Departure All other elements are 0. For an undirected graph, divide the edges into two parts with opposite directions. The corresponding correlation matrix ,in, for The corresponding correlation matrix.

[0054] Define stiffness function

[0055]

[0056] in Indicates the first Edge.

[0057] definition ,but ,in , It is a 3×3 identity matrix.

[0058] Define the stiffness matrix

[0059]

[0060] in Let be the diagonal matrix spanned by the edge vectors. It can be proven that in three-dimensional space, if the formation is infinitesimally rigid, the rank of its stiffness matrix is ​​equal to... ,Right now If a formation is minimally rigid, it means that the formation cannot maintain rigidity if any edge is missing. It can be proven that in three-dimensional space, the minimum number of edges in a formation is... .

[0061] The tracked target is considered a node in a multi-UAV system. Only the tracked target has a reference velocity and moves according to that reference velocity; it is called the "navigator." Other UAVs do not know the reference velocity and are called "trackers." The reference velocity is assumed to be bounded and uniformly continuous, denoted as . .

[0062] Expected formation It is the least rigid, meaning the formation satisfies the infinitesimal rigidity condition. And the number of sides .

[0063] Each drone can acquire the position information of the target and other drones, and maintain the desired formation by controlling the distance between them.

[0064] Consider having The kinematic model of the navigator for a multi-node unmanned aerial vehicle system is... , No. The kinematic model of the tracker is , It is the first The tracker's control input. Compact writing. ,in It is the number of followers, i.e. , yes 3D identity matrix yes Zero-dimensional vector.

[0065] Given distance constraint vector The first vector The elements are , representing two adjacent nodes The desired formation realization is defined as the square of the expected distance between them. Define the formation error vector. The first in the vector The elements are , representing the squared difference between the actual distance and the expected distance between two adjacent nodes. If the error vector... If the convergence to the vicinity of the zero vector is considered to have achieved the desired formation.

[0066] In summary, the present invention aims to design a controller. This makes it possible to have a finite time. ,when The norm of the time error vector always remains within the specified range. within, that is .

[0067] Design a controller to address the above problems.

[0068]

[0069] Under the control of this controller, a given expected error range and initial formation implementation It exists for a limited time. , making .

[0070] in, It controls the gain, which is specified by the user.

[0071] It is the stiffness matrix Divided into blocks The right half, i.e., the stiffness matrix The 2nd to the 3rd List.

[0072] It is a diagonal gain matrix. , For the current moment. In order to alleviate the chattering phenomenon inherent in sliding mode controllers while ensuring the desired control effect is achieved, the first... Adaptive gain coefficient for strip design as follows( ):

[0073]

[0074] in, Specify parameters for the user. To meet The smallest root, for The derivative. Stage, gain coefficient The distance is continuously increased until the distance error is reduced to within the preset range. ; and stage, Able to determine error components The size is adaptively adjusted: The gain increases as the distance increases and decreases as the distance decreases. This strategy effectively suppresses distance errors while significantly reducing control input chattering. Notably, this gain coefficient design does not depend on prior information about the tracked target, exhibiting strong robustness and engineering applicability.

[0075] For matrix , operation express Moore-Penrose inverse. It is a sign function, defined element-wise for vectors, that is... .

[0076] Based on the above, the present invention provides a distance-constrained UAV formation tracking target control method, which includes the following steps:

[0077] Step 1: Initialize the drone system.

[0078] Configure system parameters. System parameters include drone formation implementation. Number of drones Number of followers Minimum number of edges in a rigid formation Distance constraint vector Controller gain parameters and desired error tolerance (Require ).

[0079] Among them, drone formations achieved , This represents the position vector of the navigator. The number of followers... Minimum number of edges in a rigid formation Distance constraint vector The vector representing the desired distance between nodes, the th node... The elements are , representing two adjacent nodes The square of the expected distance between them. Controller gain parameters include... , , ,in, It refers to the proportional control gain in the controller. It is the gain coefficient. The rate of change coefficient, F It is the gain coefficient. One parameter, when hour Get the minimum value F。

[0080] Construct a UAV topology matrix based on system parameters and store the system correlation matrix. If there is an edge Reaching the node but If there is a border From node Departure The remaining elements are 0, dividing the edge into two parts with opposite directions. The corresponding correlation matrix ,in for The corresponding correlation matrix.

[0081] Step 2: Real-time sensing and data collection.

[0082] During each control cycle, each tracking drone acquires two types of information through onboard sensors (such as GPS, visual cameras, and UWB):

[0083] The location of your own drone and neighboring drones: (Regarding neighboring drones) and (itself).

[0084] Location of the tracked target: .

[0085] Step 3: Calculate the current stiffness matrix and formation error vector .

[0086] First, according to the formula Calculate the side vectors of the unmanned aerial vehicle system ,in, , It is a 3×3 identity matrix.

[0087] Then, according to the formula Calculate the current stiffness matrix ,in, It is a diagonal matrix spanned by the edge vectors.

[0088] Finally, calculate the squared distance error for each edge. This forms the formation error vector. .

[0089] Step 4: The controller dynamically adjusts the diagonal gain matrix based on the current error magnitude and stage. , , This refers to the current moment.

[0090] No. Adaptive gain coefficient corresponding to the edge as follows( ):

[0091]

[0092] in, Specify parameters for the user. To meet The smallest root.

[0093] Phase 1 (Fast Convergence Period): Gain coefficient Values Its integral increases over time until the distance error is reduced to a preset range, i.e. This phase aims to quickly bring the formation closer together.

[0094] Phase Two (Steady State Maintenance Period): Gain coefficient Values It can be based on error components The size is adaptively adjusted: It increases with the increase of distance error and decreases with the decrease of distance error. During this stage, while effectively suppressing distance error, it significantly reduces the chattering phenomenon of control input.

[0095] Step 5: Synthesize control commands.

[0096] The current stiffness matrix obtained from steps 3 and 4 Formation error vector and diagonal gain matrix In the input controller, synthesized control commands :

[0097]

[0098] in, It is about controlling the gain. It is the stiffness matrix Divided into blocks The right half, i.e., the stiffness matrix The 2nd to the 3rd List; It is a diagonal gain matrix. It is a symbolic function.

[0099] Step 6: Instruction execution and looping.

[0100] Calculated control commands The command is sent to the drone's actuators, and the drone moves according to the new speed instructions.

[0101] Continue repeating steps 2 through 6 until the task is completed.

[0102] To verify the effectiveness of the designed control method, simulation experiments were conducted in the computer software MATLAB.

[0103] Consider a system consisting of 6 drones, i.e. Among them, drone number 1 is the target being tracked, and drones 2 through 5 are the trackers. The information exchange network between the drones is... Figure 1 As shown in the topology diagram, a formation of 6 drones requires 12 edges to remain stable under this control method. .

[0104] Among them, Unit 1 does not need to observe information from other drones, and proceeds according to the given reference speed. sports.

[0105] Given the desired formation implementation And calculate the distance constraint vector accordingly. Given the initial location of Unit 1. The location of the tracking drone is randomly generated within a certain range nearby.

[0106] Applying the control method proposed in this invention, appropriate control parameters are selected according to the requirements of the implementation scheme. In this experiment, the control parameters are set as follows: , , Required error range The simulation time was set to 8 seconds, and the simulation results of UAV formation tracking target control under distance constraints were obtained as follows: Figure 2 and 3 .

[0107] Depend on Figure 2 It can be seen that the multi-UAV system can maintain its position near the desired formation while tracking the target. Figure 3 It can be seen that although the initial formation error is relatively large, it can quickly converge to near 0 under the control of the controller, and the error remains within the expected range thereafter. This meets the control requirements.

[0108] This embodiment plots the variation curve of the adaptive gain coefficient of the sliding mode controller during the simulation process, such as... Figure 4 As shown. By Figure 4 It can be seen that in the initial stage of the simulation (within the first 0.005 seconds), some gain coefficients increase rapidly to achieve rapid convergence of the tracking error; in the later stage of the simulation, the gain coefficients can adaptively adjust according to the changes in the tracking error, showing good adaptive adjustment characteristics.

[0109] In summary, this invention enables UAV swarm tracking based solely on position information even when the target's state is unknown, eliminating the need for target velocity or prior parameters and reducing information dependence. A distance-constrained modeling method ensures the stability and flexibility of the formation geometry. Sliding mode control combined with adaptive gain adjustment effectively suppresses unknown disturbances and mitigates chattering, thus achieving fast and stable target tracking and formation maintenance within a finite timeframe.

[0110] The above description is merely an embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for controlling UAV formation tracking targets based on distance constraints, characterized in that: Includes the following steps: Step 1: Initialize the drone system; Configure the drone system parameters; parameters include drone formation implementation. Number of drones Number of followers Minimum number of edges in a rigid formation Distance constraint vector Controller gain parameters and desired error tolerance ; Construct a UAV topology matrix based on system parameters and store the system correlation matrix. ; Step 2: Real-time sensing and data collection; In each control cycle, each tracking drone obtains its own position through onboard sensors. Location of neighboring drones and the location vector of the tracked person. ; Step 3: Calculate the current stiffness matrix and formation error vector ; Calculate the side vectors of the unmanned aerial vehicle system Then calculate the current stiffness matrix. ; Calculate the first Squared distance error of the strip ,in, This forms the formation error vector. ; Step 4: The controller dynamically adjusts the diagonal gain matrix based on the current error magnitude and stage. , ,in, For the first The gain coefficient corresponding to the edge. For the current moment, To meet The smallest root, when Gain coefficient The integral increases over time; when Gain coefficient According to error components The size is adaptively adjusted; Step 5: Synthesize control commands; Based on the current stiffness matrix Formation error vector and diagonal gain matrix Calculate control commands ; The control command The calculation is as follows: in, It's about controlling the gain. It is the stiffness matrix Divided into blocks The right half, i.e., the stiffness matrix The To the List, It is a matrix Moore-Penrose inverse; It is a diagonal gain matrix. It is a symbolic function; Step 6: Instruction Execution and Looping; Calculated control commands The command is sent to the drone's actuators, and the drone moves according to the new speed command. Continue repeating steps 2 through 6 until the task is completed.

2. The method for controlling UAV formation tracking targets based on distance constraints according to claim 1, characterized in that: The drone formation achieves Represented as: ,in, The position vector of the tracked entity; The number of trackers Minimum number of edges in a rigid formation .

3. The method for controlling UAV formation tracking targets based on distance constraints according to claim 1, characterized in that: The correlation matrix The construction method is as follows: If there is an edge Reaching the node but If there is a border From node Departure All other elements are 0; Divide the edge into two parts with opposite directions. Then the correlation matrix ,in for The corresponding correlation matrix.

4. The method for controlling UAV formation tracking targets based on distance constraints according to claim 3, characterized in that: The current stiffness matrix The calculation is as follows: First, according to the formula Calculate the side vectors of the unmanned aerial vehicle system ,in, , It is a 3×3 identity matrix; Then, according to the formula Calculate the current stiffness matrix ,in, It is a diagonal matrix spanned by the edge vectors.

5. The method for controlling UAV formation tracking targets based on distance constraints according to claim 1, characterized in that: The formation error vector The The elements are: Indicates adjacent nodes , The difference between the square of the actual distance and the square of the expected distance; in, Represented as a distance constraint vector The Middle element .

6. The method for controlling UAV formation tracking targets based on distance constraints according to claim 1, characterized in that: The gain coefficient Segmentation is defined as: in, For controller gain parameters greater than 0, To meet The smallest root, for The derivative of .

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