A rigid formation control method for GNSS-free unmanned aerial vehicles based on improved extremum seeking and self-triggering mechanism
By improving the extreme value search and self-triggering mechanism, a dynamic system model and communication topology for UAVs were constructed. An unbiased extreme value search controller and self-triggering mechanism were designed, which solved the stability and continuity problems of UAV formation control under GNSS denial environment and realized fast, stable and energy-saving control of UAV formation.
Patent Information
- Application Number
- CN202610741428.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-27
- Publication Date
- 2026-08-25
AI Technical Summary
In GNSS denied environments, traditional rigid formation control methods for UAVs rely on GNSS signals and are prone to failure, leading to a decline or collapse in formation control performance. Furthermore, the stringent convergence conditions for extreme value search and the self-triggering mechanism cause system discontinuity.
An improved extreme value search and self-triggering mechanism is adopted. By constructing a UAV dynamic system model and communication topology matrix, relative distance information is obtained. An improved unbiased extreme value search controller and self-triggering mechanism are designed. Combined with a transition function for signal smoothing, a nonlinear tracking controller is designed to realize rigid formation control of UAVs under GNSS-free conditions.
It achieves rapid, stable, and energy-efficient control of UAV formations in GNSS-denied environments, significantly improves algorithm applicability and convergence speed, reduces system chatter, and ensures the stability and continuity of the formation.
Smart Images
Figure CN122632886A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of UAV cooperative control technology, specifically relating to a rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism. Background Technology
[0002] Quadrotor drones, due to their flexibility, high maneuverability, and low cost, have been widely used in fields such as power line inspection, agricultural plant protection, logistics transportation, and military reconnaissance. In many complex tasks, the capabilities of a single drone are limited; therefore, multi-drone cooperative operations, especially rigid formation control with specific flight formations, have become a research hotspot. Rigid formation control aims to ensure that the drone swarm maintains a preset geometric configuration throughout its movement, which is crucial for scenarios such as coordinated payload, area coverage, and counter-jamming.
[0003] Traditional rigid formation control methods, such as position-based or displacement-based methods, typically rely heavily on Global Navigation Satellite Systems (GNSS) to provide each UAV with precise absolute position information. However, in extreme environments such as canyons, urban building clusters, indoors, or under strong electromagnetic interference, GNSS signals weaken or even fail completely, causing a sharp decline or complete collapse in the performance of GNSS-dependent formation control strategies, making it impossible to maintain formation.
[0004] To reduce reliance on GNSS, range-based rigid formation control methods have emerged. This method requires only that the UAV measures its relative distance to neighboring UAVs using onboard sensors (such as UWB, vision, or lidar) and maintains formation based on this distance information. While this method reduces dependence on absolute position, its core problem transforms into a distributed optimization problem: how to enable each UAV to autonomously calculate its optimal trajectory based solely on local distance information to minimize the overall formation's shape error.
[0005] Extreme value search, as a model-free real-time optimization method, is well-suited for solving optimization problems where an explicit expression for the cost function is unavailable. It estimates the gradient of the cost function by injecting high-frequency perturbation signals and drives the system state to converge toward the optimum.
[0006] Therefore, the technical problem that this invention aims to solve is how to address the shortcomings of rigid formation control in GNSS-denied environments, such as the inability to achieve rigid formation, stringent convergence conditions for extreme value search, and system discontinuity caused by self-triggering mechanisms, so as to achieve rigid formation control of UAVs quickly, stably, and energy-efficiently in GNSS-free environments. Summary of the Invention
[0007] The purpose of this invention is to provide a rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism, so as to solve the problems mentioned in the background art.
[0008] The objective of this invention is achieved as follows: a rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism, characterized by the following steps:
[0009] Step S1: Construct a dynamic system model and communication topology matrix for the UAV, and obtain distance information between UAVs;
[0010] Step S2: Construct a rigid formation error cost function based on relative distance and receive relative distance information within the UAV swarm;
[0011] Step S3: Design an improved unbiased extreme value search controller to obtain the optimal target trajectory for each UAV;
[0012] Step S4: Based on the cost function value at the current moment, calculate the trigger interval using the self-triggering mechanism to determine the time when each UAV will measure distance information next;
[0013] Step S5: Use a transition function to smooth the discrete measurement signal triggered by the self-triggering mechanism, and generate continuous distance information according to the information update time;
[0014] Step S6: Based on the optimal target trajectory of each UAV, design a nonlinear tracking controller to drive the UAV to track accurately.
[0015] Preferably, the construction of the UAV dynamic system model in step S1 specifically includes:
[0016] For drones The UAV dynamic system model is described as follows:
[0017] ;
[0018] in, Indicates drone The velocity vector; , It is a drone quality express Aerodynamic damping coefficient in the axial direction. express Axial aerodynamic damping coefficient Indicates drone exist Velocity in the axial direction, Indicates drone exist Velocity in the axial direction, Represents the input gain matrix. Represents the control input vector. Indicates drone exist Input in the axial direction, Indicates drone exist Input in the axial direction, Indicates drone The velocity vector, Indicates drone The acceleration vector.
[0019] Preferably, in step S2, the rigid formation error cost function based on relative distance is constructed as follows:
[0020] For drones The constructed rigid formation error cost function is: ;
[0021] in, For drones The input vector to be optimized For drones drones with neighbors Regarding distance The transition function; For drones and The expected distance between them For adjacency matrix elements, For the number of drones, Indicates drone With drones The distance.
[0022] Preferably, the dynamic equation of the unbiased extreme value search controller is:
[0023] ;
[0024] in, The estimated optimal target trajectory; For internal state variables; The filtered value is the cost function value; The time-varying bandwidth of the variable bandwidth low-pass filter. Internal state variables rate of change, This indicates the output of the low-pass filter. Indicates drone The detection frequency, Indicates drone Gain of the probe signal, It is a positive constant. Indicates the bandwidth of the low-pass filter. , A positive constant. These are the standard basis vectors.
[0025] Preferably, the time-varying bandwidth of the variable bandwidth low-pass filter is:
[0026] ;
[0027] in, , , A positive constant. This represents the bandwidth gain of a variable bandwidth low-pass filter.
[0028] Preferably, in step S4, the trigger interval is calculated using a self-triggering mechanism, and the expression for calculating the trigger interval is:
[0029] ;
[0030] in, The current trigger time, The sampling interval is... This is the upper bound of the rate of change of the cost function. In order to be in The trigger distance measurement value remains unchanged over the time period. The measured value of the performance indicator.
[0031] Preferably, in step S5, a transition function is used to smooth the discrete measurement signal triggered by the self-triggering mechanism, specifically as follows:
[0032] Transition function Used at two consecutive trigger moments and Between, the trigger signal Perform smooth interpolation; the transition function is monotonic and satisfies the boundary conditions: , And its first derivative is zero at the boundary, that is ;
[0033] Transition function It is implemented using a cubic polynomial.
[0034] Preferably, the nonlinear tracking controller is designed using an immersion and invariance method, defining the target system as... ,in, For virtual control laws;
[0035] Construction manifold deviation and tracking error ;
[0036] The virtual control law and the actual control law are designed as follows: and ;
[0037] in, , These are the control gain of the virtual control law and the control gain of the actual control law, respectively. This is a nonlinear term in UAV dynamics. This represents the rate of change of the virtual control law.
[0038] A rigid formation control system for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism, the GNSS-free UAV rigid formation control system comprising:
[0039] The sensor module is used to acquire distance information between drones;
[0040] The cost function module is used to receive relative distance information within the drone swarm and construct a cost function for each drone to characterize the formation error.
[0041] An improved extreme value search control module is used to execute an unbiased extreme value search algorithm and output the optimal target trajectory for each UAV based on the cost function.
[0042] The self-triggering decision module determines the time when each drone will next measure distance information through a self-triggering mechanism;
[0043] The signal smoothing module uses a transition function to smooth the discrete signal generated by the self-triggered mechanism and generates continuous distance information based on the information update time.
[0044] The trajectory tracking control module, through a nonlinear tracking control law, drives the UAV to accurately track the target trajectory generated by the improved extreme value search control module based on the optimal target trajectory.
[0045] Compared with the prior art, the present invention has the following improvements and advantages:
[0046] 1. By using an improved unbiased extreme value search controller, the coupling between gradient estimation error and high-frequency decay term is effectively eliminated. The constraint condition of the optimal trajectory is relaxed from the exponential convergence requirement of the traditional method to the boundedness requirement, which significantly improves the applicability and convergence speed of the algorithm, while reducing system chattering.
[0047] 2. By adopting a design that combines a self-triggering mechanism with a transition function, the system communication and computational burden is effectively reduced. At the same time, the transition function ensures the continuous differentiability of the cost function within the triggering interval, overcomes the system discontinuity problem caused by the self-triggering mechanism, and ensures that the preconditions of the extreme value search algorithm are met.
[0048] 3. A nonlinear tracking controller was designed using immersion and invariance methods, which enabled accurate tracking of the optimal trajectory. This resulted in a complete solution from trajectory optimization to trajectory tracking, with high system integration, strong practicality, and good engineering application value.
[0049] 4. A complete rigid formation control framework based on relative distance information was constructed. Through distributed optimization methods, the integrated design of trajectory generation and motion control was realized, completely eliminating the dependence on the GNSS system and enabling UAV formations to work stably and reliably in GNSS-denied environments. Attached Figure Description
[0050] Figure 1 This is a flowchart illustrating the method of the present invention.
[0051] Figure 2 This is a schematic diagram of the system structure of the present invention.
[0052] Figure 3 This is a diagram illustrating search results for a single drone.
[0053] Figure 4 This is a schematic diagram illustrating the frequency distribution of search results for a single drone.
[0054] Figure 5 This is a schematic diagram of the formation effect of drones in three-dimensional space. Detailed Implementation
[0055] The invention will be further summarized below with reference to the accompanying drawings.
[0056] like Figure 1 As shown, a rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism is presented. The method includes the following steps:
[0057] Step S1 involves constructing a dynamic system model for the unmanned aerial vehicle (UAV), specifically as follows:
[0058] For drones The UAV dynamic system model is described as follows:
[0059] ;
[0060] in, Indicates drone The velocity vector; , It is a drone quality express Aerodynamic damping coefficient in the axial direction. express Axial aerodynamic damping coefficient Indicates drone exist Velocity in the axial direction, Indicates drone exist Velocity in the axial direction, Represents the input gain matrix. Represents the control input vector. Indicates drone exist Input in the axial direction, Indicates drone exist Input in the axial direction, Indicates drone The velocity vector, Indicates drone The acceleration vector.
[0061] The communication topology graph defines the information exchange relationships between UAVs through an adjacency matrix. The specific adjacency matrix of the communication topology graph is as follows: .
[0062] The UAV dynamic system model describes the kinematic and dynamic characteristics of a single UAV, providing a mathematical description of the controlled object for the tracking controller; the communication topology graph specifies the information interaction relationship between UAVs through the adjacency matrix, enabling each UAV to obtain relative distance measurements with its neighbors.
[0063] Step S2 involves constructing a rigid formation error cost function based on relative distance, specifically as follows:
[0064] The rigid formation error cost function is constructed based on the deviation between the measured distance and the expected distance between the UAV and its neighboring UAVs, and does not rely on the absolute position information provided by the Global Navigation Satellite System (GNSS).
[0065] For drones The constructed rigid formation error cost function is: ;
[0066] in, For drones The input vector to be optimized For drones drones with neighbors Regarding distance The transition function; For drones and The expected distance between them For adjacency matrix elements, For the number of drones, Indicates drone With drones The distance.
[0067] Step S1 uses the model and communication topology to provide each UAV with its relative distance to its neighbors. Step S2 then constructs a rigid formation error cost function based on this, transforming formation shape maintenance into a problem of minimizing the sum of squared deviations between the desired and measured distances. To ensure that the cost function still satisfies the continuous differentiability required for extreme value search even when the measurement signal is discretely updated due to subsequent self-triggered mechanisms, a transition function is introduced to perform smooth interpolation processing on the distance measurements. The constructed cost function value is directly fed into step S3 as the input for the unbiased extreme value search controller to perform real-time gradient estimation and trajectory optimization.
[0068] Step S3 involves designing an improved unbiased extreme value search controller to obtain the optimal target trajectory for each UAV, specifically as follows:
[0069] The unbiased extreme value search controller introduces a variable bandwidth low-pass filter to eliminate the coupling between gradient estimation error and high-frequency attenuation term, thereby relaxing the constraint on the optimal trajectory from exponential convergence to boundedness requirement.
[0070] The unbiased extreme value search controller is:
[0071] ;
[0072] in, The estimated optimal target trajectory; For internal state variables; The filtered value is the cost function value; This represents the time-varying bandwidth of the variable bandwidth low-pass filter; Represents internal state variables rate of change, This indicates the output of the low-pass filter. Indicates drone The detection frequency, Indicates drone Gain of the probe signal, A positive constant. Indicates the bandwidth of the low-pass filter. , A positive constant. These are the standard basis vectors.
[0073] The time-varying bandwidth of the variable bandwidth low-pass filter is:
[0074] ;
[0075] in, , , A positive constant. This represents the bandwidth gain of a variable bandwidth low-pass filter.
[0076] By introducing a variable bandwidth low-pass filter, an improved unbiased extreme value search controller was designed, which effectively eliminated the coupling between gradient estimation error and high-frequency attenuation term. The constraint condition of the optimal trajectory was relaxed from the exponential convergence requirement of the traditional method to the boundedness requirement, which significantly improved the applicability and convergence speed of the algorithm, while reducing system chattering.
[0077] In step S2, the cost function cannot be explicitly expressed, so step S3 employs an unbiased extremum search controller for model-free optimization. Gradient estimation is achieved by injecting high-frequency sinusoidal perturbations and sensing the cost response; however, traditional methods suffer from the coupling between gradient estimation and high-frequency decay terms, imposing stringent requirements on optimal trajectory convergence. This step introduces a variable bandwidth low-pass filter for effective decoupling, relaxing the constraint from exponential convergence to boundedness requirements. The optimal target trajectory output by the controller is fed into step S6 for tracking control execution, while cost change information is transmitted to step S4 for self-triggering to determine the next distance measurement time.
[0078] In step S4, based on the cost function value at the current moment, the trigger interval is calculated using a self-triggering mechanism to determine the time when each UAV will next measure distance information. Specifically:
[0079] A self-triggering mechanism determines the next trigger time for each drone; the expression for calculating the trigger interval is:
[0080] ;
[0081] in, The current trigger time, The sampling interval is... This is the upper bound of the rate of change of the cost function. In order to be in The trigger distance measurement value remains unchanged over the time period. The measured value of the performance indicator.
[0082] Step S3, the extreme value search, requires continuous acquisition of cost function values dependent on real-time distance measurements; however, periodic high-frequency measurements consume excessive energy. Step S4 designs a self-triggering mechanism, where each UAV autonomously calculates the next measurement time based on the current cost change, maintaining a constant distance measurement within the trigger interval, significantly reducing communication and measurement frequency. However, the discrete distance signal generated by this mechanism causes discontinuities in the cost function, violating the continuous differentiability condition required for extreme value search. Therefore, this discrete signal must be smoothed and interpolated using a transition function in step S5 to restore continuity before being re-feeded into the cost function module and extreme value search controller, ensuring stable algorithm operation.
[0083] In step S5, a transition function is used to smooth the discrete measurement signal triggered by the self-triggering mechanism, specifically as follows:
[0084] A transition function is introduced to smooth the discrete measurement signal triggered by the self-triggering mechanism, ensuring that the rigid formation error cost function satisfies the continuity and differentiability assumptions required by the extreme value search algorithm within the triggering interval;
[0085] Transition function Used at two consecutive trigger moments and Between, the trigger signal Perform smooth interpolation; the transition function is monotonic and satisfies the boundary conditions: , And its first derivative is zero at the boundary, that is ;
[0086] Transition function It is implemented using a cubic polynomial.
[0087] In step S6, a nonlinear tracking controller is designed based on the optimal target trajectory of each UAV to drive the UAV to track accurately. Specifically:
[0088] The nonlinear tracking controller is designed using an immersion and invariance approach, defining the target system as... ,in, For virtual control laws;
[0089] Construction manifold deviation and tracking error ;
[0090] The virtual control law and the actual control law are designed as follows: and ;
[0091] in, , These are the control gain of the virtual control law and the control gain of the actual control law, respectively. This is a nonlinear term in UAV dynamics. This represents the rate of change of the virtual control law.
[0092] From the perspective of the overall system operation principle, step S1 provides the underlying information perception foundation for the formation system. Each UAV measures its relative distance to its neighbors through onboard sensors and obtains the local information required for formation through the communication topology. Step S2 constructs these raw distance information into a distributed cost function, transforming the control objective of maintaining the formation configuration into a real-time numerical optimization problem. Since the cost function does not have an explicit mathematical model, step S3 introduces extreme value search, a model-free optimization method, to search in real time for the optimal target trajectory that minimizes the cost function. However, the continuous operation of step S3 faces the problems of high measurement energy consumption and heavy communication burden in engineering practice. Step S4 uses a self-triggering mechanism to allow UAVs to update distance information only when necessary. The discrete nature of the self-triggering mechanism can disrupt the smoothness of the cost function, undermining the continuity assumption upon which the extreme value search algorithm in step S3 relies. Step S5 designs a transition function to keep the signal smooth, ensuring the normal operation of the optimization algorithm while also considering energy-saving requirements. Finally, the optimal target trajectory generated in step S3 needs to be actually executed to produce the desired formation effect. Step S6 uses a nonlinear tracking controller designed with immersion and invariance methods, which can overcome the nonlinear characteristics in UAV dynamics and drive the UAV to accurately track the optimal trajectory.
[0093] A rigid formation control system for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism includes:
[0094] The sensor module is used to acquire distance information between drones;
[0095] The cost function module is used to receive relative distance information within the drone swarm and construct a cost function for each drone to characterize the formation error.
[0096] An improved extreme value search control module is used to execute an unbiased extreme value search algorithm and output the optimal target trajectory for each UAV based on the cost function.
[0097] The self-triggering decision module determines the time when each drone will next measure distance information through a self-triggering mechanism;
[0098] The signal smoothing module uses a transition function to smooth the discrete signal generated by the self-triggered mechanism and generates continuous distance information based on the information update time.
[0099] The trajectory tracking control module, through a nonlinear tracking control law, drives the UAV to accurately track the target trajectory generated by the improved extreme value search control module based on the optimal target trajectory.
[0100] To verify the feasibility and effectiveness of this invention, the following experiments were conducted:
[0101] First, conduct a separate verification of the improved ES technology:
[0102] Single drone ES verification parameters set to , , , , The rigid formation control parameters are uniformly set to... , , , ( , ), The specific values for the frequency parameters are: , , , , , , , , , The low-pass filter bandwidth is set to , , , , .
[0103] The self-triggering mechanism parameters include the trigger interval adjustment parameter. Basic sampling interval and the upper bound of the rate of change of the cost function The tracking controller parameters include the virtual control law gain. and actual control law gain , must meet and The conditions; parameter selection follows the frequency separation principle to ensure Much greater than system dynamics, and The parameters are set to a moderate value, and the range is determined by Lyapunov stability analysis to achieve a balance between convergence speed, steady-state accuracy and anti-jamming. Different frequencies are assigned to different UAVs to avoid mutual interference.
[0104] The individual verification of the improved ES technology takes a single unmanned aerial vehicle (UAV 3) as the research object, and sets the cost function as follows. The time-varying optimal value is Improve the parameter configuration of ES technology to , , , , Simulation results show that the improved strategy can more accurately and stably track the theoretical extreme value curve. A magnified view reveals that it maintains high-precision search characteristics even in the later, shorter time periods, exhibiting superior steady-state performance and better low-frequency characteristics. These advantages help the system operate at lower cost and higher efficiency. Next, the improved ES technology is verified in a rigid formation using an STM with a self-triggering mechanism. This verification constructs a rigid formation consisting of one lead UAV and five follower UAVs, using an adjacency matrix... Define the communication connection relationship between drones and improve the parameter settings of ES technology. , , ,in , The disturbance signal frequency and low-pass filter parameters for each UAV are configured with different values, and a rigid trajectory parameter matrix is defined. Simulation results show that the improved strategy achieves the desired formation speed faster and significantly reduces UAV trajectory jitter. Taking UAV 3 as an example, its trajectory is smoother, the overall formation is more stable, and the transition function... Successfully smoothed the trigger signal This avoids signal discontinuity caused by STM, and compared with the periodic time triggering scheme, the improved STM strategy significantly reduces the number of triggering events, with a reduction of 68.83%-86.45%, effectively reducing the energy consumption of the drone.
[0105] like Figure 3 As shown, the search results closely follow the changes in the theoretical extreme value curve, showing a stable growth trend over time without significant fluctuations or deviations. In terms of search accuracy, the search results are highly consistent with the theoretical extreme value curve, with minimal overall deviation. Even in the later stages of the graph (such as when the time is close to 100s) within a small local magnified area (such as the 49.1-49.3s interval), it is clear that the search results maintain high accuracy and almost coincide with the theoretical extreme value curve. This fully demonstrates the accuracy and stability of the improved ES technology in tracking time-varying optimal values, with particularly significant performance advantages during steady-state operation.
[0106] like Figure 4 As shown, the range covers from low frequency to a specific high frequency, with values concentrated between -0.05 and 0.05, reflecting the output stability of the strategy at different frequencies. The curve representing the improved strategy in the figure shows better frequency domain characteristics overall, especially in the low frequency range. The fluctuation amplitude of this curve is extremely small, almost close to the zero point of the vertical axis, and the deviation is controlled within a very small range, close to 0.02 or -0.02, with no obvious abnormal fluctuations.
[0107] like Figure 5 As shown, the five drones are stably arranged strictly according to the preset geometric configuration. The positional distribution of each drone conforms to the constraints of a rigid formation, with no obvious positional deviations or configurational disorder, clearly demonstrating the structural integrity and geometric stability that a rigid formation should possess. Based on the background information, this formation effect is achieved through an improved extreme value search technique, which makes... Figure 4 The formation not only forms quickly, but also ensures that the positions of each UAV are stable after formation, and the overall configuration can maintain the preset rigidity characteristics, which fully verifies the effectiveness of the improved strategy in achieving rigid UAV formation control in a GNSS-free environment.
[0108] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.
Claims
1. A rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism, characterized in that: The method includes the following steps: Step S1: Construct a dynamic system model and communication topology matrix for the UAV, and obtain distance information between UAVs; Step S2: Construct a rigid formation error cost function based on relative distance and receive relative distance information within the UAV swarm; Step S3: Design an improved unbiased extreme value search controller to obtain the optimal target trajectory for each UAV; Step S4: Based on the cost function value at the current moment, calculate the trigger interval using the self-triggering mechanism to determine the time when each UAV will measure distance information next; Step S5: Use a transition function to smooth the discrete measurement signal triggered by the self-triggering mechanism, and generate continuous distance information according to the information update time; Step S6: Based on the optimal target trajectory of each UAV, design a nonlinear tracking controller to drive the UAV to track accurately.
2. The rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism according to claim 1, characterized in that: The construction of the UAV dynamic system model in step S1 is specifically as follows: For drones The UAV dynamic system model is described as follows: ； in, Indicates drone The velocity vector; , It is a drone quality express Aerodynamic damping coefficient in the axial direction. express Axial aerodynamic damping coefficient Indicates drone exist Velocity in the axial direction, Indicates drone exist Velocity in the axial direction, Represents the input gain matrix. Represents the control input vector. Indicates drone exist Input in the axial direction, Indicates drone exist Input in the axial direction, Indicates drone The velocity vector, Indicates drone The acceleration vector.
3. The rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism according to claim 1, characterized in that: In step S2, a rigid formation error cost function based on relative distance is constructed, specifically as follows: For drones The constructed rigid formation error cost function is: ; in, For drones The input vector to be optimized For drones drones with neighbors Regarding distance The transition function; For drones and The expected distance between them For adjacency matrix elements, For the number of drones, Indicates drone With drones The distance.
4. The rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism according to claim 1, characterized in that: The dynamic equation of the unbiased extreme value search controller is: ； in, The estimated optimal target trajectory; For internal state variables; The filtered value is the cost function value; The time-varying bandwidth of the variable bandwidth low-pass filter. Internal state variables rate of change, This indicates the output of the low-pass filter. Indicates drone The detection frequency, Indicates drone Gain of the probe signal, It is a positive constant. Indicates the bandwidth of the low-pass filter. , A positive constant. These are the standard basis vectors.
5. A rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism as described in claim 4, characterized in that: The time-varying bandwidth of the variable bandwidth low-pass filter is: ； in, , , A positive constant. This represents the bandwidth gain of a variable bandwidth low-pass filter.
6. The rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism according to claim 1, characterized in that: In step S4, the trigger interval is calculated using a self-triggering mechanism. The expression for calculating the trigger interval is: ； in, The current trigger time, The sampling interval is... This is the upper bound of the rate of change of the cost function. In order to be in The trigger distance measurement value remains unchanged over the time period. The measured value of the performance indicator.
7. The rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism according to claim 1, characterized in that: In step S5, a transition function is used to smooth the discrete measurement signal triggered by the self-triggering mechanism, specifically as follows: Transition function Used at two consecutive trigger moments and Between, the trigger signal Perform smooth interpolation; the transition function is monotonic and satisfies the boundary conditions: , And its first derivative is zero at the boundary, that is ; Transition function It is implemented using a cubic polynomial.
8. A rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism as described in claim 1, characterized in that: The nonlinear tracking controller is designed using an immersion and invariance approach, and the target system is defined as follows: ,in, For virtual control laws; Construction manifold deviation and tracking error ; The virtual control law and the actual control law are designed as follows: and ; in, , These are the control gain of the virtual control law and the control gain of the actual control law, respectively. This is a nonlinear term in UAV dynamics. This represents the rate of change of the virtual control law.
9. A rigid formation control system for GNSS-free unmanned aerial vehicles based on an improved extreme value search and self-triggering mechanism, characterized in that: The rigid formation control system for GNSS-free UAVs is formed according to any one of claims 1-8, which is a rigid formation control method for GNSS-free UAVs based on an improved extreme value search and self-triggering mechanism; The GNSS-free UAV rigid formation control system includes: The sensor module is used to acquire distance information between drones; The cost function module is used to receive relative distance information within the drone swarm and construct a cost function for each drone to characterize the formation error. An improved extreme value search control module is used to execute an unbiased extreme value search algorithm and output the optimal target trajectory for each UAV based on the cost function. The self-triggering decision module determines the time when each drone will next measure distance information through a self-triggering mechanism; The signal smoothing module uses a transition function to smooth the discrete signal generated by the self-triggered mechanism and generates continuous distance information based on the information update time. The trajectory tracking control module, through a nonlinear tracking control law, drives the UAV to accurately track the target trajectory generated by the improved extreme value search control module based on the optimal target trajectory.