Mpc cooperative formation method of fusion of detm and fixed-time rbf neural network observer

Abstract

The application relates to a model predictive control cooperative formation algorithm fusing a dynamic event triggering mechanism and a fixed-time RBF neural network observer. First, a fixed-time RBF neural network disturbance observer is designed, the distortion of a prediction model is eliminated through accurate feedforward compensation, and the system robustness is improved. Secondly, a penalty function is introduced in the MPC to construct an obstacle avoidance strategy, so that the unmanned aerial vehicle can sacrifice the formation to protect itself in a dangerous moment, and recover after escaping danger. In addition, the DTM mechanism designed in the application breaks the traditional time-driven mode, accurately schedules computing power to critical moments such as threshold mutation and emergency obstacle avoidance, greatly reduces the airborne computing and communication burden, and strictly proves the closed-loop stability and no Zeno behavior through Lyapunov analysis.

Description

Technical Field

[0001] This invention relates to unmanned aerial vehicle (UAV) control technology, specifically to an MPC collaborative formation method that integrates DETM and a fixed-time RBF neural network observer. Background Technology

[0002] In recent years, frequent "low, slow, and small" illegal activities in the low-altitude airspace security field have seriously threatened core municipal facilities and public safety. These targets are able to evade traditional defense systems by utilizing complex urban terrain, reflecting the limitations of existing security mechanisms.

[0003] To address this challenge, multi-UAV (Unmanned Aerial Vehicle) cooperative control, with its high mobility and intelligence, has provided solutions for various application scenarios and has become a current research hotspot. Notably, the dynamic encirclement and autonomous tracking control of multi-UAV systems has attracted in-depth research due to its ability to continuously monitor detectable targets and take intelligent countermeasures. However, existing encirclement control research largely relies on ideal models and fixed rigid formation constraints. In real low-altitude environments, there are severe time-varying wind field disturbances and unmodeled dynamics introduced by UAV movement. Although existing research has introduced RBF neural networks or various observers for disturbance compensation, traditional observers often exhibit transient response lag when dealing with such lumped disturbances, leading to distorted encirclement trajectories and making them unsuitable for applications with extremely high safety and adaptability requirements.

[0004] Furthermore, when performing encirclement tasks in narrow or complex urban spaces, static control strategies hinder formations from achieving real-time adaptive control, thus drawing widespread attention to obstacle avoidance techniques in complex 3D environments. Model predictive control (MPC) shows great potential in 3D obstacle avoidance for UAVs due to its ability to effectively handle multi-constraint optimization problems. However, when using advanced optimization algorithms to address the complex coupling between 3D obstacle avoidance and encirclement, traditional time-driven mechanisms impose significant communication and computational burdens, making it difficult to meet the limited onboard computing power of micro UAVs. Summary of the Invention

[0005] The purpose of this invention is to provide an MPC cooperative formation method that integrates DETM and fixed-time RBF neural network observers, which improves system robustness and significantly reduces the burden of airborne computing and communication.

[0006] The present invention adopts the following technical solution:

[0007] A collaborative formation method for MPC that integrates DETM and fixed-time RBF neural network observers is optimized based on the MPC framework to achieve collaborative formation control of UAVs. Specifically, it includes: (1) adding a lumped disturbance term to the prediction model to obtain a discrete state space prediction model with feedforward compensation; (2) improving the MPC cost function using obstacle avoidance and collision avoidance penalty functions; and (3) optimizing the triggering time of MPC by combining the dynamic event triggering conditions of three-dimensional obstacle avoidance perception.

[0008] Furthermore, a lumped perturbation term is introduced into the MPC framework. , No. Discrete state-space prediction model for UAVs with feedforward compensation:

[0009]

[0010] in, This is an estimate of the lumped disturbance term; The sampling period is At the current sampling time, , The prediction step size for MPC, and They represent in Predicting the future at any moment The system status and control inputs of each step.

[0011] Furthermore, the estimated value of the lumped disturbance term Estimation is performed using a fixed-time RBF neural network perturbation observer;

[0012] The RBF neural network perturbation observer is specifically:

[0013]

[0014] in, For the observed value of velocity, For actual speed, For the observation error of velocity, These are estimates of the neural network weights. The observer gain matrix is ​​a constant. ; For a fixed time independent of the initial state; diagonal matrix and These represent system parameters related to system damping and control gain, respectively.

[0015] The estimated value of the lumped disturbance can be expressed as:

[0016] in, This is the transpose matrix of the neural network weight estimates. Let Gausky function vector be the vector. For network input containing drone status information.

[0017] Furthermore, the improved MPC cost function is expressed as follows:

[0018]

[0019] in, and These are the error state and the control input increment, respectively. The positive definite weight matrix, The penalty weighting factor for obstacle avoidance, This is the penalty function for obstacle avoidance and collision prevention.

[0020] Furthermore, the obstacle avoidance and collision avoidance penalty function is:

[0021]

[0022]

[0023] in, Minimum safe distance; The radius of the threat detection area.

[0024] Furthermore, the specific conditions for triggering the dynamic event are as follows:

[0025]

[0026] in, For the first The moment when MPC optimization is triggered ; To enhance threat early warning capabilities, The obstacle threat level is calculated by the sensor at the current moment. This represents the threat level predicted by the previous MPC at the current moment.

[0027] The beneficial effects of this invention are as follows: Addressing the multi-UAV 3D target encirclement control problem under complex and disturbed environments, this invention proposes a collaborative formation algorithm that integrates a Dynamic Event Triggered Mechanism (DETM) and a fixed-time RBF neural network observer in model predictive control (MPC). First, a fixed-time RBF neural network disturbance observer is designed, eliminating prediction model distortion through precise feedforward compensation and improving system robustness. Second, a penalty function is introduced into MPC to construct an obstacle avoidance strategy, enabling UAVs to sacrifice formation to preserve themselves in critical moments and recover after escaping danger. Furthermore, the DETM mechanism designed in this invention breaks away from the traditional time-driven approach, precisely allocating computing power to critical moments such as threshold mutations and emergency obstacle avoidance, significantly reducing the onboard computing and communication burden. Moreover, its closed-loop stability has been rigorously proven through Lyapunov analysis, and it exhibits no Zeno behavior. Attached Figure Description

[0028] Figure 1 Three-dimensional trajectories for drone formation encirclement and static obstacle avoidance.

[0029] Figure 2 Comparison of the actual lumped disturbance of UAV-2 on the X / Y / Z axes with the estimates of the fixed-time RBF observer.

[0030] Figure 3 This shows the distribution of trigger times for the dynamic event triggering mechanism.

[0031] Figure 4 This represents the actual distance between each drone and the obstacle.

[0032] Figure 5 This represents the error between the drone formation and the desired trajectory. Detailed Implementation

[0033] The technical solution of the present invention will be described in detail and completely below through specific embodiments.

[0034] I. System Modeling

[0035] This section introduces the dynamic model of the unmanned aerial vehicle, as well as the three-dimensional collision avoidance and obstacle avoidance model, and designs a fixed-time RBF neural network disturbance observer.

[0036] (1) Dynamics model of UAV with lumped perturbation

[0037] Consider a formation system consisting of N drones. In three-dimensional space, the first... drone The kinematic and dynamic model can be described as follows:

[0038] (1)

[0039] in, Indicates the first The three-dimensional position vector of the UAV in the inertial coordinate system. Yaw angle This represents the velocity and yaw rate vectors. To control the input vector, This represents the rotation and translation matrix from the body coordinate system to the inertial coordinate system. (Diagonal matrix) and These represent system parameters related to system damping and control gain, respectively.

[0040] Unlike the ideal model, this invention considers the environmental disturbances that the UAV will experience during actual flight, such as unmodeled dynamics, parameter perturbations, and external wind fields. Therefore, a lumped disturbance term is introduced into the dynamic equations. To ensure the accuracy of subsequent MPC trajectory predictions, it is necessary to conduct [further research / analysis] before the controller design. To make accurate estimates and compensations.

[0041] (2) Three-dimensional space collision avoidance and obstacle avoidance model

[0042] In complex three-dimensional flight environments, UAVs not only need to maintain formation configuration, but also must avoid static or dynamic obstacles and prevent collisions between UAVs. Assuming the flight environment contains... An obstacle, which is then compared to the drone. of The neighboring nodes are collectively defined as drones. Threat set .

[0043] Assume the first One threat ( ) and the All drones can be considered as spheres, and their radii are denoted as . and , Define the drone's detection radius. and threats The relative distance vector between them is To quantify collision risk, a minimum safe distance is defined. and the radius of the threat detection area as follows:

[0044] (2)

[0045] (3)

[0046] To achieve active obstacle avoidance within the MPC framework, an artificial potential field method is used to construct collision avoidance and obstacle avoidance penalty functions. :

[0047] (4)

[0048] (5)

[0049] When a threat enters the detection area ( When this occurs, the system activates the obstacle avoidance mechanism. For drones... The total threat potential function it faces is the superposition of all penalty terms within the set, i.e. When the drone approaches the minimum safe distance, It will rise sharply and tend to infinity, thus incurring a huge cost penalty in MPC optimization, forcing drones to deviate from dangerous areas and actively adjust or temporarily abandon fixed formation structures to ensure absolute physical survival space.

[0050] (3) Design of a perturbation observer based on a fixed-time RBF neural network

[0051] Due to aggregate disturbance The disturbance is highly nonlinear and unknown, and traditional linear observers struggle to guarantee fast convergence. To provide accurate feedforward compensation for MPC, this invention employs a radial basis function (RBF) neural network to approximate the unknown disturbance. Based on the universal approximation property of the RBF neural network, continuous lumped disturbances can be designed as:

[0052] (6)

[0053] in, For the ideal optimal network weight matrix, Let Gausky function vector be the vector. Input to the network (including drone status information). For bounded network approximation error ( ).

[0054] In order to obtain the target within a fixed time period For accurate estimation, a fixed-time RBF neural network perturbation observer is designed as follows:

[0055] (7)

[0056] in, For the observed value of velocity, For actual speed, For the observation error of velocity, The weights are estimated values ​​for the neural network weights and are adjusted online by an adaptive update law. The observer gain matrix is ​​a constant. By introducing a fractional power term, this observer can ensure the accuracy of velocity observation errors. and its derivative in a fixed time independent of the initial state It converges to a minimal neighborhood of the origin.

[0057] At this point, the estimated value of the lumped disturbance can be expressed as: This high-precision disturbance estimate In the prediction model of nonlinear MPC, compensation can effectively offset the trajectory prediction deviation caused by disturbances such as wind field.

[0058] II. Event-Triggered MPC Obstacle Avoidance Controller Design

[0059] To ensure safe obstacle avoidance for UAV formations while minimizing the online optimization burden on the onboard computer, this section proposes an MPC control architecture with disturbance compensation and dynamic event triggering mechanisms.

[0060] (1) Construction of MPC prediction model based on RBF compensation

[0061] Within the MPC framework, the continuous nonlinear dynamics model of the UAV needs to be discretized. The Euler method is employed, and the estimates from the fixed-time RBF perturbation observer designed in the first part are introduced. , can obtain the first Discrete state-space prediction model for UAVs with feedforward compensation:

[0062] (8)

[0063] in, The sampling period is At the current sampling time, , The prediction step size for MPC, and They represent in Predicting the future at any moment The system status and control inputs of each step.

[0064] Thanks to the accurate estimation characteristics of RBF neural networks within a fixed time, the feedforward term It can effectively offset unmodeled lumped disturbances such as wind fields, thereby greatly improving the trajectory prediction accuracy of the model in complex environments and laying the foundation for subsequent safety obstacle avoidance planning.

[0065] (2) MPC optimization design

[0066] In a pure MPC architecture, the control objective of the formation is to enable UAVs to actively avoid static and dynamic obstacles in three-dimensional space while tracking the desired reference trajectory and maintaining a relative geometric formation.

[0067] Definition of the first A drone in The formation tracking error at time t is:

[0068] (9)

[0069] in, The position of the virtual reference target, The desired relative formation position.

[0070] To achieve multi-objective optimization, the following MPC cost function is designed, which includes tracking error penalty, control energy consumption penalty, and obstacle avoidance penalty:

[0071] (10)

[0072] in, and These are the error state and the control input increment, respectively. The positive definite weight matrix, The penalty weighting factor for obstacle avoidance, The obstacle avoidance and collision avoidance penalty functions defined in the first part.

[0073] in,

[0074] At each optimization trigger moment, the MPC solver needs to satisfy the following physical constraints:

[0075] (11)

[0076] in, and These represent the lower and upper physical bounds of the control commands that the UAV's actuators can output, respectively. and These represent the lower and upper physical bounds of the control command increment, respectively, used to limit the intensity of drone maneuvers.

[0077] By solving the above constrained nonlinear optimization problem, the optimal control input sequence can be obtained:

[0078] (12)

[0079] in, This represents the step size from the current time to the future prediction after solving the above constrained optimization problem. The optimal control input sequence within. This indicates the predicted future number in the sequence. The optimal control command for each step. In actual operation, the UAV only executes the first control command in the sequence.

[0080] The combination of tracking error and obstacle penalty function ensures that the UAV can proactively relax its strict formation constraints during critical obstacle avoidance operations to ensure survivability and smoothly restore formation after the threat is eliminated.

[0081] (3) Dynamic event triggering mechanism for integrating threat perception

[0082] Traditional continuous-time MPC in each sampling period The aforementioned cost function is solved repeatedly, leading to a huge waste of computational resources. To overcome this bottleneck, this invention innovatively proposes a dynamic event triggering mechanism that integrates tracking error threshold and obstacle threat warning.

[0083] definition For the first The moment when MPC optimization is triggered In the triggering interval Within the system, the UAV only executes the optimal control sequence obtained from the previous optimization sequentially. No further rolling solutions are performed. Due to the influence of the external environment, the actual flight state differs from the MPC. The predicted state at time t will have a bias, which is defined as:

[0084] (13)

[0085] in, This indicates the deviation in state prediction within the dynamic event triggering interval. For the drone based on the last trigger time The expected state of the current system obtained from the MPC prediction, This represents the actual system state as measured by the drone at the current moment.

[0086] To avoid the conservatism of traditional static triggering mechanisms, a dynamic auxiliary variable is introduced. Its adaptive update law is designed as follows:

[0087] (14)

[0088] in, All of these are given positive design parameters.

[0089] Triggering condition design: the wake-up time for the next optimization solution It is strictly determined by the following dynamic triggering conditions that integrate 3D obstacle avoidance perception:

[0090] (15)

[0091] in, To enhance threat early warning capabilities, The obstacle threat level is calculated by the sensor at the current moment. This represents the threat level predicted by the previous MPC at the current moment.

[0092] When there are no obstacles around and the system is minimally disturbed (i.e.) Smaller ), dynamic variables The trigger threshold has been effectively relaxed, allowing drones to operate for extended periods without performing MPC calculations, significantly conserving computing power. When a dynamic obstacle suddenly approaches, or a gust of wind causes the drone to veer towards an obstacle, the actual detected threat level is... It will be significantly larger than predicted. , It will instantly grow larger, forcibly breaking the inequality constraints, and immediately waking up the MPC solver to replan obstacle avoidance, thus ensuring the absolute flight safety of the drone under extreme conditions.

[0093] III. Feasibility and System Stability Analysis

[0094] This section will rigorously prove the recursive feasibility of the dynamic event-triggered MPC algorithm from a theoretical perspective, analyze the stability of the closed-loop formation system, and prove that the Zeno phenomenon will never occur during the system's operation.

[0095] (1) Feasibility of recursion

[0096] Theorem 1: Assume the initial time Since the MPC optimization problem has a feasible solution and the estimation error of the lumped perturbation is bounded, under the dynamic event triggering mechanism designed in this invention, for all subsequent triggering moments... The MPC optimization problem always has a set of feasible control sequences that satisfy physical constraints and obstacle avoidance requirements.

[0097] Proof: Assume at the triggering time The MPC solver obtained the optimal control sequence. At the next triggering moment We can construct the control sequence from the previous time step by shifting it and adding an auxiliary control law to one end. Candidate control sequence at time step Because the RBF perturbation observer guarantees the actual state. With predicted state The true deviation between It is controlled, and as can be seen from the event triggering conditions, in Previously always satisfied Therefore, the predicted trajectory of the state under the candidate control sequence is still strictly restricted within the boundary of the state constraint set and the safe obstacle avoidance potential field. In summary, the candidate sequence It is a set of feasible solutions that satisfy the control amplitude and increment constraints, thus proving the recursive feasibility of the problem.

[0098] (2) Stability analysis of closed-loop system

[0099] Theorem 2: Under the premise of satisfying Theorem 1, a cost function with an obstacle avoidance penalty term is adopted. As a Lyapunov function, the UAV closed-loop formation system is asymptotically stable under the control of the event-triggered MPC strategy, and the tracking error... It eventually converges to the bounded neighborhood of the origin.

[0100] Proof: Define the optimal cost function As the Lyapunov functional of the system. At any two adjacent trigger times and The evolution of the Lyapunov function is analyzed. This is achieved by utilizing the monotonically decreasing property of standard MPC and the positive definite matrix in the cost function. Based on the characteristics, the candidate cost function satisfies... .

[0101] The derivation process is as follows:

[0102] The optimal control sequence is known to be:

[0103] (16)

[0104] The optimal error state sequence is: (17)

[0105] The cost function is:

[0106] (18)

[0107] Among them, the stage cost Terminal cost Construct a candidate control sequence. Add a terminal feedback control law at the end. We can obtain:

[0108] (19)

[0109] Similarly, the candidate error state sequence is:

[0110]

[0111] time Candidate cost function for:

[0112] (20)

[0113] For MPC to be stable, the Lyapunov descent condition must be met:

[0114] (twenty one)

[0115] (twenty two)

[0116] (twenty three)

[0117] The final candidate cost function can be obtained as follows: (twenty four)

[0118] State prediction bias is caused by unpredictable external extreme disturbances or the intrusion of dynamic obstacles. This will cause the actual cost function to deviate from the ideal situation. However, the dynamic event triggering conditions designed in this invention are strictly limited. Increase in sudden threat level The upper bound of . Therefore, it can be deduced that:

[0119] (25)

[0120] in, These are constant coefficients. When the tracking error... Greater than a certain value depends on the perturbation estimation error bound. When the threshold is reached, Strictly valid.

[0121] Therefore, the system has input state stability, and the UAV formation can safely and stably converge to the desired trajectory.

[0122] (3) Zeno phenomenon excluded

[0123] The key to whether event-triggered control can be implemented in actual engineering lies in whether there is a strictly greater than zero lower bound for the triggering time interval. If the Zeno phenomenon occurs, the controller will perform an infinite number of MPC optimizations in an instant, causing the system to crash.

[0124] Theorem 3: Considering the UAV dynamics system and dynamic event triggering conditions designed in this invention, the Zeno phenomenon will never occur during operation, and the time interval between any two triggers is strictly equal to the time interval between the two triggers. The lower bound.

[0125] Proof: Examine the state prediction bias In the trigger zone The dynamic evolution rate within. For Taking the derivative and using the Lipschitz continuity, we get:

[0126] (26)

[0127] in For the system nonlinear function The Lipschitz constant at the trigger time The state deviation returns to zero, that is Solve the above differential inequality; the solution process is as follows. Based on the system's nonlinear function... The Lipschitz continuity condition yields... At the trigger time The predicted state has just been updated, so the initial bias is zero. Let scalar function We can obtain:

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134]

[0135]

[0136]

[0137] Will Substitution allows us to obtain the variation of the upper bound of the deviation over time:

[0138] (27)

[0139] Based on the aforementioned triggering conditions, at the next triggering time... When it happens, there will inevitably be Achieved by dynamic variables and error and the critical threshold formed by obstacle avoidance increment .

[0140] (28)

[0141] The lower bound of the triggering time interval can be obtained through algebraic transformation. The algebraic transformation process is as follows:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147] Divide both sides of the inequality by a constant. By swapping the positions of the left and right sides, we can obtain the lower bound of the final trigger time interval: (29)

[0148] because The result is strictly greater than zero, which proves that the system can not only achieve complex MPC obstacle avoidance control, but also fundamentally eliminate the Zeno phenomenon. This mathematically guarantees the feasibility of deploying the algorithm on actual UAV hardware platforms.

[0149] IV. Simulation Analysis and Result Analysis

[0150] To fully verify the comprehensive performance of the dynamic event-triggered model predictive control algorithm with a fixed-time RBF disturbance observer proposed in this invention, a set of continuous test scenarios was designed in this section.

[0151] The simulation sets up a scenario where five drones surround a virtual navigator in a three-dimensional spiral ascent. During the 10-second flight, the system will face multiple challenges, including stable cruise, sudden strong wind disturbances, and extreme one-sided obstacle avoidance. This scenario fully demonstrates the system's superior performance in disturbance resistance, active obstacle avoidance, and computational optimization within a single timeframe. The simulation is conducted on the MATLAB R2023b platform. The total simulation duration is set to 200 seconds, with a time step of 0.01 seconds.

[0152] In this embodiment, the key simulation parameters of the relevant model and controller are specifically set as follows:

[0153] (1) Sampling and prediction parameters: system sampling step size MPC prediction step size .

[0154] (2) Observer parameters: The gain matrix of the fixed-time RBF perturbation observer is set to , The power term parameter is set to , .

[0155] (3) MPC cost function parameters: error state weight matrix Controlling the incremental weight matrix Obstacle avoidance penalty weighting factor .

[0156] (4) Obstacle avoidance perception parameters: static obstacle half Drone safety collision avoidance radius obstacle detection radius .

[0157] (5) Dynamic Event Trigger (DETM) Parameter: Threat Warning Gain .

[0158] Figure 1 The demonstration showcased the integrated 3D flight trajectory of a drone formation over 10 seconds. In the initial phase (0-1s), five followers surrounded the virtual navigator in a spiral configuration. When a strong, time-varying crosswind suddenly appeared at 1s, the formation only experienced a minimal translational shift, without any trajectory divergence or collapse, and returned to its intended trajectory after 1.2s. Most importantly, between 2.5 and 4.5s, the formation encountered a static physical obstacle stuck at the edge of the encircling conduit. Figure 1 It can be clearly observed that when the array of drones approaches an obstacle, it actively generates an obstacle avoidance expansion curve outward, and then retracts back to its original desired trajectory after passing the obstacle.

[0159] Figure 2 This paper presents comparative data on the actual perturbations (solid black lines) of UAV2 along the X / Y / Z axes in three-dimensional space, and the estimated values ​​from the RBF neural network (dashed red lines). Before 1 second, the system is perturbation-free, and the observer output is strictly zero. At the moment of the sudden crosswind at 1 second, the actual perturbation curve undergoes a dramatic change. At this point, the fixed-time RBF observer designed in this paper responds rapidly, undergoing high-frequency weight adjustments within an extremely short transient of only about 0.2 seconds, and subsequently accurately matches the actual time-varying perturbation trajectory. This result strongly demonstrates that the observer possesses extremely fast convergence speed and feedforward compensation capability, fundamentally ensuring the high fidelity of the MPC prediction model under severe wind fields.

[0160] Figure 3The dynamic event trigger point distribution is presented intuitively. The density of the scatter plot perfectly illustrates the core design concept of reducing computing power. During the stable period (0~1s and 4.5~10s), the trigger points are extremely sparse, and the system maintains basic formation flight with very low computing power consumption. During the disturbance resistance period (1.0~1.2s), the wind field causes an increase in physical errors, and the trigger density increases briefly. MPC actively calculates to counteract external disturbances. During the computing power burst period (2.5~4.5s), when the sensor detects an approaching obstacle, the threat level in the trigger conditions increases. The inequality threshold is forcibly broken. At this point, the red scatter points in the graph are extremely dense, and MPC enters its highest frequency solution mode. Statistically, the overall average trigger rate of the system is only 16.7% during the entire 10-second complex flight mission. This means that, while achieving multiple objectives such as high-precision encirclement, strong wind resistance, and extreme obstacle avoidance, the algorithm in this paper significantly reduces the communication and computational burden by approximately 83.3% compared to traditional time-driven MPC, greatly improving its feasibility for practical engineering deployment.

[0161] Figure 4 The distances of each drone relative to the obstacle surface were recorded. The distance curves showed a slight peak between 1.0s and 1.2s, perfectly corresponding to the slight shift caused by wind disturbance. Between 2.5s and 4.5s, as the aircraft approached the obstacle, the distance curves dropped sharply, but remained within the absolute physical collision redline. This provides an absolute safety guarantee for collision avoidance from a mathematical perspective.

[0162] Figure 5 Demonstrates formation position tracking error The changes were as follows: In the initial stage of wind field disturbance (1.0s~1.2s), the error spiked slightly but was quickly smoothed out by the fixed-time RBF observer. However, after obstacle avoidance was activated at 2.5s, the system actively broke the formation constraints to ensure survival space, causing the tracking error to spike dramatically. Nevertheless, after the danger was cleared at 4.5s, all error curves showed a smooth exponential decrease and quickly converged to the zero domain, fully demonstrating the algorithm's strong robustness.

Claims

1. An MPC collaborative grouping method integrating DETM and fixed-time RBF neural network observers, characterized in that, Based on the MPC framework, optimization is carried out to realize the cooperative formation control of UAVs; specifically, it includes: (1) adding a lumped disturbance term to the prediction model to obtain a discrete state space prediction model with feedforward compensation; (2) using obstacle avoidance and collision avoidance penalty functions to improve the MPC cost function; (3) combining the dynamic event triggering conditions of three-dimensional obstacle avoidance perception to optimize the triggering time of MPC.

2. The MPC cooperative formation method according to claim 1, which integrates DETM and a fixed-time RBF neural network observer, is characterized in that... In the MPC framework, a lumped perturbation term is introduced. , No. Discrete state-space prediction model for UAVs with feedforward compensation: in, This is an estimate of the lumped disturbance term; The sampling period is At the current sampling time, , The prediction step size for MPC, and They represent in Predicting the future at any moment The system status and control inputs of each step.

3. The MPC cooperative formation method for fusing DETM and fixed-time RBF neural network observers according to claim 2, characterized in that, The estimated value of the lumped disturbance term Estimation is performed using a fixed-time RBF neural network perturbation observer; The RBF neural network perturbation observer is specifically: in, For the observed value of velocity, For actual speed, For the observation error of velocity, These are estimates of the neural network weights. The observer gain matrix is ​​a constant. ; For a fixed time independent of the initial state; diagonal matrix and These represent system parameters related to system damping and control gain, respectively. The estimated value of the lumped disturbance can be expressed as: in, This is the transpose matrix of the neural network weight estimates. Let Gausky function vector be the vector. For network input containing drone status information.

4. The MPC cooperative formation method for fusing DETM and fixed-time RBF neural network observers according to claim 3, characterized in that, The improved MPC cost function is expressed as follows: in, and These are the error state and the control input increment, respectively. The positive definite weight matrix, The penalty weighting factor for obstacle avoidance, This is the penalty function for obstacle avoidance and collision prevention.

5. The MPC cooperative formation method according to claim 4, which integrates DETM and a fixed-time RBF neural network observer, is characterized in that... The obstacle avoidance and collision avoidance penalty function is: in, Minimum safe distance; The radius of the threat detection area.

6. The MPC cooperative formation method according to claim 5, which integrates DETM and a fixed-time RBF neural network observer, is characterized in that... The specific conditions for triggering the dynamic event are as follows: in, For the first The moment when MPC optimization is triggered ; To enhance threat early warning capabilities, The obstacle threat level is calculated by the sensor at the current moment. This represents the threat level predicted by the previous MPC at the current moment.

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