A multi-four-rotor safe formation control method and system based on event-triggered anti-locking

Abstract

The application discloses a multi-four-rotor safety formation control method and system based on event triggering and anti-self-locking, and the multi-four-rotor safety formation control method comprises the following steps: establishing an underactuated four-rotor unmanned aerial vehicle dynamics model under external uncertainty, establishing a multi-four-rotor unmanned aerial vehicle formation, constructing an expected formation trajectory model, and designing multi-four-rotor unmanned aerial vehicle collision avoidance constraints; designing an outer loop formation controller based on event triggering; generating expected angular velocity and angular acceleration of the four-rotor unmanned aerial vehicle by using a designed differential flatness method; and designing a Lie algebra attitude controller for realizing global attitude stabilization and compensating for attitude uncertainty in a limited time. The application adopts a control barrier function to realize safety constraints, including collision avoidance and direct collision avoidance of robots, so as to avoid self-locking of an output of the control barrier function due to falling into a local optimum, and further avoid failure of the safety formation. The application proposes an event-triggered control barrier function to solve the self-locking problem.

Description

Technical Field

[0001] This invention relates to the field of multi-UAV safe formation technology, and in particular to a multi-quadrotor safe formation control method and system based on event-triggered anti-locking. Background Technology

[0002] In the engineering field, quadrotor drones, with their advantages of high maneuverability, small size, and high mission adaptability, have been widely used in various scenarios such as inspection, surveying, and emergency response. Compared with single aircraft, multi-quadrotor formation flight has shown significant advantages in complex tasks such as collaborative transportation, environmental monitoring, and collaborative rescue, with lower costs, higher efficiency, and stronger fault tolerance, thus gradually becoming a research hotspot in the field of unmanned systems. However, as application scenarios continue to expand from ideal environments to real and complex environments, multi-quadrotor systems face many engineering challenges in formation tracking and collaborative control. On the one hand, uncertain disturbances in the external environment, incomplete models, and actuator saturation seriously affect formation control performance; on the other hand, multiple drones must simultaneously satisfy safety collision avoidance constraints between drones and between drones and dynamic obstacles when flying in close coordination. In addition, existing formation control methods based on control barrier functions are prone to self-locking problems in practical applications, thereby limiting the feasible solution space of the system and even causing formation mission failure, further restricting its engineering applicability. Against this backdrop, given the underactuated and highly coupled dynamic characteristics of quadrotor systems, how to construct a distributed, safe, and robust multi-quadrotor formation control framework in complex and uncertain environments, while ensuring dynamic obstacle avoidance and safe collision avoidance for UAVs, and effectively coping with external uncertainties and actuator saturation constraints, has become a key scientific and technological problem that urgently needs to be solved in the engineering application of multi-quadrotor systems. Summary of the Invention

[0003] This invention provides a method and system for safe formation control of multiple quadrotors based on event-triggered anti-locking, in order to solve the technical problems mentioned in the background art.

[0004] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0005] This invention provides a method for safe formation control of multiple quadrotors based on event-triggered anti-locking, comprising the following steps:

[0006] S1. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties. The dynamic model of the underactuated quadrotor UAV includes a translational dynamics model and a rotational dynamics model. Based on the leader-follower structure, establish a multi-quadrotor UAV formation and construct the desired formation tracking trajectory.

[0007] S2. Design an event-triggered outer ring formation controller to solve the self-locking problem of multiple quadrotor UAVs. Then, input the three-dimensional spatial position of the quadrotor UAVs in the desired formation tracking trajectory into the outer ring formation controller to generate the net thrust of the quadrotor UAVs and input it into the translational motion mechanics model to realize the translational control of multiple quadrotor UAVs.

[0008] S3. Design a differential flatness method and generate the desired angular velocity and desired angular acceleration of the quadcopter UAV based on the differential flatness method.

[0009] S4. Design a super-helical observer, design an inner loop observer based on the super-helical observer, and then construct an attitude controller based on the inner loop observer, the desired angular velocity and desired angular acceleration of the quadcopter UAV. Use the attitude controller to generate torque input in real time and substitute it into the rotational dynamics model to realize the rotational control of the multi-quadcopter UAV.

[0010] Furthermore, step S1 specifically includes the following steps:

[0011] S11. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties, including a translational dynamics model and a rotational dynamics model. The translational dynamics model includes a position dynamics model and a velocity dynamics model; the rotational dynamics model includes an attitude dynamics model and an angular velocity dynamics model.

[0012] S12. Establish a multi-quadrotor drone formation based on a leader-follower structure. The multi-quadrotor drone formation includes a virtual leader and multiple followers. The desired formation of the multi-quadrotor drone formation is determined by the first... i The and the first j The expected positional deviation between the quadcopter drones d ij Sure, d ij = d i - d j ,in d i Indicates virtual navigator and the first i The expected relative position between followers d j Indicates virtual navigator and the first j The expected relative positions of the followers; the expected trajectory of the center of the multi-quadrotor drone formation is denoted as... ∈ ; Represents the set of real numbers;

[0013] S13. Construct a quadcopter drone to achieve the desired formation, while maintaining the desired formation tracking trajectory corresponding to the time-invariant formation mode;

[0014] S14. Design collision avoidance constraints between multiple quadcopter UAVs.

[0015] Furthermore, the expressions for the position dynamics model, velocity dynamics model, attitude dynamics model, and angular velocity dynamics model in S11 are as follows:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] (4)

[0020] in, Indicates the first i The spatial three-dimensional position of a quadcopter drone; , This represents the total number of quadcopter drones; a dot above the parameter indicates the first derivative of that parameter. Indicates the first i The speed of a quadcopter drone; and They represent the first i Net thrust and torque input of a quadcopter drone Indicates the first i The rotation matrix of a quadcopter drone; It is a constant vector. Represents the transpose of a matrix; It is the acceleration due to gravity; and These represent the external disturbances acting on translational and rotational motions, and the unmodeled total dynamic damping, respectively. and The first i The mass and constant symmetric inertia matrix of a quadcopter UAV; Indicates the first i Angular velocity of a quadcopter drone; superscript This represents the operation of converting a vector into an antisymmetric matrix; Represents angular velocity The corresponding antisymmetric matrix;

[0021] The expression for the desired formation tracking trajectory in S13 is as follows:

[0022] (5)

[0023] in, t Indicates time, Represent a very small positive number; Indicates "any"; Represents positive integers;

[0024] The specific collision avoidance constraints among multiple quadrotor UAVs in S14 are as follows:

[0025] (6)

[0026] in, It is the minimum collision-free distance between adjacent quadcopter drones.

[0027] Furthermore, step S2 specifically includes the following steps:

[0028] S201. Reconstruct the velocity dynamics model in the underactuated quadcopter UAV dynamics model to obtain the reconstructed velocity dynamics model;

[0029] S202. Design a robust filter to completely cancel out the first custom variable. The impact on the reconstructed velocity dynamics model, combined with the design of an initial robust compensator using a robust filter;

[0030] S203, Construct the first user-defined variable The calculation formula;

[0031] S204, Set the first user-defined variable Substituting the calculation formula into the initial robust compensator, we obtain the optimized robust compensator.

[0032] S205, Define the formation tracking error for each quadcopter drone;

[0033] S206. Calculate the time derivative of the formation tracking error for each quadcopter UAV. ;

[0034] S207, Utilizing Formation Tracking Error and time derivative Design nominal formation controller ;

[0035] S208, using the nominal formation controller The position dynamics model and velocity dynamics model in the dynamics model of the underactuated quadrotor UAV are rewritten to obtain the position subsystem dynamics model; external disturbances are solved based on the position subsystem dynamics model. With robust compensation input The difference between ;

[0036] S209. Encode the collision avoidance targets among multiple quadcopter drones into a safety set to avoid collisions. and in accordance with security set Construct a control barrier function;

[0037] S210, combining the control barrier function and utilizing the nominal formation controller and external disturbances With robust compensation input The difference between Construct security constraints;

[0038] S211, Regarding the first i The quadcopter drone and the first k Given several obstacles, construct an obstacle function;

[0039] S212. For dynamic obstacles, define relative velocity. ;

[0040] S213. Optimize the safety constraints using the obstacle function to obtain the optimized safety constraints;

[0041] S214. Based on the optimized security constraints, the first... i The thrust of a quadcopter drone is corrected to obtain the optimal solution for the modified thrust.

[0042] S215, When the optimal control input is obtained from the control barrier function When trapped in a local optimum, a formation system composed of multiple quadcopter UAVs may experience a self-locking phenomenon in its control barrier function. That is, although the formation system always satisfies the safety constraints, the control input is dominated by the constraints due to the degradation of the feasible control space, causing the formation system to stagnate and unable to continue to advance the mission objective. In order to determine whether the control barrier function used by the formation system is self-locking, a feasible margin is set.

[0043] S216. Design a switching control strategy to break out of self-locking, so as to help the control barrier function used by the formation system break out of self-locking;

[0044] S217. Design a robust formation controller for each quadcopter UAV, and then design an event-triggered control law based on the robust formation controller and the optimal solution of the modified thrust.

[0045] S218, combined with the intermediate control input to be designed Rotation matrix of quadcopter drones The quality of quadcopter drones Design an event-triggered formation controller;

[0046] This completes the construction of the outer-loop formation controller, which consists of a robust filter, a nominal formation controller, a control barrier function, and an event-triggered formation controller connected in sequence. Then, the event-triggered formation controller is used to generate the... i Net thrust of a quadcopter drone The data is then input into the translational motion mechanics model to achieve translational control of multiple quadcopter drones.

[0047] S219. Given a reference yaw angle for each quadcopter UAV. Based on the reference yaw angle Calculate the coordinates of each quadcopter UAV in the body coordinate system x Desired unit direction vector on the axis Then, based on the robust formation controller, the coordinates of each quadcopter UAV in the body coordinate system are calculated. z Desired unit direction vector on the axis ;

[0048] S220, Define each quadcopter UAV in the body coordinate system y The desired unit direction vector on the axis is ;

[0049] S221, based on each quadcopter drone in x、y、z The desired unit direction vector on the axis constructs the desired attitude of each quadcopter UAV. .

[0050] Furthermore, the reconstructed velocity dynamics model in S201 is as follows:

[0051] (7)

[0052] in, This represents the intermediate control input to be designed. First custom variable The expressions are as follows:

[0053] (8)

[0054] (9)

[0055] in, Indicates the first i Each quadcopter drone enters the expected rotation matrix corresponding to the desired formation; It is a coupling term between the velocity dynamics model and the attitude dynamics model, when At that time, the coupling term will disappear;

[0056] The initial robust compensator in S202 is specifically as follows:

[0057] (10)

[0058] in, Indicates robust compensation input; Indicates a robust filter. The three components of the robust filter are represented by their ordinal numbers. ; s is the Laplace operator; For positive constants to be determined;

[0059] The first custom variable in S203 The specific calculation formula is as follows:

[0060] (11)

[0061] The optimized robust compensator in S204 is as follows:

[0062] (12)

[0063] in, All are robust filter states; Represents three positive integers;

[0064] The specific formation tracking error for each quadcopter UAV in S205 is as follows:

[0065] (13)

[0066] in, Indicates the first i Formation tracking error of a quadcopter drone;

[0067] The formula for calculating the time derivative of the formation tracking error for each quadcopter UAV in S206 is as follows:

[0068] (14)

[0069] in, Indicates the first i The time derivative of the formation tracking error of a quadcopter drone;

[0070] The S207 is a nominally labeled formation controller. Specifically as follows:

[0071] (15)

[0072] in, For scalar coupling gain, It is a positive definite parameter matrix; Indicates the firsti The and the first j The difference in three-dimensional spatial position between four-rotor drones; Indicates the first i The and the first j The speed difference between the quadcopter drones; the two points on the parameter represent the second derivative of that parameter; Indicates virtual navigator and the first i Connection weights between quadcopter drones; Indicates the first i The and the first j Connection weights between quadcopter drones;

[0073] The specific dynamic model of the position subsystem in S208 is as follows:

[0074] (16)

[0075] in, This represents a second user-defined variable, and ; This represents a third-user user-defined variable; and ; This represents the fourth user-defined variable, and ; This represents the fifth user-defined variable, and ; Indicates the first i The difference between the external disturbance and the robust compensation input of a quadcopter drone;

[0076] The security set in S209 The expression is as follows:

[0077] (17)

[0078] in, It is a control barrier function of relative order two, and the specific expression of the control barrier function is as follows:

[0079] (18)

[0080] The specific safety constraints in S210 are as follows:

[0081] (19)

[0082] in, Indicates the first intermediate variable; Indicates the second intermediate variable; This represents the third intermediate variable, and the third intermediate variable The calculation formula is as follows:

[0083] (20)

[0084] The formula for this is:

[0085] ;

[0086] In formula (19) The formula for this is:

[0087] ;

[0088] The barrier function in S211 is as follows:

[0089] (twenty one)

[0090] in, Indicates the first i The quadcopter drone and the first k The distance relationship between the obstacles; Indicates the first i The quadcopter drone and the first k The distance between the obstacles; Indicates the first i The quadcopter drone arrived at the first k Safe distance from each obstacle; Indicates the radius of the obstacle;

[0091] The relative velocity in S212 The expression is as follows:

[0092] (twenty two)

[0093] in, Indicates obstacles k speed;

[0094] The optimized security constraints in S213 are as follows:

[0095] (twenty three)

[0096] The fourth intermediate variable The calculation formula is as follows:

[0097] (twenty four)

[0098] The corrected thrust expression in S214 is as follows:

[0099] (25)

[0100] in, This represents the optimal solution for the corrected thrust. This represents the thrust before correction, and we need to find the optimal solution.

[0101] Constraints on the revised thrust expression: ,in This represents the sixth user-defined variable; This represents the seventh user-defined variable; and the calculation formulas for both are as follows:

[0102] ;

[0103] ; ， ;

[0104] in, Indicates the total number of obstacles;

[0105] The formula for calculating the feasibility margin in S215 is as follows:

[0106] (26)

[0107] in, Indicates the feasible margin; And the self-locking duration exceeds It is determined to be a self-locking mechanism; Indicates the feasible margin threshold; This indicates the pre-set self-locking duration threshold;

[0108] The robust grouping controller in S217 is specifically as follows:

[0109] (27)

[0110] in, Indicates the event-triggered control law, used to achieve the desired tracking trajectory of the nominal translational mechanics model; robust compensation input. Used to suppress external disturbances The impact on the translational mechanical model;

[0111] Event Triggering Control Rate The calculation formula is as follows:

[0112] ;

[0113] in, Indicates the minimum directional disturbance input;

[0114] The calculation formula for the event-triggered formation controller in S218 is as follows:

[0115] (28)

[0116] The desired unit direction vector in S219 The calculation formula is as follows:

[0117] ;

[0118] The desired unit direction vector in S219 The calculation formula is as follows:

[0119] (29)

[0120] The desired unit direction vector in S220 The calculation formula is as follows:

[0121] (30)

[0122] The desired attitude of each quadcopter drone in S221 The calculation formula is as follows:

[0123] (31).

[0124] Furthermore, the switching control strategy for escaping the self-locking in S216 is as follows:

[0125] Add minimum directional perturbation input at the event trigger level The minimum directional perturbation input is the vector that minimizes the feasible margin: Solving for the minimum directional perturbation input The calculation formula is as follows:

[0126] (32)

[0127] ;

[0128] in, Indicates the perturbation input variable; Represents slack variables; This indicates the maximum permissible perturbation value and the minimum perturbation input direction. After the solution is completed, the quadcopter drone will be able to exit the self-locked state.

[0129] Furthermore, step S3 specifically includes the following steps:

[0130] S31, Given a flat output space as Here, three points on the parameter represent the third derivative of that parameter; four points on the parameter represent the fourth derivative of that parameter; the third derivatives of the three-dimensional spatial position of the quadcopter UAV are constructed respectively. The calculation formula;

[0131] S32, Given intermediate variables and intermediate variables Substituting the third derivative of the three-dimensional spatial position of the quadcopter drone In the calculation formula, the intermediate variable is obtained. The calculation formula;

[0132] S33, Regarding intermediate variables The formula for calculating the reference angular velocity is obtained by transforming the original formula.

[0133] S34, In intermediate variables The calculation formula uses accelerometer. The third derivative of the spatial three-dimensional position of a quadcopter drone The eighth user-defined variable is obtained. The calculation formula;

[0134] S35. Regarding the fourth intermediate variable The two sides of the calculation formula and the rotation component Perform a dot product operation to obtain the first derivative of the net thrust. ;

[0135] S36. First derivative with respect to net thrust Taking the derivative, we obtain the second derivative of the net thrust. ;

[0136] S37. Solve for the first derivative of the net thrust. and the second derivative of net thrust Substitute into the eighth user-defined variable In the calculation formula, the eighth custom variable is obtained. ;

[0137] S38. Utilizing the eighth user-defined variable The desired angular acceleration of the quadcopter UAV was calculated.

[0138] Furthermore, the third derivative in S31 Fourth derivative The calculation formulas are as follows:

[0139] (33)

[0140] (34)

[0141] intermediate variables in S32 The specific calculation formula is as follows:

[0142] (35)

[0143] in, Indicates the first i A quadcopter drone in the body coordinate system z Rotational component along the axial direction; The second derivative of the expected trajectory of the formation center;

[0144] The specific formula for calculating the desired angular velocity in S33 is as follows:

[0145] (36)

[0146] in, Indicates the desired angular velocity; Indicates the first i A quadcopter drone in the body coordinate system y Rotational component along the axial direction; Indicates the first i A quadcopter drone in the body coordinate system x Rotational component along the axial direction;

[0147] The eighth custom variable in S34 The specific calculation formula is as follows:

[0148] (37)

[0149] The first derivative of net thrust in S35 The specific calculation formula is as follows:

[0150] (38)

[0151] The second derivative of net thrust in S36 The specific calculation formula is as follows:

[0152] (39)

[0153] in, The derivative of jerk;

[0154] The formula for calculating the desired angular acceleration in S38 is as follows:

[0155] (40)

[0156] in, Indicates the first i The desired angular acceleration of a quadcopter drone.

[0157] Furthermore, step S4 specifically includes the following steps:

[0158] S41. A superspiral observer is proposed to identify and compensate for uncertainties in the inner loop within a finite time, where the inner loop refers to attitude error; the expression for the superspiral observer is as follows:

[0159] (41)

[0160] in, Indicates the error variable; Represents angular velocity The estimated value;

[0161] S42. Designing an inner-loop observer using a superhelical observer. Inner loop observer The expression is as follows:

[0162] (42)

[0163] in, and Gain is a positive constant. Represents error variable The derivative; express The derivative;

[0164] S43. Define the rotation matrix error. Rotation matrix error The expression is as follows:

[0165] (43)

[0166] S44, Based on rotation matrix error Logarithmic orientation error is defined on the Lie algebra space. Logarithmic configuration attitude error The expression is as follows:

[0167] (44)

[0168] in, This indicates that the antisymmetric matrix within the parentheses is converted into a three-dimensional vector;

[0169] S45. Define the relevant velocity error Related speed error The expression is as follows:

[0170] (45)

[0171] S46, Logarithmic configuration of attitude error Related speed error By taking the time derivative, we obtain the attitude error dynamic model, which is expressed as follows:

[0172] ;

[0173] (46)

[0174] in, Indicates the fifth intermediate variable; Indicates the sixth intermediate variable; Indicates the seventh intermediate variable;

[0175] Then, the solution is obtained based on the expression of the attitude error dynamics model. , The calculation formulas are as follows;

[0176] (47)

[0177] (48)

[0178] in, Represents logarithmic orientation error The antisymmetric matrix; Represents the L2 norm; Represents a 3×3 identity matrix;

[0179] S47. Based on the nominal control section and inner loop observer The attitude controller is constructed, and its calculation formula is as follows:

[0180] (49)

[0181] in, Indicates torque input. Indicates nominal control input, nominal control input The specific calculation formula is as follows:

[0182] (50)

[0183] in, and Gain is a positive constant.

[0184] S49. Construct an inner-loop controller by combining the attitude controller and the super-helical observer, and use the inner-loop controller to generate torque input in real time. This information is then incorporated into the rotational dynamics model to achieve rotational control of the multi-quadrotor UAV and to compensate for attitude uncertainties within a finite time.

[0185] In another aspect, the present invention provides an event-triggered anti-locking multi-quadrotor safe formation control system, including a multi-quadrotor UAV, wherein the multi-quadrotor UAV is configured or executes the above-described event-triggered anti-locking multi-quadrotor safe formation control method.

[0186] The beneficial effects of this invention are:

[0187] 1. This invention discloses an event-triggered anti-locking multi-quadrotor safe formation control method, which can effectively achieve dynamic obstacle avoidance in the presence of external uncertain disturbances, and at the same time consider actuator saturation constraints, significantly improving the safety and robustness of a formation system composed of multiple quadrotor UAVs.

[0188] 2. This invention designs a differential flattening method, which avoids the need for second-order numerical differentiation in robust formation controllers, and effectively reduces the system implementation complexity while ensuring control performance.

[0189] 3. Under external disturbance conditions, this invention constructs a control barrier function based on an event-triggered mechanism, achieving safe collision avoidance between multiple quadrotor UAVs and between them and dynamic obstacles, and effectively overcoming the self-locking problem that easily occurs in traditional control barrier functions. Furthermore, an attitude controller is designed and disclosed within the multi-quadrotor safe formation control method of this invention, achieving global attitude tracking performance under external disturbances. Attached Figure Description

[0190] Figure 1 This is a flowchart of the event-triggered anti-locking multi-quadrotor safe formation control method in this invention;

[0191] Figure 2 This is a schematic diagram of the event-triggered anti-locking multi-quadrotor safe formation control method in this invention. Detailed Implementation

[0192] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0193] Reference Figure 1 and Figure 2 This application provides an event-triggered anti-locking multi-quadrotor safe formation control method, including the following steps:

[0194] S1. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties. The dynamic model of the underactuated quadrotor UAV includes a translational dynamics model and a rotational dynamics model. Based on the leader-follower structure, establish a multi-quadrotor UAV formation and construct the desired formation tracking trajectory.

[0195] S2. Design an event-triggered outer ring formation controller to solve the self-locking problem of multiple quadrotor UAVs. Then, input the three-dimensional spatial position of the quadrotor UAVs in the desired formation tracking trajectory into the outer ring formation controller to generate the net thrust of the quadrotor UAVs and input it into the translational motion mechanics model to realize the translational control of multiple quadrotor UAVs.

[0196] S3. Design a differential flatness method and generate the desired angular velocity and desired angular acceleration of the quadcopter UAV based on the differential flatness method.

[0197] S4. Design a superspiral observer (STO). Based on the superspiral observer, design an inner loop observer. Then, based on the inner loop observer, the desired angular velocity and desired angular acceleration of the quadcopter UAV, construct an attitude controller. Use the attitude controller to generate torque input in real time and substitute it into the rotational dynamics model to realize the rotational control of the multi-quadcopter UAV and compensate for attitude uncertainties in a finite time.

[0198] This invention first generates a desired formation by tracking the desired formation trajectory, and then uses a control barrier function to implement safety constraints, including collision avoidance and direct collision avoidance between robots. To avoid the output of the control barrier function becoming self-locked due to getting trapped in local optima, which would lead to the failure of safe formation, this invention proposes an event-based control barrier function to solve the self-locking problem.

[0199] Furthermore, the multi-quadrotor safe formation control method of this invention discloses a geometric attitude controller based on a superspiral observer, which achieves global attitude tracking performance under external disturbances. The superspiral observer is a nonlinear observer based on second-order sliding mode control theory. It achieves high-precision estimation of the system state and features the characteristics of suppressing chattering and improving convergence speed.

[0200] In some embodiments, S1 specifically includes the following steps:

[0201] S11. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties, including a translational dynamics model and a rotational dynamics model. The translational dynamics model includes a position dynamics model and a velocity dynamics model; the rotational dynamics model includes an attitude dynamics model and an angular velocity dynamics model.

[0202] S12. Establish a multi-quadrotor drone formation based on a leader-follower structure. The multi-quadrotor drone formation includes a virtual leader and multiple followers. The desired formation of the multi-quadrotor drone formation is determined by the first... i The and the first j The expected positional deviation between the quadcopter drones d ij Sure, d ij = d i - d j ,in d i Indicates virtual navigator and the first i The expected relative position between followers d j Indicates virtual navigator and the first j The expected relative positions of the followers; the expected trajectory of the center of the multi-quadrotor drone formation is denoted as... ∈ ; Represents the set of real numbers;

[0203] S13. Construct a quadcopter drone to achieve the desired formation, while maintaining the desired formation tracking trajectory corresponding to the time-invariant formation mode;

[0204] S14. Design collision avoidance constraints between multiple quadcopter UAVs.

[0205] In some embodiments, the expressions for the position dynamics model, velocity dynamics model, attitude dynamics model, and angular velocity dynamics model in S11 are as follows:

[0206] (1)

[0207] (2)

[0208] (3)

[0209] (4)

[0210] in, Indicates the first i The spatial three-dimensional position of a quadcopter drone; , This represents the total number of quadcopter drones; a dot above the parameter indicates the first derivative of that parameter. Indicates the first i The speed of a quadcopter drone; and They represent the first iNet thrust and torque input of a quadcopter drone Indicates the first i The rotation matrix of a quadcopter drone; It is a constant vector. Represents the transpose of a matrix; It is the acceleration due to gravity; and These represent the external disturbances acting on translational and rotational motions, and the unmodeled total dynamic damping, respectively. and The first i The mass and constant symmetric inertia matrix of a quadcopter UAV; Indicates the first i Angular velocity of a quadcopter drone; superscript This represents the operation of converting a vector into an antisymmetric matrix; Represents angular velocity The corresponding antisymmetric matrix;

[0211] The expression for the desired formation tracking trajectory in S13 is as follows:

[0212] (5)

[0213] in, t Indicates time, Represent a very small positive number; Indicates "any"; Represents positive integers;

[0214] The specific collision avoidance constraints among multiple quadrotor UAVs in S14 are as follows:

[0215] (6)

[0216] in, It is the minimum collision-free distance between adjacent quadcopter drones.

[0217] In some embodiments, S2 specifically includes the following steps:

[0218] S201. Reconstruct the velocity dynamics model in the underactuated quadcopter UAV dynamics model to obtain the reconstructed velocity dynamics model;

[0219] S202. Design a robust filter to completely cancel out the first custom variable. The impact on the reconstructed velocity dynamics model, combined with the design of an initial robust compensator using a robust filter;

[0220] S203, due to the first user-defined variable It cannot be measured directly, but it can be calculated, so we construct the first custom variable. The calculation formula;

[0221] S204, Set the first user-defined variable Substituting the calculation formula into the initial robust compensator, we obtain the optimized robust compensator.

[0222] S205, Define the formation tracking error for each quadcopter drone;

[0223] S206. Calculate the time derivative of the formation tracking error for each quadcopter UAV. ;

[0224] S207, Utilizing Formation Tracking Error and time derivative Design nominal formation controller ;

[0225] S208, using the nominal formation controller The position dynamics model and velocity dynamics model in the dynamics model of the underactuated quadrotor UAV are rewritten to obtain the position subsystem dynamics model; external disturbances are solved based on the position subsystem dynamics model. With robust compensation input The difference between ;

[0226] S209. Encode the collision avoidance targets among multiple quadcopter drones into a safety set to avoid collisions. and in accordance with security set Construct a control barrier function;

[0227] S210, combining the control barrier function and utilizing the nominal formation controller and external disturbances With robust compensation input The difference between Construct security constraints;

[0228] S211, Regarding the first i The quadcopter drone and the first k Given several obstacles, construct an obstacle function;

[0229] S212. For dynamic obstacles, define relative velocity. ;

[0230] S213. Optimize the safety constraints using the obstacle function to obtain the optimized safety constraints;

[0231] S214. Based on the optimized security constraints, the first... iThe thrust of a quadcopter drone is corrected to obtain the optimal solution for the modified thrust.

[0232] S215, When the optimal control input is obtained from the control barrier function When trapped in a local optimum, a formation system composed of multiple quadcopter UAVs may experience a self-locking phenomenon in its control barrier function. That is, although the formation system always satisfies the safety constraints, the control input is dominated by the constraints due to the degradation of the feasible control space, causing the formation system to stagnate and unable to continue to advance the mission objective. In order to determine whether the control barrier function used by the formation system is self-locking, a feasible margin is set.

[0233] S216. Design a switching control strategy to help the control barrier function (CBF) used by the quadcopter drone escape self-locking.

[0234] S217. Design a robust formation controller for each quadcopter UAV, and then design an event-triggered control law based on the robust formation controller and the optimal solution of the modified thrust.

[0235] S218, combined with the intermediate control input to be designed Rotation matrix of quadcopter drones The quality of quadcopter drones Design an event-triggered formation controller;

[0236] This completes the construction of the outer-loop formation controller, which consists of a robust filter, a nominal formation controller, a control barrier function, and an event-triggered formation controller connected in sequence. Then, the event-triggered formation controller is used to generate the... i Net thrust of a quadcopter drone The data is then input into the translational motion mechanics model to achieve translational control of multiple quadcopter drones.

[0237] S219. Given a reference yaw angle for each quadcopter UAV. Based on the reference yaw angle Calculate the coordinates of each quadcopter UAV in the body coordinate system x Desired unit direction vector on the axis Then, based on the robust formation controller, the coordinates of each quadcopter UAV in the body coordinate system are calculated. z Desired unit direction vector on the axis ;

[0238] S220, Define each quadcopter UAV in the body coordinate system y The desired unit direction vector on the axis is ;

[0239] S221, based on each quadcopter drone in x、y、zThe desired unit direction vector on the axis constructs the desired attitude of each quadcopter UAV. .

[0240] In some embodiments, the reconstructed velocity-dynamic model in S201 is specifically as follows:

[0241] (7)

[0242] in, This represents the intermediate control input to be designed. First custom variable The expressions are as follows:

[0243] (8)

[0244] (9)

[0245] in, Indicates the first i Each quadcopter drone enters the expected rotation matrix corresponding to the desired formation; It is a coupling term between the velocity dynamics model and the attitude dynamics model, when At that time, the coupling term will disappear;

[0246] The initial robust compensator in S202 is specifically as follows:

[0247] (10)

[0248] in, Indicates robust compensation input; Indicates a robust filter. The three components of the robust filter are represented by their ordinal numbers. ; s is the Laplace operator; For the positive constant to be determined; positive constant The bigger it is, the more Lu The wider the frequency bandwidth, the closer the robust filter gain is to 1 within that bandwidth.

[0249] The first custom variable in S203 The specific calculation formula is as follows:

[0250] (11)

[0251] The optimized robust compensator in S204 is as follows:

[0252] (12)

[0253] in, All are robust filter states and can be arbitrarily initialized; Represents three positive integers;

[0254] The specific formation tracking error for each quadcopter UAV in S205 is as follows:

[0255] (13)

[0256] in, Indicates the first i Formation tracking error of a quadcopter drone; It is the center of the formation and the first i The time-invariant positional deviation between the quadrotor drones satisfies ;

[0257] The formula for calculating the time derivative of the formation tracking error for each quadcopter UAV in S206 is as follows:

[0258] (14)

[0259] in, Indicates the first i The time derivative of the formation tracking error of a quadcopter drone;

[0260] The S207 is a nominally labeled formation controller. Specifically as follows:

[0261] (15)

[0262] in, For scalar coupling gain, It is a positive definite parameter matrix; Indicates the first i The and the first j The difference in three-dimensional spatial position between four-rotor drones; Indicates the first i The and the first j The speed difference between the quadcopter drones; the two points on the parameter represent the second derivative of that parameter; Indicates virtual navigator and the first i Connection weights between quadcopter drones; Indicates the first i The and the first j Connection weights between quadcopter drones;

[0263] The specific dynamic model of the position subsystem in S208 is as follows:

[0264] (16)

[0265] in, This represents a second user-defined variable, and ; This represents a third-user user-defined variable; and ; This represents the fourth user-defined variable, and ; This represents the fifth user-defined variable, and ; Indicates the first i The difference between the external disturbance and the robust compensation input of a quadcopter drone;

[0266] The security set in S209 The expression is as follows:

[0267] (17)

[0268] in, It is a control barrier function of relative order two, and the specific expression of the control barrier function is as follows:

[0269] (18)

[0270] The specific safety constraints in S210 are as follows:

[0271] (19)

[0272] in, Indicates the first intermediate variable; Indicates the second intermediate variable; This represents the third intermediate variable, and the third intermediate variable The calculation formula is as follows:

[0273] (20)

[0274] The formula for this is:

[0275] ;

[0276] In formula (19) The formula for this is:

[0277] ;

[0278] The barrier function in S211 is as follows:

[0279] (twenty one)

[0280] in, Indicates the first i The quadcopter drone and the firstk The distance relationship between the obstacles; Indicates the first i The quadcopter drone and the first k The distance between the obstacles; Indicates the first i The quadcopter drone arrived at the first k Safe distance from each obstacle; Indicates the radius of the obstacle;

[0281] The relative velocity in S212 The expression is as follows:

[0282] (twenty two)

[0283] in, Indicates obstacles k speed;

[0284] The optimized security constraints in S213 are as follows:

[0285] (twenty three)

[0286] The fourth intermediate variable The calculation formula is as follows:

[0287] (twenty four)

[0288] The corrected thrust expression in S214 is as follows:

[0289] (25)

[0290] in, This represents the optimal solution for the corrected thrust. This represents the thrust before correction, and we need to find the optimal solution.

[0291] Constraints on the revised thrust expression: ,in This represents the sixth user-defined variable; This represents the seventh user-defined variable; and the calculation formulas for both are as follows:

[0292] ;

[0293] ; ， ;

[0294] in, Indicates the total number of obstacles;

[0295] The feasible margin calculation formula in S215 is as follows:

[0296] (26)

[0297] in, Indicates the feasible margin; And the self-locking duration exceeds It is determined to be a self-locking mechanism; Indicates the feasible margin threshold; This indicates the pre-set self-locking duration threshold;

[0298] The robust grouping controller in S217 is specifically as follows:

[0299] (27)

[0300] in, Indicates the event-triggered control law, used to achieve the desired tracking trajectory of the nominal translational mechanics model; robust compensation input. Used to suppress external disturbances The impact on the translational mechanical model;

[0301] Event Triggering Control Rate The calculation formula is as follows:

[0302] ;

[0303] in, Indicates the minimum directional disturbance input;

[0304] The calculation formula for the event-triggered formation controller in S218 is as follows:

[0305] (28)

[0306] The desired unit direction vector in S219 The calculation formula is as follows:

[0307] ;

[0308] The desired unit direction vector in S219 The calculation formula is as follows:

[0309] (29)

[0310] The desired unit direction vector in S220 is: The calculation formula is as follows:

[0311] (30)

[0312] The desired attitude of each quadcopter drone in S221 The calculation formula is as follows:

[0313] (31).

[0314] In some embodiments, the switching control strategy for escaping self-locking in S216 is specifically as follows:

[0315] Add minimum directional perturbation input at the event trigger level The minimum directional perturbation input is the vector that minimizes the feasible margin: Solving for the minimum directional perturbation input The calculation formula is as follows:

[0316] (32)

[0317] ;

[0318] in, Indicates the perturbation input variable; Represents slack variables; Indicates the maximum allowable perturbation value; minimum directional perturbation input. After the solution is completed, the quadcopter drone will be able to exit the self-locked state.

[0319] In some embodiments, S3 specifically includes the following steps:

[0320] S31, Given a flat output space as Here, three points on the parameter represent the third derivative of that parameter; four points on the parameter represent the fourth derivative of that parameter; the third derivatives of the three-dimensional spatial position of the quadcopter UAV are constructed respectively. The calculation formula;

[0321] S32, Given intermediate variables and intermediate variables Substituting the third derivative of the three-dimensional spatial position of the quadcopter drone In the calculation formula, the intermediate variable is obtained. The calculation formula;

[0322] S33, Regarding intermediate variables The formula for calculating the reference angular velocity is obtained by transforming the original formula.

[0323] S34, In intermediate variables The calculation formula uses accelerometer. The third derivative of the spatial three-dimensional position of a quadcopter drone The eighth user-defined variable is obtained. The calculation formula;

[0324] S35. Regarding the fourth intermediate variable The two sides of the calculation formula and the rotation component Perform a dot product operation to obtain the first derivative of the net thrust. ;

[0325] S36. First derivative with respect to net thrust Taking the derivative, we obtain the second derivative of the net thrust. ;

[0326] S37. Solve for the first derivative of the net thrust. and the second derivative of net thrust Substitute into the eighth user-defined variable In the calculation formula, the eighth custom variable is obtained. ;

[0327] S38. Utilizing the eighth user-defined variable The desired angular acceleration of the quadcopter UAV was calculated.

[0328] In some embodiments, the third derivative in S31 Fourth derivative The calculation formulas are as follows:

[0329] (33)

[0330] (34)

[0331] intermediate variables in S32 The specific calculation formula is as follows:

[0332] (35)

[0333] in, Indicates the first i A quadcopter drone in the body coordinate system z Rotational component along the axial direction; The second derivative of the specified reference trajectory at the center of the formation;

[0334] The specific formula for calculating the reference angular velocity in S33 is as follows:

[0335] (36)

[0336] in, Indicates the reference angular velocity; Indicates the first i A quadcopter drone in the body coordinate system y Rotational component along the axial direction; Indicates the first iA quadcopter drone in the body coordinate system x Rotational component along the axial direction;

[0337] The eighth custom variable in S34 The specific calculation formula is as follows:

[0338] (37)

[0339] The first derivative of net thrust in S35 The specific calculation formula is as follows:

[0340] (38)

[0341] The second derivative of net thrust in S36 The specific calculation formula is as follows:

[0342] (39)

[0343] in, The derivative of jerk;

[0344] The formula for calculating the desired angular acceleration in S38 is as follows:

[0345] (40)

[0346] in, Indicates the first i The desired angular acceleration of a quadcopter drone.

[0347] In some embodiments, S4 specifically includes the following steps:

[0348] S41. A superspiral observer is proposed to identify and compensate for uncertainties in the inner loop within a finite time, where the inner loop refers to attitude error; the expression for the superspiral observer is as follows:

[0349] (41)

[0350] in, Represents error variable Represents angular velocity The estimated value;

[0351] S42. Designing an inner-loop observer using a superhelical observer. Inner loop observer The expression is as follows:

[0352] (42)

[0353] in, and Gain is a positive constant. Represents error variable The derivative; express The derivative;

[0354] S43. Define the rotation matrix error. Rotation matrix error The expression is as follows:

[0355] (43)

[0356] S44, Based on rotation matrix error Logarithmic orientation error is defined on the Lie algebra space. Logarithmic configuration attitude error The expression is as follows:

[0357] (44)

[0358] in, This indicates that the antisymmetric matrix within the parentheses is converted into a three-dimensional vector;

[0359] S45. Define the relevant velocity error Related speed error The expression is as follows:

[0360] (45)

[0361] S46, Logarithmic configuration of attitude error Related speed error By taking the time derivative, we obtain the attitude error dynamic model, which is expressed as follows:

[0362] ;

[0363] (46)

[0364] in, Indicates the fifth intermediate variable; Indicates the sixth intermediate variable; Indicates the seventh intermediate variable;

[0365] Then, the solution is obtained based on the expression of the attitude error dynamics model. , The calculation formulas are as follows;

[0366] (47)

[0367] (48)

[0368] in, Represents logarithmic orientation error The antisymmetric matrix; Represents the L2 norm; Represents a 3×3 identity matrix;

[0369] S47. Based on the nominal control section and inner loop observer The attitude controller is constructed, and its calculation formula is as follows:

[0370] (49)

[0371] in, Indicates torque input. Indicates nominal control input, nominal control input The specific calculation formula is as follows:

[0372] (50)

[0373] in, and Gain is a positive constant.

[0374] S49. Construct an inner-loop controller by combining the attitude controller and the super-helical observer, and use the inner-loop controller to generate torque input in real time. This information is then incorporated into the rotational dynamics model to achieve rotational control of the multi-quadrotor UAV and to compensate for attitude uncertainties within a finite time.

[0375] In another aspect, the present invention provides an event-triggered anti-locking multi-quadrotor safe formation control system, including a multi-quadrotor UAV, wherein the multi-quadrotor UAV is configured or executes the above-described event-triggered anti-locking multi-quadrotor safe formation control method.

[0376] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for safe formation control of multiple quadrotors based on event-triggered anti-locking, characterized in that, Includes the following steps: S1. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties. The dynamic model of the underactuated quadrotor UAV includes a translational dynamics model and a rotational dynamics model. Based on the leader-follower structure, establish a multi-quadrotor UAV formation and construct the desired formation tracking trajectory. Design collision avoidance constraints between multi-quadrotor UAVs. S2. Design a robust filter to completely cancel out the first custom variable. The impact on the reconstructed velocity dynamics model is considered, and an initial robust compensator is designed in conjunction with a robust filter. The collision avoidance target among multiple quadrotor UAVs is encoded as a safe set to avoid collisions. and in accordance with security sets Construct a control barrier function; combine the control barrier function with the nominal formation controller. F i N and external disturbances With robust compensation input The difference between Construct safety constraints; design an event-triggered outer-loop formation controller; solve the self-locking problem of multiple quadrotor UAVs based on the outer-loop formation controller; set a feasible margin to determine whether the control barrier function used by the formation system is self-locking; design a switching control strategy to help the control barrier function used by the formation system escape self-locking. Then, the spatial three-dimensional position of the quadrotor UAV in the desired formation tracking trajectory is input into the outer ring formation controller to generate the net thrust of the quadrotor UAV, and input into the translational motion mechanics model to realize the translational control of multiple quadrotor UAVs. The specific switching control strategy for escaping self-locking is as follows: Add minimum directional perturbation input at the event trigger level The minimum directional perturbation input is the vector that minimizes the increase in feasible margin: S3. Design a differential flatness method and generate the desired angular velocity and desired angular acceleration of the quadcopter UAV based on the differential flatness method. S4. Design a super-helical observer, design an inner loop observer based on the super-helical observer, and then construct an attitude controller based on the inner loop observer, the desired angular velocity and desired angular acceleration of the quadcopter UAV. Use the attitude controller to generate torque input in real time and substitute it into the rotational dynamics model to realize the rotational control of the multi-quadcopter UAV. The formula for calculating the feasible margin is as follows: in, Indicates the feasible margin; And the self-locking duration exceeds It is determined to be a self-locking mechanism; Indicates the feasible margin threshold; This indicates the pre-set self-locking duration threshold; This represents the sixth user-defined variable; This represents the seventh user-defined variable; i Indicates the first i A quadcopter drone.

2. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 1, characterized in that, S1 specifically includes the following steps: S11. Establish a dynamic model of an underactuated quadrotor UAV under external uncertainties, including a translational dynamics model and a rotational dynamics model. The translational dynamics model includes a position dynamics model and a velocity dynamics model; the rotational dynamics model includes an attitude dynamics model and an angular velocity dynamics model. S12. Establish a multi-quadrotor drone formation based on a leader-follower structure. The multi-quadrotor drone formation includes a virtual leader and multiple followers. The desired formation of the multi-quadrotor drone formation is determined by the first... i The and the first j The expected positional deviation between the quadcopter drones δ ij Sure, δ ij = δ i δ j ,in δ i Indicates virtual navigator and the first i The expected relative position between followers δ j Indicates virtual navigator and the first j The expected relative positions of the followers; the expected trajectory of the center of the multi-quadrotor drone formation is denoted as... ∈ ; Represents the set of real numbers; S13. Construct a quadcopter drone to achieve the desired formation, while maintaining the desired formation tracking trajectory corresponding to the time-invariant formation mode; S14. Design collision avoidance constraints between multiple quadcopter UAVs.

3. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 2, characterized in that, The expressions for the position dynamics model, velocity dynamics model, attitude dynamics model, and angular velocity dynamics model in S11 are as follows: （1） （2） （3） （4） in, Indicates the first i The spatial three-dimensional position of a quadcopter drone; , This represents the total number of quadcopter drones; a dot above the parameter indicates the first derivative of that parameter. Indicates the first i The speed of a quadcopter drone; and They represent the first i The net thrust and torque input of a quadcopter drone Indicates the first i The rotation matrix of a quadcopter drone; It is a constant vector. Represents the transpose of a matrix; It is the acceleration due to gravity; and These represent the external disturbances acting on translational and rotational motions, and the unmodeled total dynamic damping, respectively. and The first i The mass and constant symmetric inertia matrix of a quadcopter UAV; Indicates the first i Angular velocity of a quadcopter drone; superscript This represents the operation of converting a vector into an antisymmetric matrix; Represents angular velocity The corresponding antisymmetric matrix; The expression for the desired formation tracking trajectory in S13 is as follows: （5） in, t Indicates time, Represent a very small positive number; Indicates "any"; Represents positive integers; The specific collision avoidance constraints among multiple quadrotor UAVs in S14 are as follows: （6） in, It is the minimum collision-free distance between adjacent quadcopter drones.

4. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 3, characterized in that, S2 specifically includes the following steps: S201. Reconstruct the velocity dynamics model in the underactuated quadcopter UAV dynamics model to obtain the reconstructed velocity dynamics model; S202. Design a robust filter to completely cancel out the first custom variable. The impact on the reconstructed velocity dynamics model, combined with the design of an initial robust compensator using a robust filter; S203, Construct the first user-defined variable The calculation formula; S204, Set the first user-defined variable Substituting the calculation formula into the initial robust compensator, we obtain the optimized robust compensator. S205, Define the formation tracking error for each quadcopter drone; S206. Calculate the time derivative of the formation tracking error for each quadcopter UAV. ; S207, Utilizing Formation Tracking Error and time derivative Design nominal formation controller F i N ; S208, using the nominal formation controller F i N The position dynamics model and velocity dynamics model in the dynamics model of the underactuated quadrotor UAV are rewritten to obtain the position subsystem dynamics model; external disturbances are solved based on the position subsystem dynamics model. With robust compensation input The difference between ; S209. Encode the collision avoidance targets among multiple quadcopter drones into a safety set to avoid collisions. and in accordance with security sets Construct a control barrier function; S210, combining the control barrier function and utilizing the nominal formation controller F i N and external disturbances With robust compensation input The difference between Construct security constraints; S211, Regarding the first i The quadcopter drone and the first k Given several obstacles, construct an obstacle function; S212. For dynamic obstacles, define relative velocity. ; S213. Optimize the safety constraints using the obstacle function to obtain the optimized safety constraints; S214. Based on the optimized security constraints, the first... i The thrust of a quadcopter drone is corrected to obtain the optimal solution for the modified thrust. S215, When the optimal control input is obtained from the control barrier function When trapped in a local optimum, a formation system composed of multiple quadcopter UAVs may experience a self-locking phenomenon in its control barrier function. That is, although the formation system always satisfies the safety constraints, the control input is dominated by the constraints due to the degradation of the feasible control space, causing the formation system to stagnate and unable to continue to advance the mission objective. In order to determine whether the control barrier function used by the formation system is self-locking, a feasible margin is set. S216. Design a switching control strategy to break out of self-locking, so as to help the control barrier function used by the formation system break out of self-locking; S217. Design a robust formation controller for each quadcopter UAV, and then design an event-triggered control law based on the robust formation controller and the optimal solution of the modified thrust. S218, Combined with the intermediate control input to be designed Rotation matrix of quadcopter drones The quality of quadcopter drones Design an event-triggered formation controller; This completes the construction of the outer-loop formation controller, which consists of a robust filter, a nominal formation controller, a control barrier function, and an event-triggered formation controller connected in sequence. Then, the event-triggered formation controller is used to generate the... i Net thrust of a quadcopter drone The data is then input into the translational motion mechanics model to achieve translational control of multiple quadcopter drones. S219. Given a reference yaw angle for each quadcopter UAV. Based on the reference yaw angle Calculate the coordinates of each quadcopter UAV in the body coordinate system x Desired unit direction vector on the axis ; Then, based on the robust formation controller, the coordinates of each quadcopter UAV in the body coordinate system are calculated. z Desired unit direction vector on the axis ; S220, Define each quadcopter UAV in the body coordinate system y The desired unit direction vector on the axis is ; S221, based on each quadcopter drone in x, y, z The desired unit direction vector on the axis constructs the desired attitude of each quadcopter UAV. .

5. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 4, characterized in that, The reconstructed velocity-dynamic model in S201 is as follows: （7） in, This represents the intermediate control input to be designed. First custom variable The expressions are as follows: （8） （9） in, Indicates the first i Each quadcopter drone enters the expected rotation matrix corresponding to the desired formation; It is a coupling term between the velocity dynamics model and the attitude dynamics model, when At that time, the coupling term will disappear; The initial robust compensator in S202 is specifically as follows: （10） in, Indicates robust compensation input; Indicates a robust filter. The three components of the robust filter are represented by their ordinal numbers. ; s is the Laplace operator; For positive constants to be determined; The first custom variable in S203 The specific calculation formula is as follows: （11） The optimized robust compensator in S204 is as follows: （12） in, All are robust filter states; Represents three positive integers; The specific formation tracking error for each quadcopter UAV in S205 is as follows: （13） in, Indicates the first i Formation tracking error of a quadcopter drone; The formula for calculating the time derivative of the formation tracking error for each quadcopter UAV in S206 is as follows: （14） in, Indicates the first i The time derivative of the formation tracking error of a quadcopter drone; The S207 is a nominally labeled formation controller. F i N Specifically as follows: （15） in, For scalar coupling gain, It is a positive definite parameter matrix; Indicates the first i The and the first j The difference in three-dimensional spatial position between four-rotor drones; Indicates the first i The and the first j The speed difference between the quadcopter drones; the two points on the parameter represent the second derivative of that parameter; Indicates virtual navigator and the first i Connection weights between quadcopter drones; Indicates the first i The and the first j Connection weights between quadcopter drones; The specific dynamic model of the position subsystem in S208 is as follows: （16） in, This represents a second user-defined variable, and ; This represents a third-user user-defined variable; and ; This represents a fourth user-defined variable, and ; This represents the fifth user-defined variable, and ; Indicates the first i External disturbances of a quadcopter drone With robust compensation input The difference between them; The security set in S209 The expression is as follows: （17） in, It is a control barrier function of relative order two, and the specific expression of the control barrier function is as follows: （18） The specific safety constraints in S210 are as follows: （19） in, Indicates the first intermediate variable; Indicates the second intermediate variable; This represents the third intermediate variable, and the third intermediate variable The calculation formula is as follows: （20） The formula for this is: In formula (19) The formula for this is: ； The barrier function in S211 is as follows: （21） in, Indicates the first i The quadcopter drone and the first k The distance relationship between the obstacles; Indicates the first i The quadcopter drone and the first k The distance between the obstacles; Indicates the first i The first quadcopter drone to the k Safe distance from each obstacle; Indicates the radius of the obstacle; The relative velocity in S212 The expression is as follows: （22） in, Indicates obstacles k speed; The optimized security constraints in S213 are as follows: （23） The fourth intermediate variable The calculation formula is as follows: （24） The corrected thrust expression in S214 is as follows: （25） in, This represents the optimal solution for the corrected thrust. This represents the thrust before correction, and we need to find the optimal solution. Constraints on the revised thrust expression: , , The calculation formulas are as follows: ； ， ； in, Indicates the total number of obstacles; The robust grouping controller in S217 is specifically as follows: （27） in, Indicates the event-triggered control law, used to achieve the desired tracking trajectory of the nominal translational mechanics model; robust compensation input. Used to suppress external disturbances The impact on the translational mechanical model; Event Triggering Control Rate The calculation formula is as follows: in, Indicates the minimum directional disturbance input; The calculation formula for the event-triggered formation controller in S218 is as follows: （28） The desired unit direction vector in S219 The calculation formula is as follows: ； The desired unit direction vector in S219 The calculation formula is as follows: （29） The desired unit direction vector in S220 The calculation formula is as follows: （30） The desired attitude of each quadcopter drone in S221 The calculation formula is as follows: （31）。 6. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 5, characterized in that, The minimum directional disturbance input The calculation formula is as follows: （32） in, Indicates the perturbation input variable; Represents slack variables; This indicates the maximum permissible perturbation value and the minimum perturbation input direction. After the solution is completed, the quadcopter drone will be able to exit the self-locked state.

7. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 6, characterized in that, S3 specifically includes the following steps: S31, Given a flat output space as Here, three points on the parameter represent the third derivative of that parameter; four points on the parameter represent the fourth derivative of that parameter; the third derivatives of the three-dimensional spatial position of the quadcopter UAV are constructed respectively. The calculation formula; S32, Given intermediate variables and intermediate variables Substituting the third derivative of the three-dimensional spatial position of the quadcopter drone In the calculation formula, the intermediate variable is obtained. The calculation formula; S33, Regarding intermediate variables The formula for calculating the reference angular velocity is obtained by transforming the original formula. S34, In intermediate variables The calculation formula uses accelerometer. The third derivative of the spatial three-dimensional position of a quadcopter drone The eighth user-defined variable is obtained. The calculation formula; S35. Regarding the fourth intermediate variable The two sides of the calculation formula and the rotation component Perform a dot product operation to obtain the first derivative of the net thrust. ; S36. First derivative with respect to net thrust Taking the derivative, we obtain the second derivative of the net thrust. ; S37. Solve for the first derivative of the net thrust. and the second derivative of net thrust Substitute into the eighth user-defined variable In the calculation formula, the eighth custom variable is obtained. ; S38. Utilizing the eighth user-defined variable The desired angular acceleration of the quadcopter UAV was calculated.

8. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 7, characterized in that, The third derivative in S31 Fourth derivative The calculation formulas are as follows: （33） （34） intermediate variables in S32 The specific calculation formula is as follows: （35） in, Indicates the first i A quadcopter drone in the body coordinate system z Rotational component along the axial direction; The second derivative of the expected trajectory of the formation center; The specific formula for calculating the desired angular velocity in S33 is as follows: （36） in, Indicates the desired angular velocity; Indicates the first i A quadcopter drone in the body coordinate system y Rotational component along the axial direction; Indicates the first i A quadcopter drone in the body coordinate system x Rotational component along the axial direction; The eighth custom variable in S34 The specific calculation formula is as follows: （37） The first derivative of net thrust in S35 The specific calculation formula is as follows: （38） The second derivative of net thrust in S36 The specific calculation formula is as follows: （39） in, The derivative of jerk; The formula for calculating the desired angular acceleration in S38 is as follows: （40） in, Indicates the first i The desired angular acceleration of a quadcopter drone.

9. The event-triggered anti-locking multi-quadrotor safe formation control method according to claim 8, characterized in that, S4 specifically includes the following steps: S41. A superspiral observer is proposed to identify and compensate for uncertainties in the inner loop within a finite time, where the inner loop refers to attitude error; the expression for the superspiral observer is as follows: （41） in, Indicates the error variable; Represents angular velocity The estimated value; S42. Designing an inner-loop observer using a superhelical observer. Inner loop observer The expression is as follows: （42） in, and Gain is a positive constant. Represents error variable The derivative; express The derivative; S43. Define the rotation matrix error. Rotation matrix error The expression is as follows: （43） S44, Based on rotation matrix error Define logarithmic orientation error on Lie algebra space Logarithmic configuration attitude error The expression is as follows: （44） in, This indicates that the antisymmetric matrix within the parentheses is converted into a three-dimensional vector; S45. Define the relevant velocity error Related speed error The expression is as follows: （45） S46, Logarithmic configuration attitude error Related speed error By taking the time derivative, we obtain the attitude error dynamic model, which is expressed as follows: （46） in, Indicates the fifth intermediate variable; Indicates the sixth intermediate variable; Indicates the seventh intermediate variable; Then, the solution is obtained based on the expression of the attitude error dynamics model. , The calculation formulas are as follows; （47） （48） in, Represents logarithmic orientation error The antisymmetric matrix; Represents the L2 norm; Represents a 3×3 identity matrix; S47. Based on the nominal control section and inner loop observer The attitude controller is constructed, and its calculation formula is as follows: （49） in, Indicates torque input. Indicates nominal control input, nominal control input The specific calculation formula is as follows: （50） in, and Gain is a positive constant. S49. Construct an inner-loop controller by combining the attitude controller and the super-helical observer, and use the inner-loop controller to generate torque input in real time. This information is then incorporated into the rotational dynamics model to achieve rotational control of the multi-quadrotor UAV and to compensate for attitude uncertainties within a finite time.

10. A multi-quadrotor safety formation control system based on event-triggered anti-locking, characterized in that, The invention includes a multi-quadcopter drone, which is configured to perform or execute the event-triggered anti-locking multi-quadcopter safe formation control method according to any one of claims 1 to 9.

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