Fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems

Abstract

The invention discloses a fixed-time fuzzy self-adaptive output feedback formation collision avoidance control method for a multi-unmanned system, and the method comprises the steps: constructing an artificial potential energy function for collision avoidance constraint through the formation position error of the multi-unmanned formation system, so as to build a collision avoidance condition, and achieve the collision avoidance function in the formation process of the multi-unmanned system. A fuzzy state observer is constructed according to an unmanned system state equation, the problem that speed information of an unmanned system cannot be measured due to the fact that unmanned system carrying equipment may have limitation or has accidental faults and interference is solved, a fixed-time fuzzy self-adaptive formation collision avoidance virtual controller is constructed, and the speed information of the unmanned system can be measured. A formation controller is constructed in combination with a parameter adaptive law and a fuzzy state observer, and in order to realize a formation control target, uninterrupted network information transmission is generally needed, and problems of communication redundancy, communication limitation and the like can occur, an event triggering mechanism of a dynamic threshold value is designed to reduce waste of network communication resources; and a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on an event triggering mechanism is constructed, so that fixed-time formation collision avoidance control of the multi-unmanned system with unknown dynamics and unmeasurable speed is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of formation collision avoidance of multiple unmanned systems, and in particular to a fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems. Background Art

[0002] Unmanned systems refer to a type of system that can autonomously complete operational tasks based on its own perception, decision-making and execution capabilities, including ground unmanned vehicles, unmanned surface ships, unmanned underwater vehicles and drones. With the rapid development of artificial intelligence, information technology and robotics, unmanned systems have been widely used in intelligent transportation, search and rescue reconnaissance, environmental monitoring, ocean exploration, industrial production and military fields. With the increase in the scope, intensity and complexity of operational tasks, relying solely on a single unmanned system can no longer meet the existing operational needs, so multiple unmanned systems are required to work together. Formation control is one of the key technologies for achieving collaborative operations of multiple unmanned systems. It has become a research hotspot and has received widespread attention from researchers. Each unmanned system requires a certain amount of space to maintain the formation movement, otherwise collisions may occur between unmanned systems. At the same time, multiple unmanned systems may encounter obstacles in a complex and changing environment, resulting in collisions. Therefore, formation collision avoidance control of multiple unmanned systems is very important.

[0003] At present, the equipment carried by unmanned systems may have limitations or unexpected failures and interference, which may make it impossible to measure the speed information of the unmanned system itself, making the formation control of multiple unmanned systems difficult. In addition, since multiple unmanned systems are currently forming formations in complex and changing environments, it is impossible to accurately avoid collisions between multiple unmanned systems and obstacles or multiple unmanned systems during the formation process, which in turn causes damage to multiple unmanned systems. At the same time, in order to achieve the formation control goal, uninterrupted network information transmission is usually required, which will lead to problems such as communication redundancy and communication limitation. In addition, considering the parameter uncertainty, unmodeled dynamics and external environmental disturbances in the dynamic model of the unmanned system, the traditional unmanned system formation control design is challenging. Summary of the invention

[0004] The present invention provides a fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems to overcome the above technical problems.

[0005] In order to achieve the above object, the technical solution of the present invention is:

[0006] A fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems, specifically comprising the following steps:

[0007] S1: Construct a mathematical model of the unmanned system considering environmental disturbances;

[0008] Rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system;

[0009] And according to the state equation of the unmanned system, the leading unmanned system and the following unmanned system are defined to obtain a multi-unmanned formation system;

[0010] S2: Obtain the formation position error of the multi-unmanned formation system, and construct an artificial potential energy function for collision avoidance constraint based on the formation position error, and obtain the partial derivative of the artificial potential energy function;

[0011] S3: Construct a fuzzy state observer based on the state equation of the unmanned system;

[0012] S4: Based on the fuzzy state observer and the preset first-order filter, a virtual controller for fixed-time fuzzy adaptive formation collision avoidance is constructed according to the partial derivative of the artificial potential energy function;

[0013] S5: Construct parameter adaptation law based on fuzzy state observer;

[0014] A formation controller is constructed based on the virtual controller, parameter adaptive law and fuzzy state observer;

[0015] S6: According to the formation controller, a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on event trigger mechanism is constructed to realize fixed-time fuzzy adaptive output feedback formation collision avoidance control of multiple unmanned systems.

[0016] Furthermore, the S1 specifically includes the following steps:

[0017] S11: Construct a mathematical model of the unmanned system, which is expressed as

[0018]

[0019] Where: represents the inertia matrix of the unmanned system and represents the Coriolis force-centrifugal force matrix of the unmanned system and represents the gravity vector of the unmanned system; q i , Represent the position vector, velocity vector and acceleration vector of the unmanned system respectively and τ i represents the control input and σ i represents environmental disturbance and represents the space of all n×n real matrices; represents n-dimensional Euclidean space;

[0020] S12: Let x 1,i =q i and but

[0021] Rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system;

[0022] The expression of the state equation of the unmanned system is:

[0023]

[0024] Where: M i (x 2,i ) represents the inertia matrix under the state equation; C i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Respectively represent x 1,i ,x 2,i The first derivative of ;

[0025] According to the state equation of the unmanned system, the leading unmanned system and the following unmanned system are defined to obtain a multi-unmanned formation system.

[0026] Furthermore, the S2 specifically includes the following steps:

[0027] S21: Define the monitoring distance set between the leading unmanned system and the following unmanned system and environmental obstacles to obtain the formation position error of the multi-unmanned formation system, and its expression is:

[0028]

[0029] e 1,i =x 1,i -x 1,j

[0030] e o,i =x 1,i -x 1,0

[0031] Where: x 1,i With x 1,j Respectively represent the positions of the i-th and j-th following unmanned systems; x 1,0 Indicates the location of obstacles in the environment; Indicates the detection range of the unmanned system; represents the monitoring distance set; e 1,irepresents the formation position error between the leading unmanned system and the i-th following unmanned system; e o,i Indicates the position distance between the leading unmanned system and environmental obstacles;

[0032] S22: constructing an artificial potential energy function for collision avoidance constraint based on the formation position error;

[0033] The expression of the artificial potential energy function is:

[0034]

[0035] e c,i =x 1,i -x c,i , 0 m =[0,…,0] T

[0036] Where: P c,i (e c,i ) represents the artificial potential energy function; e c,i represents the formation position error between the ith following unmanned system and the cth leading unmanned system; r Indicates the minimum safe distance for unmanned system formation;

[0037] S23: Calculate the partial derivative of the artificial potential energy function to obtain the partial derivative of the artificial potential energy function.

[0038] The expression of the partial derivative of the artificial potential energy function is

[0039]

[0040] Furthermore, in S3, a fuzzy state observer is constructed according to the state equation of the unmanned system, which specifically includes the following steps:

[0041] S31: Define the unknown nonlinear function f 2,i (x 1,i ,x 2,i );

[0042] And let f 2,i (x 1,i ,x 2,i )=-M i (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i ));

[0043] S32: Use fuzzy logic system to approximate unknown nonlinear functions, whose expression is

[0044]

[0045] Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of i Represents the approximation error, and there are unknown constants satisfy and ζ i represents the fuzzy basis function;

[0046] S33: Based on step S32, the state equation of the unmanned system is rewritten as

[0047]

[0048] S34: According to the rewritten state equation of the unmanned system, the fuzzy state observer is constructed as follows:

[0049]

[0050] Where: Represents x 1,i An estimated value of Represents x 2,i An estimated value of represents the observation error and express The first derivative of express The first derivative of Represents x 2,i Estimated inertia matrix; express An estimated value of express The first derivative of k i,1 ,k i,2 ,k i,3 represents the observation gain.

[0051] Furthermore, the S4 specifically includes the following steps:

[0052] S41: performing coordinate transformation on the formation position error to obtain a formation position error vector;

[0053] And the formation velocity error vector is defined according to the fuzzy state observer, and its expression is:

[0054]

[0055] Where: e 1,irepresents the formation position error vector; e 2,i The formation velocity error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; N represents the total number of unmanned systems; a i,j represents the connection edge between the i-th unmanned system and the j-th neighbor unmanned system of the i-th unmanned system; x 1d represents the desired position; x 1,j represents the location of the jth neighbor unmanned system; represents the time-varying distance between the ith unmanned system and the leading unmanned system; represents the time-varying distance between the jth unmanned system and the leading unmanned system; a i,0 represents the connection edge between the i-th unmanned system and the leading unmanned system; represents virtual control input;

[0056] And the virtual control input satisfies the preset first-order filter:

[0057]

[0058] Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i represents the design constant and φ i >0; express The first derivative of α i (0) means α i The initial value of

[0059] S42: Construct the first Lyapunov function V according to the formation position error vector 1,i , whose expression is

[0060] And according to the formation position error vector, the connection edge between the unmanned system and its neighboring unmanned systems is obtained, and its expression is:

[0061]

[0062] in

[0063] Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of express The first derivative of represents the deviation between the actual speed and the estimated speed of the jth neighbor unmanned system of the ith unmanned system;

[0064] S43: Based on the connection edges between the unmanned system and its neighboring unmanned systems, obtain the first Lyapunov function V 1,i The derivative with respect to time is

[0065]

[0066] S44: Based on the partial derivative of the artificial potential energy function, construct a function that satisfies the first Lyapunov function V 1,i The virtual controller of fixed-time fuzzy adaptive formation collision avoidance with respect to time derivative stability is expressed as

[0067]

[0068] Where: c 1,i , c i,a ,q,ρ are design parameters and c 1,i >0, c i,a >0,q>1 and 0<ρ<1; Represents the position x 1,i The partial derivative of

[0069]

[0070] sig 2ρ-1 (·)=sign(·)|·| 2ρ-1

[0071] Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in ; sign(·) represents the sign function.

[0072] Furthermore, the S5 specifically includes the following steps:

[0073] S51: construct parameter adaptation law based on fuzzy state observer;

[0074] The expression of the parameter adaptation law is:

[0075]

[0076] Where: express The first derivative of i represents the design parameters of the adaptive law; c w,irepresents the design parameters and c w,i >0; represents the design parameters of the adaptive law;

[0077] S52: Obtain the derivative of the first-order filter output error according to the virtual controller, and its expression is:

[0078]

[0079] Where: B i (·) indicates the variable e 1,i , A continuous function of Represents the first-order filter output error The derivative of

[0080] S53: Based on the derivative of the first-order filter output error, the formation speed error vector e is calculated according to the fuzzy state observer 2,i Derivative, get the formation velocity error vector derivative Its expression is

[0081]

[0082] S54: According to the formation speed error vector e 2,i Construct the second Lyapunov function, whose expression is

[0083]

[0084] Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; e 2,i represents the formation velocity error vector; Indicates e 2,i The transpose of Represents the first-order filter output error; express The transpose of express The transpose of

[0085] And according to the formation velocity error vector derivative Get the derivative of the second Lyapunov function as

[0086]

[0087] Where: c 2,i , c w,i represents the design parameters and c 2,i >0, cw,i >0;

[0088] S55: Construct a formation controller that satisfies the derivative stability of the second Lyapunov function. The expression of the formation controller is:

[0089]

[0090] Where:

[0091] sig 2ρ-1 (·)=sign(·)|·| 2ρ-1 Where: e M2,i Indicates e 2,i The error of the Mth element in; M represents e 2,i The element number in ; sign(·) represents the sign function.

[0092] Furthermore, the fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on event-triggered mechanism is constructed in S6;

[0093] The expression of the event trigger mechanism is:

[0094] τ i (t) = ω i (t h ),t∈[t h ,t h+1 )

[0095] t h+1 = inf{t>t h :|τ i -ω i |≥p(t)|τ i (t)|+q(t)}

[0096]

[0097] Where: τ i (t) represents the actual control input; ω i (t h ) indicates that at t h The event of the unmanned system at time i triggers the controller vector and h=1,2,…; t h ,t h+1 represents the sampling time; t represents time; inf{·} represents the lower bound function; τ i represents the control input vector of the ith unmanned system; p(t), q(t) represent the dynamic parameter variables in the event triggering mechanism; represents the intermediate parameter quantity and represents the design parameters;

[0098] The fixed-time fuzzy adaptive output feedback formation collision avoidance controller is expressed as:

[0099]

[0100] Where: r1(t), r2(t) represent design constants, and for any There exist constants |r1|≤1,|r2|≤1.

[0101] Beneficial effects: The present invention provides a fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems. An artificial potential energy function for collision avoidance constraint is constructed according to the formation position error of the multiple unmanned formation system. The collision avoidance function in the formation process of the multiple unmanned systems is realized through the collision avoidance condition established by the artificial potential energy function. A fuzzy state observer is constructed according to the state equation of the unmanned system, so as to solve the problem that the speed information of the unmanned system itself cannot be measured due to the limitations of the equipment carried by the unmanned system or unexpected failures and interference. A virtual controller for fixed-time fuzzy adaptive formation collision avoidance is constructed according to the partial derivative of the artificial potential energy function, and a formation controller is constructed by combining the parameter adaptive law and the fuzzy state observer. In order to achieve the formation control goal, it is usually necessary to carry out network information transmission uninterruptedly, which will cause problems such as communication redundancy and communication limitation. Therefore, an event trigger mechanism of dynamic threshold is designed to reduce the waste of network communication resources, and it is introduced into the formation controller to obtain a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on the event trigger mechanism, so as to realize the fixed-time fuzzy adaptive output feedback formation collision avoidance control of multiple unmanned systems, and then the fixed-time formation collision avoidance control of multiple unmanned systems with unknown dynamics and unmeasurable speed can be realized. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0103] Figure 1 It is a flow chart of the fixed-time fuzzy adaptive output feedback formation collision avoidance control method of the multi-unmanned system of the present invention;

[0104] Figure 2 It is a structural block diagram of the fixed-time fuzzy adaptive output feedback formation collision avoidance control method of multiple unmanned systems in this embodiment;

[0105] Figure 3This is a core program flow chart of the fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems in this embodiment. DETAILED DESCRIPTION

[0106] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0107] This embodiment provides a fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems, such as Figures 1 to 3 As shown, the specific steps include:

[0108] S1: Construct a mathematical model of the unmanned system considering environmental disturbances, rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system, and define the leading unmanned system and the following unmanned system according to the state equation of the unmanned system to obtain a multi-unmanned formation system;

[0109] The specific steps include:

[0110] S11: Consider a formation system composed of N unmanned systems, where the i-th unmanned system can be described by the following Euler-Lagrangian system (i = 1, 2, ..., N), that is, the mathematical model of the unmanned system is constructed, and its expression is

[0111]

[0112] Where: represents the inertia matrix of the unmanned system and represents the Coriolis force-centrifugal force matrix of the unmanned system and represents the gravity vector of the unmanned system; q i , Represent the position vector, velocity vector and acceleration vector of the unmanned system respectively and τ i represents the control input and σ i represents environmental disturbance and represents the space of all n×n real matrices; represents n-dimensional Euclidean space;

[0113] S12: To facilitate control design, let x 1,i =qi and but

[0114] Rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system;

[0115] The expression of the state equation of the unmanned system is:

[0116]

[0117] Where: M i (x 2,i ) represents the inertia matrix under the state equation; C i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Respectively represent x 1,i ,x 2,i The first derivative of ;

[0118] And according to the state equation of the unmanned system, the leading unmanned system and the following unmanned system are defined to obtain a multi-unmanned formation system;

[0119] S2: Obtain the formation position error of the multi-unmanned formation system, and construct an artificial potential energy function for collision avoidance constraint based on the formation position error, and obtain the partial derivative of the artificial potential energy function;

[0120] The specific steps include:

[0121] S21: Considering that there is no collision between each following unmanned system and its potential obstacles (leading unmanned system and obstacles), a set of monitoring distances between the leading unmanned system and the following unmanned system and environmental obstacles is defined to obtain the formation position error of the multi-unmanned formation system, which is expressed as:

[0122]

[0123] e 1,i =x 1,i -x 1,j

[0124] e o,i =x 1,i -x 1,0

[0125] Where: x 1,i With x 1,jRespectively represent the positions of the i-th and j-th following unmanned systems; x 1,0 Indicates the location of obstacles in the environment; Indicates the detection range of the unmanned system; represents the monitoring distance set; e 1,i represents the formation position error between the leading unmanned system and the i-th following unmanned system; e o,i Indicates the position distance between the leading unmanned system and the environmental obstacles; set Including the environmental obstacles of the i-th following unmanned system, in order to achieve no collision between the leading unmanned system and its potential obstacles (leading unmanned system and obstacles), it is necessary to construct the following artificial potential energy function:

[0126] S22: constructing an artificial potential energy function for collision avoidance constraint based on the formation position error;

[0127] The expression of the artificial potential energy function is:

[0128]

[0129] e c,i -x 1,i -x c,i , 0 m =[0,…,0] T

[0130] Where: P c,i (e c,i ) represents the artificial potential energy function; e c,i represents the formation position error between the ith following unmanned system and the cth leading unmanned system; r Indicates the minimum safe distance for unmanned system formation;

[0131] S23: Calculate the partial derivative of the artificial potential energy function to obtain the partial derivative of the artificial potential energy function.

[0132] The expression of the partial derivative of the artificial potential energy function is

[0133]

[0134] S3: Construct a fuzzy state observer based on the state equation of the unmanned system, which includes the following steps

[0135] S31: Define the unknown nonlinear function f 2,i (x 1,i ,x 2,i );

[0136] And let f 2,i (x 1,i ,x 2,i )=-Mi (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i ));

[0137] S32: Use fuzzy logic system to approximate unknown nonlinear functions, whose expression is

[0138]

[0139] Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of i Represents the approximation error, and there are unknown constants satisfy and ζ i represents the fuzzy basis function;

[0140] S33: Based on step S32, the state equation of the unmanned system is rewritten as

[0141]

[0142] S34: According to the rewritten state equation of the unmanned system, the fuzzy state observer is constructed as follows:

[0143]

[0144] Where: Represents x 1,i An estimated value of Represents x 2,i An estimated value of represents the observation error and express The first derivative of express The first derivative of Represents x 2,i Estimated inertia matrix; express An estimated value of express The first derivative of k i,1 ,k i,2 ,k i,3 represents the observation gain;

[0145] S4: Based on the fuzzy state observer and the preset first-order filter, a virtual controller for fixed-time fuzzy adaptive formation collision avoidance is constructed according to the partial derivative of the artificial potential energy function;

[0146] The specific steps include:

[0147] S41: performing coordinate transformation on the formation position error to obtain a formation position error vector;

[0148] And the formation velocity error vector is defined according to the fuzzy state observer, and its expression is:

[0149]

[0150] Where: e 1,i represents the formation position error vector; e 2,i The formation velocity error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; N represents the total number of unmanned systems; a i,j represents the connection edge between the i-th unmanned system and the j-th neighboring unmanned system of the i-th unmanned system, wherein the connection edge is the information transmission path between the unmanned system and its neighboring unmanned system in the multi-unmanned formation system under the preset environmental conditions; x 1d represents the desired position; x 1,j represents the location of the jth neighbor unmanned system; represents the time-varying distance between the ith unmanned system and the leading unmanned system; represents the time-varying distance between the jth unmanned system and the leading unmanned system; a i,0 represents the connection edge between the i-th unmanned system and the leading unmanned system; represents virtual control input;

[0151] And the virtual control input satisfies the preset first-order filter:

[0152]

[0153] Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i represents the design constant and φ i >0; express The first derivative of α i (0) means α i The initial value of

[0154] S42: Construct the first Lyapunov function V according to the formation position error vector 1,i , whose expression is

[0155]

[0156] And according to the formation position error vector, the connection edge between the unmanned system and its neighboring unmanned systems is obtained, and its expression is:

[0157]

[0158] in

[0159] Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of express The first derivative of represents the deviation between the actual speed and the estimated speed of the jth neighbor unmanned system of the ith unmanned system;

[0160] S43: Based on the connection edges between the unmanned system and its neighboring unmanned systems, obtain the first Lyapunov function V 1,i The derivative with respect to time is

[0161]

[0162] S44: Based on the partial derivative of the artificial potential energy function, construct a function that satisfies the first Lyapunov function V 1,i The virtual controller of fixed-time fuzzy adaptive formation collision avoidance with respect to time derivative stability is expressed as

[0163]

[0164] Where: c 1,i , c i,a ,q,ρ are design parameters and c 1,i >0, c i,a >0,q>1 and 0<ρ<1; Represents the position x 1,i The partial derivative of

[0165]

[0166] sig 2ρ-1 (·)=sign(·)|·| 2ρ-1

[0167] Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in; sign(·) represents the sign function. In this embodiment, z takes the value of 1, then

[0168]

[0169] S5: Construct parameter adaptation law based on fuzzy state observer;

[0170] A formation controller is constructed based on the virtual controller, parameter adaptive law and fuzzy state observer;

[0171] Furthermore, the S5 specifically includes the following steps:

[0172] S51: construct parameter adaptation law based on fuzzy state observer;

[0173] The expression of the parameter adaptation law is:

[0174]

[0175] Where: express The first derivative of i represents the design parameters of the adaptive law; c w,i represents the design parameters and c w,i >0; represents the design parameters of the adaptive law;

[0176] S52: Obtain the derivative of the first-order filter output error according to the virtual controller, and its expression is:

[0177]

[0178] Where: B i (·) indicates the variable e 1,i , A continuous function of Represents the first-order filter output error The derivative of

[0179] S53: Based on the derivative of the first-order filter output error, the formation speed error vector e is calculated according to the fuzzy state observer 2,i Derivative, get the formation velocity error vector derivative Its expression is

[0180]

[0181] S54: According to the formation speed error vector e 2,iConstruct the second Lyapunov function, whose expression is

[0182]

[0183] Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; e 2,i represents the formation velocity error vector; Indicates e 2,i The transpose of Represents the first-order filter output error; express The transpose of express The transpose of

[0184] And according to the formation velocity error vector derivative Get the derivative of the second Lyapunov function as

[0185]

[0186] Where: c 2,i , c w,i represents the design parameters and c 2,i >0, c w,i >0;

[0187] S55: Construct a formation controller that satisfies the derivative stability of the second Lyapunov function. The expression of the formation controller is:

[0188]

[0189] Where:

[0190] sig 2ρ-1 (·)=sign(·)|·| 2ρ-1 Where: e M2,i Indicates e 2,i The error of the Mth element in; M represents e 2,i The element number in; sign(·) represents the sign function. In this embodiment, M takes the value of 1, then

[0191] In the specific embodiment, the virtual controller and the formation controller of this embodiment respectively introduce the intermediate calculation parameter sig 2ρ-1 (e 1,i ) and sig 2ρ-1 (e 2,i), so that the convergence speed of the control method of this embodiment can converge within a fixed time;

[0192] S6: According to the formation controller, a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on event trigger mechanism is constructed to realize the fixed-time fuzzy adaptive output feedback formation collision avoidance control of multiple unmanned systems;

[0193] Since multi-unmanned systems usually have problems such as waste of transmission resources or frequent triggering when exchanging information and performing tasks, an event trigger mechanism based on dynamic thresholds is constructed;

[0194] The expression of the event trigger mechanism is:

[0195] τ i (t) = ω i (t h ),t∈[t h ,t h+1 )

[0196] t h+1 = inf{t>t h :|τ i -ω i |≥p(t)|τ i (t)|+q(t)}

[0197]

[0198] Where: τ i (t) represents the actual control input; ω i (t h ) indicates that at t h The event of the unmanned system at time i triggers the controller vector and h=1,2,…; t h ,t h+1 represents the sampling time; t represents time; inf{·} represents the lower bound function; τ i represents the control input vector of the ith unmanned system; p(t), q(t) represent the dynamic parameter variables in the event triggering mechanism; represents the intermediate parameter quantity and represents the design parameters;

[0199] The fixed-time fuzzy adaptive output feedback formation collision avoidance controller is expressed as:

[0200]

[0201] Where: r1(t), r2(t) represent design constants, and for any There exist constants |r1|≤1,|r2|≤1.

[0202] In this embodiment, an artificial potential energy function for collision avoidance constraint is constructed through the formation position error of multiple unmanned formation systems. The collision avoidance function in the formation process of multiple unmanned systems is realized through the collision avoidance condition established by the artificial potential energy function. A fuzzy state observer is constructed according to the state equation of the unmanned system, which solves the problem that the speed information of the unmanned system itself cannot be measured due to limitations of the equipment carried by the unmanned system or unexpected failures and interference. A virtual controller for fixed-time fuzzy adaptive formation collision avoidance is constructed according to the partial derivative of the artificial potential energy function, and a formation controller is constructed by combining the parameter adaptive law and the fuzzy state observer. In order to achieve the formation control goal, it is usually necessary to transmit network information uninterruptedly, which will cause problems such as communication redundancy and communication limitation. Therefore, an event trigger mechanism of dynamic threshold is designed to reduce the waste of network communication resources, and it is introduced into the formation controller to obtain a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on the event trigger mechanism, so as to realize the fixed-time fuzzy adaptive output feedback formation collision avoidance control of multiple unmanned systems, thereby realizing the fixed-time formation collision avoidance control of multiple unmanned systems with unknown dynamics and unmeasurable speed.

[0203] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems, characterized in that: The specific steps include: S1: Construct a mathematical model of the unmanned system considering environmental disturbances; Rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system; And according to the state equation of the unmanned system, the leading unmanned system and the following unmanned system are defined to obtain a multi-unmanned formation system; S2: Obtain the formation position error of the multi-unmanned formation system, construct an artificial potential energy function for collision avoidance constraint based on the formation position error, and obtain the partial derivative of the artificial potential energy function; S3: Construct a fuzzy state observer based on the state equation of the unmanned system; S4: Based on the fuzzy state observer and the preset first-order filter, a virtual controller for fixed-time fuzzy adaptive formation collision avoidance is constructed according to the partial derivative of the artificial potential energy function; S5: Construct parameter adaptation law based on fuzzy state observer; A formation controller is constructed based on the virtual controller, parameter adaptive law and fuzzy state observer; S6: According to the formation controller, a fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on event trigger mechanism is constructed to realize fixed-time fuzzy adaptive output feedback formation collision avoidance control of multiple unmanned systems.

2. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 1, characterized in that: The S1 specifically includes the following steps S11: Construct a mathematical model of the unmanned system, which is expressed as Where: represents the inertia matrix of the unmanned system and represents the Coriolis force-centrifugal force matrix of the unmanned system and represents the gravity vector of the unmanned system; q i , Represent the position vector, velocity vector and acceleration vector of the unmanned system respectively and τ i represents the control input and σ i represents environmental disturbance and represents the space of all n×n real matrices; represents n-dimensional Euclidean space; S12: Let x 1,i =q i and but Rewrite the mathematical model of the unmanned system to obtain the state equation of the unmanned system; The expression of the state equation of the unmanned system is: Where: M i (x 2,i ) represents the inertia matrix under the state equation; C i (x 1,i ,x 2,i ) represents the Coriolis force-centrifugal force matrix under the state equation; g i (x 2,i ) represents the gravity vector under the state equation; x 1,i represents the position vector under the state equation; x 2,i represents the velocity vector under the state equation; Respectively represent x 1,i ,x 2,i The first derivative of ; According to the state equation of the unmanned system, the leading unmanned system and the following unmanned system are defined to obtain a multi-unmanned formation system.

3. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 1, characterized in that: The S2 specifically includes the following steps S21: Define the monitoring distance set between the leading unmanned system and the following unmanned system and environmental obstacles to obtain the formation position error of the multi-unmanned formation system, and its expression is: e 1,i =x 1,i -x 1,j e o,i =x 1,i -x 1,0 Where: x 1,i With x 1,j Respectively represent the positions of the i-th and j-th following unmanned systems; x 1,0 Indicates the location of obstacles in the environment; Indicates the detection range of the unmanned system; represents the monitoring distance set; e 1,i represents the formation position error between the leading unmanned system and the i-th following unmanned system; e o,i Indicates the position distance between the leading unmanned system and environmental obstacles; S22: constructing an artificial potential energy function for collision avoidance constraint based on the formation position error; The expression of the artificial potential energy function is: Where: P c,i (e c,i ) represents the artificial potential energy function; e c,i represents the formation position error between the ith following unmanned system and the cth leading unmanned system; r Indicates the minimum safe distance for unmanned system formation; S23: Calculate the partial derivative of the artificial potential energy function to obtain the partial derivative of the artificial potential energy function. The expression of the partial derivative of the artificial potential energy function is 4. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 1, characterized in that: In S3, a fuzzy state observer is constructed according to the state equation of the unmanned system, which specifically includes the following steps: S31: Define the unknown nonlinear function f 2,i (x 1,i ,x 2,i ); And let f 2,i (x 1,i ,x 2,i )=-M i (x 2,i ) -1 (C i (x 1,i ,x 2,i )x 2,i +g i (x 2,i )); S32: Use fuzzy logic system to approximate unknown nonlinear functions, whose expression is Where: represents a fuzzy logic system; represents the fuzzy parameter matrix; express The transpose of i Represents the approximation error, and there are unknown constants satisfy and ζ i represents the fuzzy basis function; S33: Based on step S32, the state equation of the unmanned system is rewritten as S34: According to the rewritten state equation of the unmanned system, the fuzzy state observer is constructed as follows: Where: Represents x 1,i An estimated value of Represents x 2,i An estimated value of represents the observation error and express The first derivative of express The first derivative of Represents x 2,i Estimated inertia matrix; express An estimated value of express The first derivative of k i,1 ,k i,2 ,k i,3 represents the observation gain.

5. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 4, characterized in that: The S4 specifically includes the following steps S41: performing coordinate transformation on the formation position error to obtain a formation position error vector; And the formation velocity error vector is defined according to the fuzzy state observer, and its expression is: Where: e 1,i represents the formation position error vector; e 2,i The formation velocity error vector; j represents the index number of the neighboring unmanned system of the i-th unmanned system; N represents the total number of unmanned systems; a i,j represents the connection edge between the ith unmanned system and the jth neighbor unmanned system of the ith unmanned system; x 1d represents the desired position; x 1,j represents the location of the jth neighbor unmanned system; represents the time-varying distance between the ith unmanned system and the leading unmanned system; represents the time-varying distance between the jth unmanned system and the leading unmanned system; a i,0 represents the connection edge between the i-th unmanned system and the leading unmanned system; represents virtual control input; And the virtual control input satisfies the preset first-order filter: Where: Represents the first-order filter output error; α i Represents a virtual controller; φ i represents the design constant and φ i >0; express The first derivative of α i (0) means α i The initial value of S42: Construct the first Lyapunov function V according to the formation position error vector 1,i , whose expression is And according to the formation position error vector, the connection edge between the unmanned system and its neighboring unmanned systems is obtained, and its expression is: in Where: Indicates e 1,i The first derivative of i,d represents an intermediate variable; represents the deviation between the actual speed and the estimated speed of the i-th unmanned system; express The first derivative of express The first derivative of represents the deviation between the actual speed and the estimated speed of the jth neighbor unmanned system of the ith unmanned system; S43: Based on the connection edges between the unmanned system and its neighboring unmanned systems, obtain the first Lyapunov function V 1,i The derivative with respect to time is S44: Based on the partial derivative of the artificial potential energy function, construct a function that satisfies the first Lyapunov function V 1,i The virtual controller of fixed-time fuzzy adaptive formation collision avoidance with respect to time derivative stability is expressed as Where: c 1,i , c i,a ,q,ρ are design parameters and c 1,i >0, c i,a >0,q>1 and 0<ρ<1; Represents the position x 1,i The partial derivative of say 2ρ-1 (·)=sign(·)|·| 2ρ-1 Where: e z1,i Indicates e 1,i The error of the zth element in ; z represents e 1,i The element number in ; sign(·) represents the sign function.

6. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 5, characterized in that: S5 specifically includes the following steps S51: construct parameter adaptation law based on fuzzy state observer; The expression of the parameter adaptation law is: Where: express The first derivative of i represents the design parameters of the adaptive law; c w,i represents the design parameters and c w,i >0; represents the design parameters of the adaptive law; S52: Obtain the derivative of the first-order filter output error according to the virtual controller, and its expression is: Where: B i (·) indicates the variable e 1,i , A continuous function of Represents the first-order filter output error The derivative of S53: Based on the derivative of the first-order filter output error, the formation speed error vector e is calculated according to the fuzzy state observer 2,i Derivative, get the formation velocity error vector derivative Its expression is S54: According to the formation speed error vector e 2,i Construct the second Lyapunov function, whose expression is Where: V 2,i represents the second Lyapunov function; represents the error between the ideal parameters and the estimated parameters; e 2,i represents the formation velocity error vector; Indicates e 2,i The transpose of Represents the first-order filter output error; express The transpose of express The transpose of And according to the formation velocity error vector derivative Get the derivative of the second Lyapunov function as Where: c 2,i , c w,i represents the design parameters and c 2,i >0, c w,i >0; S55: Construct a formation controller that satisfies the derivative stability of the second Lyapunov function. The expression of the formation controller is: Where: sig 2ρ-1 (·)=sign(·)|·| 2ρ-1 Where: e M2,i Indicates e 2,i The error of the Mth element in; M represents e 2,i The element number in ; sign(·) represents the sign function.

7. The fixed-time fuzzy adaptive output feedback formation collision avoidance control method for multiple unmanned systems according to claim 6, characterized in that: The fixed-time fuzzy adaptive output feedback formation collision avoidance controller based on event-triggered mechanism constructed in S6; The expression of the event trigger mechanism is: τ i (t)=ω i (t h ),t∈[t h ,t h+1 ) t h+1 =inf{t>t h :|τ i -ω i |≥p(t)|τ i (t)|+q(t)} Where: τ i (t) represents the actual control input; ω i (t h ) indicates that at t h The event of the unmanned system at time i triggers the controller vector and h=1,2,…; t h ,t h+1 represents the sampling time; t represents time; inf{·} represents the lower bound function; τ i represents the control input vector of the ith unmanned system; p(t), q(t) represent the dynamic parameter variables in the event triggering mechanism; represents the intermediate parameter quantity and represents the design parameters; The fixed-time fuzzy adaptive output feedback formation collision avoidance controller is expressed as: Where: r1(t), r2(t) represent design constants, and for any There exist constants |r1|≤1,|r2|≤1.

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