A robust swarming control method for multi-robot systems based on neural networks

Abstract

The present invention discloses a method for robust swarming control of a multi-robot system based on a neural network. First, a multi-robot dynamics model is established, and a reference signal form is determined. The matching / non-matching disturbance in the system is expressed by using a parameterized neural network paradigm, and an estimation weight function and a basis function form are defined. Then, based on the parameterized neural network estimator constructed in the above steps, a robust swarming controller is designed, and the adaptive update law of the neural network estimation parameters is generated by using the Lyapunov stability theorem, and then the stability of the closed-loop error system is analyzed to realize robust swarming control of the multi-robot system under interference. The method of the present invention is aimed at a second-order multi-robot system, and the situation of dual-channel interference is considered. The method of the neural network is used to realize the robust swarming control of the multi-robot. There is no Lipnitz limit for the interference of nonlinear dynamics, which is closer to the interference in the actual situation, and is suitable for the swarming control field of the multi-robot system.

Description

Technical Field

[0001] The present invention belongs to the technical field of cooperative control of multi-robot systems, and in particular relates to a robust swarming control method for multi-robot systems based on neural networks. Background Art

[0002] With the rapid development of modern communications and intelligent computing, the collaborative control of multi-robot systems has attracted the attention of more and more scholars. Due to its advantages of low cost, networked operation, and high flexibility, it has been proven to be effective in many practical applications. Multi-robot collaborative control is to form regular and orderly movements through the cooperation of multiple robots. Multi-robot distributed collaborative control not only has basic theoretical value, but also has important engineering application prospects. It is mainly used in the fields of drone formation flight and swarm warfare. For practical system models that can widely characterize spacecraft, robots, unmanned vehicles, etc., studying the design of distributed collaborative control algorithms for multi-robot systems is an urgent problem to be solved by technicians in this field.

[0003] In actual engineering applications, multi-robot systems are inevitably subject to external interference. How to reduce the interference to the system and enhance the robustness of the system is an urgent problem to be solved in multi-robot swarming control. At present, there have been many research works on the interference problem of swarming control. However, on the one hand, most studies only consider the nonlinear dynamic interference under a single channel, and many studies have imposed Lipnitz restrictions on the nonlinear dynamic interference, which is obviously not desirable in actual situations. On the other hand, there are relatively few studies on dual-channel interference, but in actual applications, all channels of the system are inevitably subject to interference. Research on interference under dual channels is very meaningful. Summary of the invention

[0004] To solve the above technical problems, the present invention provides a neural network-based robust swarming control method for a multi-robot system, which is used to solve the problem of nonlinear dynamic interference of the multi-robot system under dual channels and realize robust swarming control of the multi-robots.

[0005] The technical solution of the present invention is: a robust swarming control method for a multi-robot system based on a neural network, and the specific steps are as follows:

[0006] S1. Establish a multi-robot dynamic model with matching / non-matching disturbance effects, determine the generation form of reference signals, and then clarify the swarming control problem;

[0007] S2. Use the parameterized neural network paradigm to express the matching / non-matching disturbances in the system, and then define the estimated weight function and basis function form to achieve the approximation of the relevant disturbances;

[0008] S3, based on the parameterized neural network estimator constructed in step S2, a robust swarming controller is designed, and the Lyapunov stability theorem is used to generate an adaptive update law for the neural network estimation parameters, and then the stability of the closed-loop error system is analyzed;

[0009] S4. Realize robust swarming control of multi-robot systems under disturbance conditions.

[0010] Furthermore, in step S1, the dynamic model of the follower robot is as follows:

[0011]

[0012] The reference signal is defined as follows:

[0013]

[0014] in, ( is a real number space, n∈{1,2,3} represents the dimension of robot motion) represents the position and speed of the i-th robot, N represents the number of robots, For p i ,q i The first derivative of . represents the control input, They respectively represent the nonlinear dynamic interferences on the two channels. represents the location information of the reference signal, represents the speed information of the reference signal, Respectively represent p r ,q r The first-order derivative with respect to time. In this system, it is assumed that all follower robots can obtain the position and velocity information of the reference signal.

[0015] Furthermore, in step S2, the matching / non-matching disturbances in the system are expressed using a parameterized neural network paradigm, and then an estimated weight function and a basis function form are defined, thereby achieving approximation of the relevant disturbances;

[0016] According to the RBF neural network method, the interference f i (p i ),g i (q i ) can be expressed as follows:

[0017]

[0018] Among them, f i , g i They represent the non-matching interference and matching interference suffered by the i-th robot, respectively. The non-matching interference f iOnly with position p i Related, matching interference g i Only with speed q i related. is the weight matrix, m represents the number of radial basis functions, T represents the transpose of the matrix, ∈ fi and It is the approximation error caused by the neural network approximating the nonlinear dynamic terms (assumed to be all 0). is a radial basis function, the i-th, i={1,2,...,m} (m is the number of radial basis functions) element s i is defined as follows:

[0019]

[0020] in, is a pre-set vector with the same dimension as p i ,q i Similarly, in the specific operation, p i ,q i Substitute Calculate in and σ are unknown parameters, and ||·|| represents the 2-norm operation of the vector.

[0021] is the neural network pair g i (q i ), f i (p i ) is expressed as follows:

[0022]

[0023] in, Represents the weight matrix Estimates.

[0024] use Represents the estimation error, which is expressed as follows:

[0025]

[0026] in, They represent the error between the estimated value and the true value of the weight matrix respectively.

[0027] Further, in step S3, based on the parameterized neural network estimator constructed in step S2, a robust swarming controller is designed, and the Lyapunov stability theorem is used to generate an adaptive update law of the neural network estimation parameters, and then the stability of the closed-loop error system is analyzed;

[0028] First, construct the following auxiliary variables:

[0029]

[0030] Among them, x i represents the position deviation between the ith robot and the reference signal, v i represents the velocity deviation between the ith robot and the reference signal plus the estimate of the non-matching disturbance

[0031] Then define the neighborhood N of the i-th robot i and σ transformation ||·|| σ , N i is defined as follows:

[0032] N i ={j∈G:||p i -p j ||<r} (8)

[0033] Where G represents the set of all robots, ||p i -p j || represents the geometric distance between the i-th and j-th robots, and r represents the communication range of each robot.

[0034] σ transformation||·|| σ is defined as follows:

[0035]

[0036] Among them, ∈ is a parameter greater than 0, z is the independent variable of the transformation (hereinafter, z represents the independent variable of the function), and ||·|| represents the 2-norm operation of the vector.

[0037] We further define the virtual potential energy ψ between the two robots α (||x j -x i || σ ), x i 、x j Respectively represent the position deviation between the i-th and j-th robots and the reference signal, ψ α (z) is defined as follows:

[0038]

[0039] Among them, d α =||d|| σ represents the σ transformation of the expected distance d between the two robots when the swarming behavior is finally formed, s is the integral variable, φ α (||x j -x i ||σ ) represents the virtual force (gravitational or repulsive force) between the two robots, φ α The specific expression of (z) is as follows:

[0040] φ α (z) = ρ h (z / r α )φ(zd α ) (11)

[0041] Among them, r α =||r|| σ represents the σ transformation of the robot communication range r, ρ h is the concave-convex function, and its expression is:

[0042]

[0043] h∈(0,1) is a pre-set parameter, ρ h (z) is smooth and continuous on [0,1], and its derivative is bounded on this interval.

[0044] The form of φ(z) is as follows:

[0045]

[0046] Among them, a, b, c are pre-set variables and satisfy σ1 represents a function of the setting.

[0047] In further defining the adjacency matrix A(p) of the system, a ij (p) represents the element in the i-th row and j-th column of the system adjacency matrix A(p), and the specific expression is as follows:

[0048] a ij (p) = ρ h (||p j -p i || σ / r α ) (14)

[0049] Finally, the following robust swarming controller is designed:

[0050]

[0051] in, is virtual potential energy The derivative with respect to time, vector represents ||x j -x i || σ The derivative with respect to time, ∈ is a parameter greater than 0, p jrepresents the position of the jth robot, v j represents the estimated value of the velocity deviation between the jth robot and the reference signal plus the non-matching interference c1, c2 are parameters greater than 0, express The first derivative with respect to time, represents radial basis function For vector p i The derivative of .

[0052] Then construct the following Lyapunov function:

[0053]

[0054] Among them, γ and β are parameters greater than 0. Represents the virtual potential energy between the i-th and j-th robots.

[0055] Derivative the above Lyapunov function to obtain And request Thus, the following neural network estimation parameters are designed: The adaptive update law of is:

[0056]

[0057] Furthermore, in step S4, robust swarming control of the multi-robot system under interference is implemented, and the controller designed in step S3 is deployed to the follower robot group, which can realize swarming behavior under the conditions of matched interference and non-matched interference at the same time.

[0058] Beneficial effects of the present invention: The method of the present invention first establishes a multi-robot dynamics model and determines the form of a reference signal, uses a parameterized neural network paradigm to express the matching / non-matching disturbances in the system, defines the estimated weight function and the basis function form, and then designs a robust swarming controller based on the parameterized neural network estimator constructed in the above steps, and uses the Lyapunov stability theorem to generate an adaptive update law for the neural network estimation parameters, and then analyzes the stability of the closed-loop error system to achieve robust swarming control of the multi-robot system under interference. The method of the present invention is aimed at a second-order multi-robot system, takes into account the situation of dual-channel interference, and uses a neural network method to achieve robust swarming control of multi-robots. There is no Lipnitz limit for the interference of nonlinear dynamics, which is closer to the interference in real situations, and is suitable for the swarming control field of multi-robot systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 The present invention is a flowchart of a neural network-based robust swarming control method for a multi-robot system.

[0060] Figure 2 Schematic diagram of the initial state of the given reference signal and the follower and the robot (N=40) in an embodiment of the present invention.

[0061] Figure 3 Schematic diagram of the ideal swarming behavior that is ultimately presented after the robust swarming controller is deployed to followers (N=40) in an embodiment of the present invention. DETAILED DESCRIPTION

[0062] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0063] like Figure 1 As shown, a flowchart of a robust swarming control method for a multi-robot system based on a neural network of the present invention is shown, and the specific steps are as follows:

[0064] S1. Establish a multi-robot dynamic model with matching / non-matching disturbance effects, determine the generation form of reference signals, and then clarify the swarming control problem.

[0065] The dynamic model of the follower robot is as follows:

[0066]

[0067] The reference signal is defined as follows:

[0068]

[0069] in, ( is a real number space, n∈{1,2,3} represents the dimension of robot motion) represents the position and speed of the i-th robot, N represents the number of robots, For p i ,q i The first derivative with respect to time. represents the control input, They respectively represent the nonlinear dynamic interferences on the two channels. represents the location information of the reference signal, represents the speed information of the reference signal, Respectively represent p r ,q r The first-order derivative with respect to time. In this system, it is assumed that all follower robots can obtain the position and velocity information of the reference signal.

[0070] like Figure 2 As shown in the figure, the reference signal and the initial state diagram of the follower robot, the designed controller can achieve Figure 3 control effect.

[0071] S2. Use the parameterized neural network paradigm to express the matching / non-matching disturbances in the system, and then define the estimated weight function and basis function form to achieve the approximation of the relevant disturbances.

[0072] According to the RBF neural network method, the interference f i (p i ),g i (q i ) can be expressed as follows:

[0073]

[0074] Among them, f i , g i They represent the non-matching interference and matching interference suffered by the i-th robot, respectively. The non-matching interference f i Only with position p i Related, matching interference g i Only with speed q i related. is the weight matrix, m represents the number of radial basis functions, T represents the transpose of the matrix, ∈ fi and It is the approximation error caused by the neural network approximating the nonlinear dynamic terms (assumed to be all 0). is a radial basis function, the i-th, i={1,2,...,m} (m is the number of radial basis functions) element s i is defined as follows:

[0075]

[0076] in, is a pre-set vector with the same dimension as p i ,q i Similarly, in the specific operation, p i ,q i Substitute Calculate in and σ are unknown parameters, and ||·|| represents the 2-norm operation of the vector.

[0077] is the neural network pair g i (q i ), f i (p i ) is expressed as follows:

[0078]

[0079] in, Represents the estimation of weight matrices W and Z.

[0080] use Represents the estimation error, which is expressed as follows:

[0081]

[0082] in, They represent the error between the estimated value and the true value of the weight matrix respectively.

[0083] S3, based on the parameterized neural network estimator constructed in S2, a robust swarming controller is designed, and the Lyapunov stability theorem is used to generate an adaptive update law for the neural network estimation parameters, and then the stability of the closed-loop error system is analyzed.

[0084] First, construct the following auxiliary variables:

[0085]

[0086] Among them, x i represents the position deviation between the ith robot and the reference signal, v i represents the velocity deviation between the ith robot and the reference signal plus the estimate of the non-matching disturbance

[0087] Then define the neighborhood N of the i-th robot i and σ transformation ||·|| σ , N i is defined as follows:

[0088] N i ={j∈G:||p i -p j ||<r} (25)

[0089] Where G represents the set of all robots, ||p i -p j || represents the geometric distance between the i-th and j-th robots, and r represents the communication range of each robot.

[0090] σ transformation||·|| σ is defined as follows:

[0091]

[0092] Among them, ∈ is a parameter greater than 0, z is the independent variable of the transformation, and ||·|| represents the 2-norm operation of the vector.

[0093] We further define the virtual potential energy ψ between the two robots α (||x j-x i || σ ), x j 、x i Respectively represent the position deviation between the i-th and j-th robots and the reference signal, ψ α (z) is defined as follows:

[0094]

[0095] where d α =||d|| σ represents the σ transformation of the expected distance d between the two robots when the swarming behavior is finally formed, s is the integral variable, φ α (||x j -x i || σ ) represents the virtual force (gravitational or repulsive force) between the two robots, φ α The specific expression of (z) is as follows:

[0096] φ α (z) = ρ h (z / r α )φ(zd α ) (28)

[0097] Among them, r α =||r|| σ represents the robot's communication range r, σ transformation, ρ h is the concave-convex function, and its expression is:

[0098]

[0099] h∈(0,1) is a preset parameter, ρ h (z) is smooth and continuous on [0,1], and its derivative is bounded on this interval.

[0100] The form of φ(z) is as follows:

[0101]

[0102] Among them, a, b, c are pre-set variables and satisfy σ1 represents a function of the setting.

[0103] In further defining the adjacency matrix A(p) of the system, a ij (p) represents the element in the i-th row and j-th column of the system adjacency matrix A(p), and the specific expression is as follows:

[0104] a ij (p) = ρ h (||pj -p i || σ / r α ) (31)

[0105] Finally, the following robust swarming controller is designed:

[0106]

[0107] in, is virtual potential energy The derivative with respect to time, vector represents ||x j -x i || σ The derivative with respect to time, ∈ is a parameter greater than 0, p j represents the position of the jth robot, v j represents the estimated value of the velocity deviation between the jth robot and the reference signal plus the non-matching interference c1, c2 are parameters greater than 0, express The first derivative with respect to time, represents radial basis function For vector p i The derivative of .

[0108] Then construct the following Lyapunov function:

[0109]

[0110] Among them, γ and β are parameters greater than 0. Represents the virtual potential energy between the i-th and j-th robots.

[0111] Derivative the above Lyapunov function to obtain And request Thus, the following neural network estimation parameters are designed: The adaptive update law of is:

[0112]

[0113] S4, realize the robust swarming control of multi-robot system under disturbance,

[0114] The controller designed in S3 is deployed to the following robot group, which can realize swarming behavior under the condition of matching interference and non-matching interference at the same time. The final effect is as follows Figure 3 shown.

Claims

1. A robust swarming control method for a multi-robot system based on a neural network, the specific steps are as follows: S1. Establish a multi-robot dynamic model with matching / non-matching disturbance effects, determine the generation form of reference signals, and then clarify the swarming control problem; S2. Use the parameterized neural network paradigm to express the matching / non-matching disturbances in the system, and then define the estimated weight function and basis function form to achieve the approximation of the relevant disturbances; S3, based on the parameterized neural network estimator constructed in step S2, a robust swarming controller is designed, and the Lyapunov stability theorem is used to generate an adaptive update law for the neural network estimation parameters, and then the stability of the closed-loop error system is analyzed; S4, realizing robust swarming control of multi-robot systems under disturbance conditions; In step S1: The dynamic model of the follower robot is as follows: The reference signal is defined as follows: in, ( is a real number space, n∈{1,2,3} represents the dimension of robot motion) represents the position and speed of the i-th robot, N represents the number of robots, For p i ,q i The first derivative of represents the control input, They represent the nonlinear dynamic disturbances of the two channels respectively. represents the location information of the reference signal, Indicates the speed information of the reference signal; In step S2: Interference i (p i ),g i (q i ) is expressed as follows: Among them, f i , g i They represent the non-matching interference and matching interference suffered by the i-th robot, respectively. The non-matching interference f i Only with position p i Related, matching interference g i Only with speed q i related, is the weight matrix, m represents the number of radial basis functions, T represents the transpose of the matrix, ∈ fi and is the approximate error caused by the neural network approximating the nonlinear dynamics term, is a radial basis function, the i,i={1,2,...,m}th element s i is defined as follows: in, is a pre-set vector with the same dimension as p i ,q i Similarly, in the specific operation, p i ,q i Substitute Calculate in and σ are unknown parameters, and ||·|| represents the 2-norm operation of the vector; is the neural network pair g i (q i ), f i (p i ) is expressed as follows: in, Represents the weight matrix estimates; use It represents the estimation error and is expressed as follows: in, They represent the error between the estimated value and the true value of the weight matrix respectively.

2. The method for robust swarming control of a multi-robot system based on a neural network according to claim 1, characterized in that: In step S3: Construct auxiliary variables: Among them, x i represents the position deviation between the ith robot and the reference signal, v i represents the velocity deviation between the ith robot and the reference signal plus the estimate of the non-matching disturbance Define the neighborhood N of the i-th robot i and σ transformation ||·|| σ , N i is defined as follows: N i ={j∈G:||p i -p j ||<r} (8) Where G represents the set of all robots, ||p i -p j || represents the geometric distance between the i-th and j-th robots, and r represents the communication range of each robot; σ transformation||·|| σ is defined as follows: Among them, ∈ is a parameter greater than 0, z is the independent variable of the transformation, and ||·|| represents the 2-norm operation of the vector; Define the virtual potential energy ψ between the two robots α (||x j -x i || σ ), x j 、x i Respectively represent the position deviation between the i-th and j-th robots and the reference signal, ψ α The specific definition of (z) is as follows: Among them, d α =||d|| σ represents the σ transformation of the expected distance d between the two robots when the swarming behavior is finally formed, s represents the integral variable, φ α (||x j -x i || σ ) represents the virtual force (gravitational or repulsive force) between the two robots, φ α The specific expression of (z) is as follows: φ α (z)=ρ h (z / r α )φ(z-d α ) (11) Among them, r α =||r|| σ represents the σ transformation of the communication range r between two robots, ρ h is the concave-convex function, and its expression is: h∈(0,1) is a pre-set parameter, ρ h (z) is smooth and continuous on [0,1], and its derivative is bounded on this interval; The form of φ(z) is as follows: Among them, a, b, c are pre-set variables and satisfy σ1 represents a set function; In further defining the adjacency matrix A(p) of the system, a ij (p) represents the element in the i-th row and j-th column of the system adjacency matrix A(p), and the specific expression is as follows: a ij (p)6ρ h (||p j -p i || σ / r α ) (14) Design the following robust flocking controller: in, is virtual potential energy ) with respect to time, the vector represents ||x j -x i || σ The derivative with respect to time, ∈ is a parameter greater than 0, p j represents the position of the jth robot, v j represents the estimated value of the velocity deviation between the jth robot and the reference signal plus the non-matching interference c1, c2 are parameters greater than 0, express The first derivative with respect to time, represents radial basis function For vector p i The derivative of Construct the following Lyapunov function: Among them, γ and β are parameters greater than 0. represents the virtual potential energy between the i-th and j-th robots; Derivative the above Lyapunov function to obtain And request The following adaptive update law for the estimated parameters of the neural network is designed:

3. The method for robust swarming control of a multi-robot system based on a neural network according to claim 1, characterized in that: In step S4: Deploying the controller designed in step S3 to a group of follower robots can achieve swarming behavior under both matching and non-matching interference.

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