A robot adaptive neural sliding mode control method, device and medium

Abstract

The embodiments of the present application disclose a robot adaptive neural sliding mode control method, device, and medium. Based on a preset performance function, the tracking error of the robot is determined, and the tracking error is converted based on a preset conversion function to obtain a conversion error; based on the conversion error and the finite-time non-singular terminal sliding mode surface corresponding to the conversion error, the adaptive law corresponding to the robot is determined; through a preset RBF neural network, the lumped nonlinearity corresponding to the finite-time non-singular terminal sliding mode surface is compensated; through a preset Lyapunov function, the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error are subjected to boundedness analysis, and the robot is tracked according to the analysis results. Through the above method, the tracking accuracy of the robotic arm is improved.

Description

Technical Field

[0001] The present application relates to the field of robotics technology, and in particular to a method, device, and medium for adaptive neural sliding mode control of a robot. Background Art

[0002] Currently, robots are widely used in space exploration, surgical robots, and industrial applications. In order to meet the control performance requirements, various advanced control technologies can be applied to robot controllers, such as robust control, sliding mode control, fuzzy control, neural network control, etc.

[0003] However, backlash is a common phenomenon in physical systems and devices such as servo mechanisms, Wiener systems, and aircraft. Backlash occurs when a manipulator drives its joints in reverse motion. This backlash and system uncertainties (such as disturbances, nonlinear friction, and coupling terms) affect the accuracy of the manipulator's tracking control. These uncertainties are difficult to predict in advance, resulting in poor tracking accuracy for the manipulator. Summary of the Invention

[0004] The embodiments of the present application provide a robot adaptive neural sliding mode control method, device and medium for solving the following technical problems: the gap lag and system uncertainty of the manipulator affect the accuracy of the manipulator tracking control, and these uncertainties are not easy to obtain in advance, resulting in poor tracking accuracy of the manipulator.

[0005] The embodiments of this application adopt the following technical solutions:

[0006] The present invention provides a method for adaptive neural sliding mode control of a robot. The method comprises: determining the tracking error of the robot based on a preset performance function, converting the tracking error based on a preset conversion function to obtain a conversion error; determining an adaptive law corresponding to the robot based on the conversion error and a finite-time nonsingular terminal sliding mode surface corresponding to the conversion error; compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface using a preset RBF neural network; and performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error using a preset Lyapunov function, so as to track the robot based on the analysis results.

[0007] In order to ensure the transient and steady-state performance of the closed-loop system, the embodiment of the present application combines a preset performance function to perform non-singular terminal sliding mode control with self-adjusting gain coefficients. Secondly, based on the sliding mode variable, a new adaptive law is proposed, which can effectively estimate the upper bound of the system uncertainty without the need for prior knowledge. In addition, in order to approximate the nonlinear functions and unknown dynamics of the system, a radial basis function neural network is introduced to compensate for the lumped nonlinearity. The Lyapunov function is used to determine that all signals are consistent and ultimately bounded. This can effectively weaken the influence of gap hysteresis and achieve high-precision tracking performance of the robot.

[0008] In one implementation of the present application, the tracking error of the robot is determined based on a preset performance function, and the tracking error is converted based on a preset conversion function to obtain a conversion error, specifically including: determining the expected tracking trajectory corresponding to the robot based on the joint position vector corresponding to the robot; determining the tracking error of the robot based on the preset performance function and the expected tracking trajectory, converting the tracking error into an unrestricted error form, and converting the unrestricted error form based on the preset conversion function to obtain a conversion error.

[0009] In one implementation of the present application, the tracking error of the robot is determined based on a preset performance function and a desired tracking trajectory, the tracking error is converted into an unconstrained error form, and the unconstrained error form is converted based on a preset conversion function to obtain a conversion error, specifically including: defining the tracking error as

[0010] q e =qq d

[0011] Based on preset performance functions

[0012] F μi =(μ 0i -μ ∞i )exp(-a(k)t)+μ ∞i

[0013] Determine the tracking error of the robot; based on the conversion function

[0014] q ei =F μi (t)S(σ i )

[0015]

[0016] Convert the unrestricted error form to obtain the converted error

[0017]

[0018] Where q∈R n×1is the robot joint position vector, q d represents the desired tracking trajectory, μ 0i >μ ∞i >0, the tracking error satisfies the inequality -ε i F μi (t) ei <ε i F μi (t),q ei (i=1,2,…,n) represents the i-th error element, 0<ε i ≤1 and the parameter a(k) will be set by the interval time t F Adjustment; S(σ i ) is the conversion function, σ i is the i-th conversion error, μ n =[μ n1 ,μ n2 ,…,μ nm ] T is the center vector.

[0019] In one implementation of the present application, the adaptive law corresponding to the robot is determined based on the conversion error and the finite-time non-singular terminal sliding surface corresponding to the conversion error, specifically including: determining the derivative corresponding to the conversion error; determining the finite-time non-singular terminal sliding surface based on the derivative of the conversion error; determining the derivative of the finite-time non-singular terminal sliding surface; determining the control law corresponding to the robot based on the derivative, and determining the adaptive law corresponding to the robot based on the control law.

[0020] In one implementation of the present application, the control law corresponding to the robot is determined based on the derivative, and the adaptive law corresponding to the robot is determined based on the control law, specifically including:

[0021]

[0022] Determine H

[0023]

[0024] The control law is

[0025] τ=τ1+τ2

[0026]

[0027]

[0028] The adaptive law corresponding to the robot is

[0029]

[0030] ​

[0031]

[0032] in, υ1,υ2,υ3 are positive constants, ξ is the set dead zone size; q∈R n×1 is the robot joint position vector, is the robot velocity vector; M(q)∈R n×n is the inertia matrix, is the centripetal Coriolis matrix, G(q)∈R n×1 is the gravitational vector; d(t) is the system uncertainty, is a constant; the tracking error q e =qq d , where q d represents the desired tracking trajectory; θ1, θ2, θ3 are all unknown positive quantities, ||·|| represents the Euclidean norm of the vector; q ei (i=1,2,…,n) represents the i-th error element; τ is the input of the gap lag.

[0033] In one implementation of the present application, after compensating the lumped nonlinearity corresponding to the finite-time non-singular terminal sliding mode surface by presetting the RBF neural network, the method further includes:

[0034] H=W *T X(N)+ω

[0035] Determine the lumped nonlinearity;

[0036] Function-based

[0037] τ=τ 1N +τ2

[0038]

[0039]

[0040]

[0041] The control law and adaptive law are determined; among them, ω is the approximation error of the RBF neural network; It's W * The estimated weight matrix of Y i and g i are two positive constants; q∈R n×1 is the robot joint position vector, is the robot velocity vector; M(q)∈Rn×n is the inertia matrix, is the centripetal Coriolis matrix, G(q)∈R n ×1 is the gravitational vector.

[0042] In one implementation of the present application, a boundedness analysis is performed on the sliding mode variable, conversion error, and the derivative corresponding to the conversion error by presetting a Lyapunov function, so as to track the robot according to the analysis results, specifically including: determining the derivative of the preset Lyapunov function; obtaining the Young's inequality corresponding to the derivative of the preset Lyapunov function based on the control law and adaptive law obtained after lumped nonlinear compensation; and performing a boundedness analysis on the sliding mode variable, conversion error, and the derivative corresponding to the conversion error based on the Young's inequality.

[0043] In one implementation of the present application, a boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error based on Young's inequality, specifically including:

[0044] In the case of ||σ||≥κ

[0045]

[0046] Determine the Lyapunov function

[0047]

[0048] Solve the derivative of the Lyapunov function and get

[0049]

[0050] exist In the case of Function-based

[0051]

[0052] get The bounded set of

[0053]

[0054] where σ i is the i-th conversion error; Δ s is a bounded set; is the derivative of the conversion error; b is a constant greater than 0; 0.5 <p1<1。

[0055] An embodiment of the present application provides a robot adaptive neural sliding mode control device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so as to enable the at least one processor to: determine the tracking error of the robot based on a preset performance function, and convert the tracking error based on a preset conversion function to obtain a conversion error; determine the adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error; compensate for the lumped nonlinearity corresponding to the finite-time non-singular terminal sliding mode surface through a preset RBF neural network; and perform boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error through a preset Lyapunov function, so as to track the robot according to the analysis results.

[0056] An embodiment of the present application provides a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to: determine a tracking error of a robot based on a preset performance function, and convert the tracking error based on a preset conversion function to obtain a conversion error; determine an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding surface corresponding to the conversion error; compensate for the lumped nonlinearity corresponding to the finite-time non-singular terminal sliding surface through a preset RBF neural network; and perform boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error through a preset Lyapunov function, so as to track the robot based on the analysis results.

[0057] At least one of the above technical solutions adopted in the embodiments of the present application can achieve the following beneficial effects: In order to ensure the transient and steady-state performance of the closed-loop system, the embodiments of the present application combine the preset performance function to perform non-singular terminal sliding mode control with self-adjusting gain coefficients. Secondly, based on the sliding mode variable, a new adaptive law is proposed, which can effectively estimate the upper bound of the system uncertainty without the need for prior knowledge. In addition, in order to approximate the nonlinear functions and unknown dynamics of the system, a radial basis function neural network is introduced to compensate for the lumped nonlinearity. The Lyapunov function is used to determine that all signals are consistent and ultimately bounded. This can effectively weaken the influence of gap hysteresis and achieve high-precision tracking performance of the robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments described in the present application. For those skilled in the art, other drawings can be obtained based on these drawings without inventive work. In the drawings:

[0059] Figure 1 A flowchart of a robot adaptive neural sliding mode control method provided in an embodiment of the present application;

[0060] Figure 2 A schematic diagram of a robot gap hysteresis curve provided in an embodiment of the present application;

[0061] Figure 3 A schematic structural diagram of a robot adaptive neural sliding mode control device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0062] The embodiments of the present application provide a robot adaptive neural sliding mode control method, device and medium.

[0063] In order to enable those skilled in the art to better understand the technical solutions in this application, the following will clearly and completely describe the technical solutions in the embodiments of this application in conjunction with the drawings in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of this application.

[0064] Currently, robots are widely used in space exploration, surgical robots, and industrial applications. In order to meet the control performance requirements, various advanced control technologies can be applied to robot controllers, such as robust control, sliding mode control, fuzzy control, neural network control, etc.

[0065] However, backlash is a common phenomenon in physical systems and devices such as servo mechanisms, Wiener systems, and aircraft. Backlash occurs when a manipulator drives its joints in reverse motion. This backlash and system uncertainties (such as disturbances, nonlinear friction, and coupling terms) affect the accuracy of the manipulator's tracking control. These uncertainties are difficult to predict in advance, resulting in poor tracking accuracy for the manipulator.

[0066] In order to solve the above problems, the embodiments of the present application provide a robot adaptive neural sliding mode control method, device and medium. In order to ensure the transient and steady-state performance of the closed-loop system, a non-singular terminal sliding mode control with self-adjusting gain coefficient is performed in combination with a preset performance function. Secondly, based on the sliding mode variable, a new adaptive law is proposed, which can effectively estimate the upper bound of the system uncertainty without the need for prior knowledge. Then, in order to approximate the nonlinear functions and unknown dynamics of the system, a radial basis function neural network is introduced to compensate for the lumped nonlinearity. The Lyapunov function is used to determine that all signals are consistent and ultimately bounded. This can effectively weaken the influence of gap hysteresis and achieve high-precision tracking performance of the robot.

[0067] The technical solutions proposed in the embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0068] Figure 1 This is a flow chart of a robot adaptive neural sliding mode control method provided in an embodiment of the present application. Figure 1 As shown in FIG, the robot adaptive neural sliding mode control method includes the following steps:

[0069] S101 . Determine a tracking error of the robot based on a preset performance function, and convert the tracking error based on a preset conversion function to obtain a conversion error.

[0070] In one embodiment of the present application, the continuous gap hysteresis function of the robot arm is

[0071]

[0072] where τ is the gap hysteresis of the input, l, f is a constant that satisfies The equation (Formula 1) can be transformed into

[0073]

[0074]

[0075] where ρ(τ) is bounded and |ρ(τ)|≤h, where h is a positive constant.

[0076] Figure 2 This is a schematic diagram of a robot gap hysteresis curve provided in an embodiment of the present application. Figure 2 For l = 1, When f = 0.35, τ = asin(3t), a = 3, 4, 5, 6, and the initial condition u(0) = 0, the gap hysteresis curve trend between the manipulators over time is obtained.

[0077] Consider a continuous system Where f(0) = 0. Assume that there exists a continuous positive definite function V(x) such that

[0078]

[0079] where ρ>0 and γ>0. This shows that x(t) is eventually uniformly bounded.

[0080] RBF neural network can be used to approximate any continuous function f(x). f(x):R m →R in the compact domain Ω N ∈R m The definition of above is

[0081]

[0082] where S(x)=[s1(x),s2(x),…,s l (x)] T is the basis function vector, ω represents the approximation error, satisfying in is a normal quantity W * is the ideal weight vector of the neural network, which minimizes the approximation error ω. Therefore

[0083]

[0084] The Gaussian kernel function l is defined as

[0085]

[0086] where η n is the width of the Gaussian function, μ n =[μ n1 ,μ n2 ,…,μ nm ] T is the center vector.

[0087] In one embodiment of the present application, a desired tracking trajectory corresponding to the robot is determined based on the joint position vectors corresponding to the robot. A tracking error of the robot is determined based on a preset performance function and the desired tracking trajectory. The tracking error is converted into an unconstrained error form, and the unconstrained error form is converted based on a preset conversion function to obtain the converted error.

[0088] Specifically, in the embodiment of the present application, taking into account the uncertainty of the manipulator and the influence of the gap hysteresis, the dynamic model of the n-DOF robot can be described as follows:

[0089]

[0090] where q∈R n×1 、 M(q)∈R n×n is the inertia matrix, is the centripetal Coriolis matrix, G(q)∈R n×1 is the gravitational vector,

[0091] u is the control input vector, and d(t) is the system uncertainty.

[0092] According to the definition of Formula 1, the dynamic model of the robot arm (Formula 7) can be rewritten as

[0093]

[0094] in

[0095] Assume that the uncertainty and disturbance of the model are bounded, which can be given by

[0096]

[0097] in is the upper bound, θ1, θ2, θ3 are all unknown positive constants ||·|| represents the Euclidean norm of the vector.

[0098] In order to improve the transient performance of the closed-loop system, it is particularly necessary to limit the tracking error within the specified boundaries. The tracking error is defined as q e =qq d , where q d The embodiment of the present application proposes an improved performance function

[0099] F μi =(μ 0i -μ ∞i )exp(-a(k)t)+μ ∞i (Formula 10)

[0100] where μ 0i >μ ∞i >0, the tracking error satisfies the inequality -ε i F μi (t) ei <ε i F μi (t),q ei (i=1,2,…,n) represents the i-th error element, 0<ε i ≤1 and the parameter a(k) will be set by the interval time t F Make adjustments and meet the following conditions

[0101] ​

[0102] Among them 1 <c2≤c1。

[0103] The tracking error is converted into an unconstrained error form

[0104] q ei =F μi (t)S(σ i ) (Formula 12)

[0105] σ i is the i-th conversion error. The conversion function S(σ i ) as shown below

[0106]

[0107] The error after conversion can be expressed as

[0108]

[0109] The derivative of the conversion error can be derived as

[0110]

[0111] where σ=[σ1,σ2,…,σ n ] T , diagonal matrix ψ=diag{ψ1,ψ2,…,ψ n}in Θ=diag{F μ1 (t),F μ2 (t),…,F μn (t)}.

[0112] The embodiment of the present application is different from the traditional preset performance control. Since a(k) can be adjusted in real time according to the judgment conditions, the improved performance function can provide a faster convergence boundary.

[0113] S102: Determine an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error.

[0114] In one embodiment of the present application, a derivative corresponding to a conversion error is determined, and a finite-time non-singular terminal sliding mode surface is determined based on the derivative of the conversion error. The derivative of the finite-time non-singular terminal sliding mode surface is determined, and a control law corresponding to the robot is determined based on the derivative, and an adaptive law corresponding to the robot is determined based on the control law.

[0115] Specifically, the dynamics of the manipulator tracking error can be expressed as

[0116]

[0117] In order to make the conversion error σ stable in finite time, a finite-time non-singular terminal sliding mode surface based on the conversion error is designed.

[0118]

[0119] where s=[s1,s2,…,s n ] T ,b>0, R(σ)=[R(σ1),R(σ2),…,R(σ n )] T ,

[0120]

[0121] in 0.5<{p_1}<1, 1 <p2<2, and

[0122] Taking the derivative of the sliding surface s, we can get

[0123]

[0124] in

[0125]

[0126] Formula 18 can be rewritten as

[0127]

[0128] in

[0129] Therefore, the control law can be designed as

[0130] τ=τ1+τ2

[0131]

[0132]

[0133] Design the adaptive law as

[0134]

[0135]

[0136]

[0137] in υ1,υ2,υ3 are positive constants, and ξ is the set dead zone size.

[0138] In practical applications, the sliding mode variable s cannot always remain zero. Therefore, it will lead to To solve this problem, the dead zone technology is introduced in the embodiment of the present application.

[0139] The embodiment of the present application proposes an adaptive law combined with a sliding mode variable, which effectively estimates the bound of system uncertainty, not only ensures the robustness of the closed-loop system, but also is more suitable for application in robot control.

[0140] Assuming the dynamic model of the manipulator (Formula 8), under the control law (Formula 20) and the adaptive law (Formula 21), the signals s and It is bounded.

[0141] Proof: Definition Define the Lyapunov function V1 as

[0142]

[0143] Considering (Formula 19) and the adaptive law (Formula 21), the derivative of the Lyapunov function can be deduced as follows

[0144]

[0145] Substituting the control law (Formula 20) into (Formula 23) yields the following result:

[0146]

[0147] Using Young's inequality, we can get

[0148]

[0149]

[0150]

[0151] The inequality (Formula 26) can be rewritten as

[0152]

[0153] Where V1(0) is the initial value of V1(t).

[0154] Based on the Lyapunov stability theorem, the closed-loop system is semi-globally uniformly eventually bounded. According to Lemma 2, s and It is bounded.

[0155] Compared with the existing sliding mode control that does not consider transient characteristics, the finite-time non-singular terminal sliding mode control based on conversion error proposed in the embodiment of the present application can achieve tracking error within a given boundary, and the sliding surface is continuous and has no singularity.

[0156] S103 , compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network.

[0157] In one embodiment of the present application, the lumped nonlinear H in Formula 19 is too complex and difficult to obtain accurately. In this embodiment of the present application, an RBF neural network is used to approximate H, as shown below:

[0158] H=W *T X(N)+ω (Formula 28)

[0159] in ω is the approximation error of the RBF neural network.

[0160] Then, the control law based on RBF neural network is designed as

[0161] τ=τ 1N +τ2

[0162]

[0163]

[0164] in It's W * The estimated weight matrix of .

[0165] The adaptive law of RBF neural network is designed as

[0166]

[0167] where Y i and g i are two positive constants.

[0168] S104 , performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error using the preset Lyapunov function, so as to track the robot according to the analysis result.

[0169] In one embodiment of the present application, a derivative of a preset Lyapunov function is determined, and based on the control law and adaptive law obtained after lumped nonlinear compensation, a Young's inequality corresponding to the derivative of the preset Lyapunov function is obtained. Based on the Young's inequality, a boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error.

[0170] definition Assume that the Lyapunov function is

[0171]

[0172] Taking the derivative of V2, we can get

[0173]

[0174] Substituting the adaptive law (Equation 30) and the control law (Equation 29) into the formula (Equation 32) and using Young's inequality, we can obtain

[0175]

[0176] in

[0177]

[0178] To ensure that ρ2>0, the gains r1,ψ,Θ will be chosen to satisfy the condition Will will be kept at the defined Δ s , In a bounded set

[0179]

[0180]

[0181]

[0182] If ||σ||≥κ,

[0183]

[0184] Consider the following Lyapunov function

[0185]

[0186] Taking the derivative of V3, we get

[0187]

[0188] if This means that the transformed error σ will converge to the bounded set in finite time. Combined with the case of ||σ||<κ, the transformed error σ will eventually converge to the bounded set

[0189]

[0190] According to formula 40, The bounded set of

[0191]

[0192] Based on the above analysis, we can conclude that s,σ, are all bounded. Since σ is bounded, by ε i The transformation function S(σ i ) will also be bounded. Finally, the system can simultaneously achieve a given performance and convergence of the tracking error in finite time.

[0193] In one embodiment of the present application, the robot adaptive neural sliding mode control method is verified through numerical simulation of a 2-DOF manipulator.

[0194] Based on Equation 8, the dynamics of the manipulator can be described as

[0195]

[0196]

[0197]

[0198] in,

[0199] p3=m2l1l c1 ,p4=m1l c2 +m2l1,p5=m2l c2 ,l c1 =0.5l1,l c2 =0.5l2. The system parameters of the robot are listed in Table 1:

[0200] Related parameters Parameter Description Numerical <![CDATA[m1]]> Mass of connecting rod 1 2.00kg <![CDATA[m2]]> Mass of connecting rod 2 0.85kg <![CDATA[l1]]> Length of connecting rod 1 0.35m <![CDATA[l2]]> Length of connecting rod 2 0.31m <![CDATA[J1]]> Instantaneous inertia of connecting rod 1 <![CDATA[61.25×10 -3 kg.m 2 ]]> <![CDATA[J2]]> Instantaneous inertia of connecting rod 2 <![CDATA[20.42×10 -3 kg.m 2 ]]> g Gravity <![CDATA[9.8m / s 2 ]]>

[0201] Table 1

[0202] The controller parameters are listed in Table 2:

[0203]

[0204] Table 2

[0205] Select the desired tracking signal as q d1 = sin(t)+cos(2t) and q d2 =sin(2t)+cos(t). The initial state of the robot is set to q1(0)=1.2, q2(0)=0.8, It has been verified that the positions and tracking curves of the two joints can converge to the desired trajectory in a short time. The method in the embodiment of the present application can make the tracking error converge to a steady state in advance, and the tracking error can also be strictly limited to a given convergence boundary.

[0206] In order to ensure the transient and steady-state performance of the closed-loop system, the embodiment of the present application combines a preset performance function to perform non-singular terminal sliding mode control with self-adjusting gain coefficients. Secondly, based on the sliding mode variable, a new adaptive law is proposed, which can effectively estimate the upper bound of the system uncertainty without the need for prior knowledge. Then, in order to approximate the nonlinear functions and unknown dynamics of the system, a radial basis function neural network is introduced to compensate for the lumped nonlinearity. The Lyapunov function is used to determine that all signals are consistent and ultimately bounded. This can effectively weaken the influence of gap hysteresis and achieve high-precision tracking performance of the robot.

[0207] Figure 3 This is a schematic diagram of the structure of a robot adaptive neural sliding mode control device provided in an embodiment of the present application. Figure 3 As shown, the robot adaptive neural sliding mode control device includes:

[0208] at least one processor; and,

[0209] a memory communicatively connected to the at least one processor; wherein,

[0210] The memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to:

[0211] Determining a tracking error of the robot based on a preset performance function, and converting the tracking error based on a preset conversion function to obtain a conversion error;

[0212] determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error;

[0213] Compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network;

[0214] By using the preset Lyapunov function, boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error, so as to track the robot according to the analysis result.

[0215] The present application also provides a non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured as follows:

[0216] Determining a tracking error of the robot based on a preset performance function, and converting the tracking error based on a preset conversion function to obtain a conversion error;

[0217] determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error;

[0218] Compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network;

[0219] By using the preset Lyapunov function, boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error, so as to track the robot according to the analysis result.

[0220] The various embodiments in this application are described in a progressive manner. Similar portions between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from the other embodiments. In particular, the device, apparatus, and non-volatile computer storage medium embodiments are generally similar to the method embodiments, so their descriptions are relatively simple. For relevant portions, refer to the descriptions of the method embodiments.

[0221] The foregoing description describes specific embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims can be performed in an order different from that described in the embodiments and still achieve the desired results. Furthermore, the processes depicted in the accompanying drawings do not necessarily require the specific order shown or the sequential order to achieve the desired results. In certain embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0222] The foregoing is merely an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the embodiments of the present application may have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included within the scope of the claims of the present application.

Claims

1. A robot adaptive neural sliding mode control method, characterized in that: The method comprises: Determining a tracking error of the robot based on a preset performance function, and converting the tracking error based on a preset conversion function to obtain a conversion error; determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error; Compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network; Performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function, so as to track the robot according to the analysis result; The determining of the tracking error of the robot based on the preset performance function and converting the tracking error based on the preset conversion function to obtain the conversion error specifically includes: Determining a desired tracking trajectory corresponding to the robot according to a joint position vector corresponding to the robot; Determining a tracking error of the robot based on a preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error; The determining of the tracking error of the robot based on the preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error specifically includes: The tracking error is defined as q e =q-q d Based on preset performance functions F μi =(μ 0i -m ∞i )exp(-a(k)t)+μ ∞i determining a tracking error of the robot; Based on the conversion function what ei =F μi (t)S(σ i ) The unrestricted error form is converted to obtain the converted error Where q∈R n×1 is the robot joint position vector, q d represents the desired tracking trajectory, μ 0i >μ ∞i >0,μ 0i is the initial center vector; μ ∞i is the limit center vector; the tracking error satisfies the inequality -ε i F μi (t) ei <ε i F μi (t),q ei (i=1,2,…,n) represents the i-th error element, 0<ε i ≤1 and the parameter a(k) will be set by the interval time t F Adjustment; S(σ i ) is the conversion function, σ i is the i-th conversion error, μ i is the center vector;​ The step of determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error specifically includes: determining a derivative corresponding to the conversion error; Based on the derivative of the conversion error, the finite-time non-singular terminal sliding surface is determined; determining a derivative of the finite-time non-singular terminal sliding mode surface; determining a control law corresponding to the robot based on the derivative, and determining an adaptive law corresponding to the robot based on the control law; The method of performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function to track the robot according to the analysis results specifically includes: Determining a derivative of the preset Lyapunov function; Based on the control law and adaptive law obtained after lumped nonlinear compensation, the Young's inequality corresponding to the derivative of the preset Lyapunov function is obtained; Based on the Young's inequality, a boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error.

2. A robot adaptive neural sliding mode control method according to claim 1, characterized in that: Determining the control law corresponding to the robot based on the derivative, and determining the adaptive law corresponding to the robot based on the control law, specifically includes: Based on the derivative Determine H The control law is τ=τ1+τ2 The adaptive law corresponding to the robot is in, υ1,υ2,υ3 are positive constants, ξ is the set dead zone size; q∈R n×1 is the robot joint position vector, is the robot velocity vector; M(q)∈R n×n is the inertia matrix, is the centripetal Coriolis matrix, G(q)∈R n×1 is the gravitational vector; d(t) is the system uncertainty, is a constant; the tracking error q e =qq d , where q d represents the desired tracking trajectory; θ1, θ2, θ3 are all unknown positive quantities, ||·|| represents the Euclidean norm of the vector; q ei (i=1,2,…,n) represents the i-th error element; τ is the input of the gap lag; ψ′ is the nonlinear transformation function; Θ. is the estimated value of the unknown parameter; b is a constant greater than 0; R(σ) is the sliding surface convergence function; σ is the sliding surface variable; r1 is the first transformation error vector.

3. The robot adaptive neural sliding mode control method according to claim 1, characterized in that: After compensating the lumped nonlinearity corresponding to the finite-time non-singular terminal sliding mode surface by presetting the RBF neural network, the method further includes: By presetting the RBF neural network H=W *T X(N)+ω determining the lumped nonlinearity; Function-based τ=τ 1N +τ2 The control law and the adaptive law are determined; wherein, ω is the approximation error of the RBF neural network; It's W * The estimated weight matrix of i and g i are two positive constants; q∈R n×1 is the robot joint position vector, is the robot velocity vector; M(q)∈R n×n is the inertia matrix, is the centripetal Coriolis matrix, G(q)∈R n ×1 is the gravitational vector.

4. The robot adaptive neural sliding mode control method according to claim 1, characterized in that: The boundedness analysis of the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error based on the Young's inequality specifically includes: In the case of ||σ||≥κ Determine the Lyapunov function Solve the derivative of the Lyapunov function and get exist In the case of Function-based get The bounded set of where σ i is the i-th conversion error; Δ s is a bounded set; is the derivative of the conversion error; b is a constant greater than 0; 0.5 < p1 < 1; κ is a set critical value.

5. A robot adaptive neural sliding mode control device comprising: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to: Determining a tracking error of the robot based on a preset performance function, and converting the tracking error based on a preset conversion function to obtain a conversion error; determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error; Compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network; Performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function, so as to track the robot according to the analysis result; The determining of the tracking error of the robot based on the preset performance function and converting the tracking error based on the preset conversion function to obtain the conversion error specifically includes: Determining a desired tracking trajectory corresponding to the robot according to a joint position vector corresponding to the robot; Determining a tracking error of the robot based on a preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error; The determining of the tracking error of the robot based on the preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error specifically includes: The tracking error is defined as q e =q-q d Based on preset performance functions F μi =(μ 0i -m ∞i )exp(-a(k)t)+μ ∞i determining a tracking error of the robot; Based on the conversion function what ei =F μi (t)S(σ i ) The unrestricted error form is converted to obtain the converted error Where q∈R n×1 is the robot joint position vector, q d represents the desired tracking trajectory, μ 0i >μ ∞i >0,μ 0i is the initial center vector; μ ∞i is the limit center vector; the tracking error satisfies the inequality -ε i F μi (t) ei <ε i F μi (t),q ei (i=1,2,…,n) represents the i-th error element, 0<ε i ≤1 and the parameter a(k) will be set by the interval time t F Adjustment; S(σ i ) is the conversion function, σ i is the i-th conversion error, μ i is the center vector;​ The step of determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error specifically includes: determining a derivative corresponding to the conversion error; Based on the derivative of the conversion error, the finite-time non-singular terminal sliding surface is determined; determining a derivative of the finite-time non-singular terminal sliding mode surface; determining a control law corresponding to the robot based on the derivative, and determining an adaptive law corresponding to the robot based on the control law; The method of performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function to track the robot according to the analysis results specifically includes: Determining a derivative of the preset Lyapunov function; Based on the control law and adaptive law obtained after lumped nonlinear compensation, the Young's inequality corresponding to the derivative of the preset Lyapunov function is obtained; Based on the Young's inequality, a boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error.

6. A non-volatile computer storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to: Determining a tracking error of the robot based on a preset performance function, and converting the tracking error based on a preset conversion function to obtain a conversion error; determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error; Compensating for the lumped nonlinearity corresponding to the finite-time nonsingular terminal sliding mode surface by presetting an RBF neural network; Performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function, so as to track the robot according to the analysis result; The determining of the tracking error of the robot based on the preset performance function and converting the tracking error based on the preset conversion function to obtain the conversion error specifically includes: Determining a desired tracking trajectory corresponding to the robot according to a joint position vector corresponding to the robot; Determining a tracking error of the robot based on a preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error; The determining of the tracking error of the robot based on the preset performance function and the desired tracking trajectory, converting the tracking error into an unconstrained error form, and converting the unconstrained error form based on the preset conversion function to obtain the conversion error specifically includes: The tracking error is defined as q e =q-q d Based on preset performance functions F μi =(μ 0i -m ∞i )exp(-a(k)t)+μ ∞i determining a tracking error of the robot; Based on the conversion function what ei =F μi (t)S(σ i ) The unrestricted error form is converted to obtain the converted error Where q∈R n×1 is the robot joint position vector, q d represents the desired tracking trajectory, μ 0i >μ ∞i >0,μ 0i is the initial center vector; μ ∞i is the limit center vector; the tracking error satisfies the inequality -ε i F μi (t) ei <ε i F μi (t),q ei (i=1,2,…,n) represents the i-th error element, 0<ε i ≤1 and the parameter a(k) will be set by the interval time t F Adjustment; S(σ i ) is the conversion function, σ i is the i-th conversion error, μ i is the center vector;​ The step of determining an adaptive law corresponding to the robot based on the conversion error and a finite-time non-singular terminal sliding mode surface corresponding to the conversion error specifically includes: determining a derivative corresponding to the conversion error; Based on the derivative of the conversion error, the finite-time non-singular terminal sliding surface is determined; determining a derivative of the finite-time non-singular terminal sliding mode surface; determining a control law corresponding to the robot based on the derivative, and determining an adaptive law corresponding to the robot based on the control law; The method of performing boundedness analysis on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error by using the preset Lyapunov function to track the robot according to the analysis results specifically includes: Determining a derivative of the preset Lyapunov function; Based on the control law and adaptive law obtained after lumped nonlinear compensation, the Young's inequality corresponding to the derivative of the preset Lyapunov function is obtained; Based on the Young's inequality, a boundedness analysis is performed on the sliding mode variable, the conversion error, and the derivative corresponding to the conversion error.

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