Segmented sliding mode surface-based terminal sliding mode controller design method and system

Abstract

The invention discloses a terminal sliding mode controller design method and system based on a sectional sliding mode surface, and belongs to the technical field of mechanical arm control. The method comprises the steps that a multi-joint mechanical arm dynamic model is established; establishing a joint angle tracking error and an angular velocity tracking error of the mechanical arm; designing a sectional sliding mode surface, and analyzing the convergence of a joint angle tracking error in a sliding stage; constructing a sectional type power reaching law; and designing a terminal sliding mode controller based on the mechanical arm dynamic model, the sectional sliding mode surface, the joint angle tracking error and the sectional power reaching law. The terminal sliding mode controller designed by the invention has the characteristics of no singularity, rapid convergence, strong robustness, higher precision and the like, the singularity problem occurring in the control process of the mechanical arm is completely eliminated, the system convergence time can adjust parameter setting according to the actual situation, the response speed is favorably improved, the operation efficiency of the mechanical arm is ensured, and the control precision is improved. And meanwhile, higher control precision can be realized.

Description

Technical Field

[0001] The present invention relates to the technical field of robot arm control, and more particularly to a design method and system of a terminal sliding mode controller based on a segmented sliding mode surface. Background Art

[0002] At present, with the continuous development of robotics, industrial automation and intelligent manufacturing, robotic arms, as an important part of industrial robots, have received extensive attention and in-depth research in the fields of assembly, palletizing, painting, polishing, etc. High-precision and high-dynamic performance trajectory tracking control technology has become the focus of research.

[0003] Sliding mode control (SMC) is one of the most effective methods for dealing with nonlinear systems with uncertainties, perturbations, and bounded external disturbances. In traditional SMC, the most commonly used sliding surface is linear, which can only guarantee the asymptotic stability of the system in the sliding stage, that is, the system state converges to the equilibrium state in infinite time. In order to achieve finite-time convergence of the system state in the sliding stage, terminal SMC (TSMC) based on nonlinear sliding surface was proposed. However, traditional TSMC has two main disadvantages: (1) TSMC has a singularity problem, which may lead to the unboundedness of the control input; (2) When the system state is far from the equilibrium state, the convergence speed of TSMC is slower than that of traditional SMC.

[0004] The singularity problem is one of the important problems and shortcomings in TSMC. Domestic researchers have made various improvements in the design of sliding surfaces to avoid singularity problems. The research team of Beijing Institute of Technology proposed a non-singular terminal sliding surface, which solves the singularity problem by introducing small positive numbers to avoid the denominator being zero. Researchers from Tsinghua University and other institutions have studied high-order sliding mode control, which avoids the singularity problem by introducing high-order derivatives and dynamically adjusting the sliding surface. Many well-known foreign universities and research institutions have also conducted extensive research on this. Researchers at the Massachusetts Institute of Technology in the United States have proposed a variety of non-singular TSMC (Non-singular Terminal Sliding Mode Control, NTSMC) methods, using improved sliding surface design to avoid singularity problems in traditional sliding mode control. The research team of the University of Tokyo in Japan combined adaptive control with TSMC, solved the singularity problem by adjusting the control parameters online, and improved the robustness of the system.

[0005] TSMC has become one of the important directions of robot arm control because it can effectively handle system uncertainty and improve response speed. Domestic and foreign scholars have done a lot of work on TSMC theory, especially in improving traditional SMC to improve system performance. Many studies focus on designing new terminal sliding surfaces and control laws to achieve faster convergence speed and better robustness.

[0006] Therefore, in order to solve the trajectory tracking control problem of the above-mentioned robot arm, a fixed-time non-singular terminal sliding mode controller based on a piecewise sliding surface is considered to be designed to achieve the characteristics of non-singularity, fast convergence, strong robustness and higher precision, so as to better track and control the trajectory of the robot arm. Summary of the invention

[0007] In view of this, in order to solve the problems existing in the prior art, the present invention provides a terminal sliding mode controller design method and system based on a segmented sliding surface, which is conducive to completely eliminating the singularity problem occurring in the robot arm control process. The system convergence time can adjust the parameter settings according to the actual situation, so that the convergence time is independent of the initial state of the system, thereby realizing terminal trajectory tracking, improving the response speed, ensuring the operation efficiency of the robot arm, and achieving higher control accuracy.

[0008] To achieve the above object, the technical solution adopted by the present invention is:

[0009] In a first aspect, the present invention provides a method for designing a terminal sliding mode controller based on a segmented sliding surface, wherein the designed terminal sliding mode controller is used to control a robotic arm; the method comprises the following steps:

[0010] S1. Establish a dynamic model of a multi-joint robotic arm;

[0011] S2. Based on the mechanical arm dynamics model, establish the joint angle tracking error and joint angular velocity tracking error of the mechanical arm;

[0012] S3, design the segmented sliding surface and analyze the convergence of the joint angle tracking error during the sliding stage;

[0013] S4. constructing a piecewise power reaching law according to the piecewise sliding surface;

[0014] S5. Based on the robot arm dynamics model, piecewise sliding surface, joint angle tracking error and piecewise power reaching law, a fixed-time non-singular terminal sliding mode controller is designed.

[0015] In an optional embodiment, in step S1, a multi-joint mechanical arm dynamics model with external interference is constructed according to the dynamics principle, and the model expression is:

[0016]

[0017] Where q=[q 1 ,q 2 , ..., q n ] T is the joint angle of the robot arm, is the joint angular velocity of the robot arm, is the joint angular acceleration of the robot, n represents the nth joint of the robot; M(q)∈R n×n is a symmetric and positive definite inertia term, is the Coriolis force and centrifugal force term, G(q)∈R n×1 is the gravity term, τ d ∈R n×1 represents the bounded external disturbance torque generated by the accidental collision with the environment, τ∈R n×1 is the joint input torque.

[0018] In an optional embodiment, in step S2, the expressions of the joint angle tracking error and the joint angular velocity tracking error of the robot arm are:

[0019] e=qq d

[0020]

[0021] Among them, e, They represent joint angle tracking error and angular velocity tracking error, q, Respectively represent the actual joint angle and angular velocity, q d , Represent the desired joint angle and angular velocity respectively.

[0022] In an optional embodiment, in step S3, before designing the segmented sliding surface, a nonlinear function s is introduced. (u，v) (x) and the nonlinear function sig v (x), the function formula is:

[0023]

[0024] sig v (x)=|x| v sgn(x)

[0025] Among them, 0<u<1, v>1 and 0<ξ 2 <ξ 1 <1 are four positive constant parameters to be designed; sgn(x) represents the sign function;

[0026] Define vector S (u，v) (e), Sig v (e)∈R n :

[0027] S (u，v) (e) = [s (u，v) (e 1 ), …, s (u，v) (en )] T

[0028] Sig v (e) = [sig v (e 1 ),…,sig v (e n )] T

[0029] Among them, e i Represents the i-th component of vector e, i = 1, 2,…, n.

[0030] In an optional embodiment, according to the nonlinear function s (u，v) (·) and sig v The properties of (·) are used to design the segmented sliding surface. The designed segmented sliding surface is:

[0031]

[0032] Where s represents the segmented sliding surface, K 1 , K 2 ∈R n×n is a constant positive definite diagonal gain matrix.

[0033] In an optional implementation, in step S4, a piecewise power reaching law is constructed according to the piecewise sliding surface, specifically:

[0034] Segmented sliding surface The first-order derivative about e is:

[0035]

[0036] Depend on have to:

[0037]

[0038] In the formula, represents the angular acceleration error of the joint, represents the desired joint angular acceleration;

[0039] On the basis of the power reaching law, a piecewise power reaching law is constructed, and its specific form is:

[0040]

[0041]

[0042] Where, 0<u<1, v>1, ε 1 , ε 2is a positive constant parameter to be designed and satisfies 0<ε 2 <ε 1 <1; sign(·) represents the sign function, Ξ(·) represents the piecewise power function, ρ 1 >0 is the gain of the linear term, which is used to suppress the disturbance of linear growth; ρ 2 >0 is the gain of the piecewise power term.

[0043] In an optional implementation, in step S5, the designed terminal sliding mode controller is:

[0044]

[0045] Among them, u 0 represents the terminal sliding mode controller.

[0046] In a second aspect, the present invention further provides a terminal sliding mode controller design system based on a segmented sliding surface, which is applied to the above-mentioned terminal sliding mode controller design method based on a segmented sliding surface, designs a terminal sliding mode controller based on a segmented sliding surface, and controls a robotic arm. The system includes:

[0047] A robot arm dynamics model building module is used to build a robot arm dynamics model;

[0048] A tracking error establishment module, used to establish a joint angle tracking error and an angular velocity tracking error of the robotic arm based on the robotic arm dynamics model;

[0049] Segmented sliding surface design module, used to design segmented sliding surface and analyze the convergence of joint angle tracking error during the sliding phase;

[0050] A reaching law construction module, used for constructing a piecewise power reaching law according to the piecewise sliding surface;

[0051] The controller design module is used to design a fixed-time non-singular terminal sliding mode controller based on the mechanical arm dynamics model, the piecewise sliding mode surface, the joint angle tracking error and the piecewise power reaching law.

[0052] In a third aspect, an embodiment of the present invention further provides an electronic device, comprising a processor and a memory, wherein the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement the above-mentioned method for designing a terminal sliding mode controller based on a segmented sliding surface.

[0053] In a fourth aspect, the present invention also provides a storage medium having stored thereon one or more programs readable by a computing device, wherein the one or more programs include instructions which, when executed by the computing device, enable the computing device to execute a terminal sliding mode controller design method based on a segmented sliding surface as described above.

[0054] Compared with the prior art, the present invention has at least the following beneficial technical effects:

[0055] 1. The terminal sliding mode controller designed by the present invention has the characteristics of no singularity, fast convergence, strong robustness and higher precision; the singularity problem occurring in the robot control process can be completely eliminated, and the system convergence time can adjust the parameter setting according to the actual situation, so that the convergence time is independent of the initial state of the system, thereby realizing terminal trajectory tracking, improving the response speed, ensuring the operation efficiency of the robot, and achieving higher control accuracy.

[0056] 2. The present invention eliminates the singularity problem by introducing a nonlinear function to design a piecewise sliding surface; accelerates the convergence speed of the sliding mode controller by introducing piecewise power terms into the reaching law and optimizing the sliding surface; and accelerates the convergence speed of the nonlinear terminal sliding mode controller, improves the tracking accuracy, and reduces the error by optimizing and improving the sliding surface.

[0057] Other features and advantages of the present invention will be described in the following description, and partly become apparent from the description, or understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained by the structures particularly pointed out in the written description and the accompanying drawings.

[0058] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, a brief introduction will be given below to 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 application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0060] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0061] Figure 1 A schematic flow chart of a method for designing a terminal sliding mode controller based on a segmented sliding surface is provided in an embodiment of the present invention.

[0062] Figure 2 The nonlinear function sig provided in the embodiment of the present invention v (x) and s (u，v) Schematic diagram of (x).

[0063] Figure 3 A schematic diagram of a two-degree-of-freedom robotic arm joint angle tracking curve provided in an embodiment of the present invention.

[0064] Figure 4 A schematic diagram of a two-degree-of-freedom robotic arm joint angular velocity tracking curve provided by an embodiment of the present invention.

[0065] Figure 5 A schematic diagram of the change in joint angle tracking error of a two-degree-of-freedom robotic arm provided in an embodiment of the present invention.

[0066] Figure 6 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions 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 only part of the embodiments of the present invention, not all of the embodiments.

[0068] In the description of the present invention, it should be noted that: in some processes described in the specification and drawings of this application, multiple operations appearing in a specific order are included, but it should be clearly understood that these operations may not be performed in the order in which they appear in this document or may be performed in parallel. In addition, various serial numbers are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0069] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. 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.

[0070] Embodiment 1:

[0071] See also Figure 1As shown, for the trajectory tracking control problem of a robotic arm, an embodiment of the present invention provides a terminal sliding mode controller design method based on a segmented sliding surface. The terminal sliding mode controller designed by the method is used to control the robotic arm, so that the tracking errors of the joint angles of the robotic arm system can be quickly converged, and the relevant parameters can be adjusted to control the convergence time; the singularity problem that occurs in the robotic arm control process is completely eliminated, and the convergence time is made independent of the initial state of the system, thereby realizing terminal trajectory tracking, improving the response speed, ensuring the operation efficiency of the robotic arm, and achieving higher control accuracy; the specific steps of the method are as follows:

[0072] Step 1: Establish a multi-joint robotic arm dynamics model:

[0073] In this embodiment, a dynamic model with external interference is established according to the dynamic principle:

[0074]

[0075] Where q=[q 1 ,q 2 , ..., q n ] T is the joint angle of the robot arm, is the joint angular velocity of the robot arm, is the joint angular acceleration of the robot, and n represents the nth joint of the robot. n×n is a symmetric and positive definite inertia term, is the Coriolis force and centrifugal force term, G(q)∈R n×1 is the gravity term, τ d ∈R n×1 represents the bounded external disturbance torque generated by the accidental collision with the environment, τ∈R n×1 is the joint input torque.

[0076] Step 2: Establish the joint angle and angular velocity tracking error of the robot arm:

[0077] In this embodiment, the tracking angle error of each joint of the robot arm is defined as e, and the angular velocity tracking error is defined as The specific expression is:

[0078] e=qq d

[0079]

[0080] Among them, q represents the actual joint angle, q d , Represent the desired joint angle and angular velocity respectively.

[0081] Step 3: Design a segmented sliding surface and analyze the convergence of the system during the sliding phase:

[0082] In this embodiment, before designing the segmented sliding surface, the nonlinear function s is first introduced. (u，v) (x) are as follows:

[0083]

[0084] s (u，v) The first-order derivative of (x) with respect to x is:

[0085]

[0086] Another nonlinear function sig v (x) are as follows:

[0087] sig v (x)=|x| v sgn(x)

[0088] Among them, 0<u<1, v>1 and 0<ξ 2 <ξ 1 <1 are four positive constant parameters to be designed.

[0089] In this embodiment, Figure 2 Shows the nonlinear function s (u，v) (x) and sig v (x), where ξ 1 =0.6,ξ 2 =0.01, u=0.2, v=2. Figure 2 It can be clearly seen that the function sig v (x) has the characteristics of increasing with large parameters and decreasing with small parameters, while for function s (u，v) (x), the first short segment has the opposite characteristics, that is, small parameters amplify and large parameters shrink, and then with the function sig v (x) have the same characteristics.

[0090] Furthermore, we define the vector S (u，v) (e), Sig v (e)∈R n as follows:

[0091] S (u，v) (e) = [s (u，v) (e 1 ), …, s (u，v) (e n )] T

[0092] Sig v (e) = [sig v(e 1 ),…,sig v (e n )] T

[0093] F (u，v) (e) = diag(f (u，v) (e 1 ), …, f (u，v) (e n ))

[0094] Where diag(·) represents a diagonal matrix, e i Represents the i-th component of vector e, i = 1, 2,…, n.

[0095] In summary, this embodiment uses the nonlinear function s (u，v) (·) and sig v (·) properties, a segmented sliding surface is designed as:

[0096]

[0097] Among them, K 1 , K 2 ∈R n×n is a constant positive definite diagonal gain matrix.

[0098] Furthermore, the convergence of the joint angle tracking error is analyzed by the following three cases:

[0099] First, we introduce two theorems as follows:

[0100] Theorem 1: Assume there exists a positive definite continuous function V(x): U→R, with real numbers α, β>0, 0<u<1, v>1, and an open neighborhood of the origin Make x∈U 0 {0}. Then the origin of the system is fixed-time stable. In addition, if U = R n , V(x) is positive definite, and In R n {0} takes a negative value, then the origin is globally fixed-time stable. The uniform upper bound of the convergence time is:

[0101]

[0102] Theorem 2: For any ξ 1 ,ξ 2 , ..., ξ n ≥0, r is a positive constant, the following inequality holds:

[0103]

[0104]

[0105] The proof is as follows:

[0106] If at time T s The sliding surface s = 0 is reached, and the closed-loop system dynamics is:

[0107]

[0108] (1)||e||>ξ 1 :

[0109] The dynamics are redesigned to:

[0110]

[0111] Choose a positive definite Lyapunov function V 1 for:

[0112]

[0113] V 1 Find the first derivative of e for:

[0114]

[0115]

[0116]

[0117] Among them, k 1i ,,k 2i Denote the diagonal matrix K 1 , K 2 The ith element of .

[0118] According to Theorem 2, The upper bound of can be designed as:

[0119]

[0120] Right now:

[0121]

[0122] Among them, λ min (K 1 ), λ min (K 2 ) represent the diagonal matrix K 1 , K 2 The minimum eigenvalue of .

[0123] From Theorem 1, we can see that the position tracking error converges directly to an arbitrarily small ξ centered at 01 , and the convergence time is clearly given by Theorem 1.

[0124] (2)ξ 2 ≤||e||≤ξ 1 :

[0125] The dynamics are redesigned to:

[0126]

[0127] The selected positive definite Lyapunov functions are:

[0128]

[0129] According to Theorem 2, The upper bound of can be designed as:

[0130]

[0131] Right now:

[0132]

[0133] From Theorem 1, we can conclude that the position tracking error converges directly to an arbitrarily small ξ centered at 0. 2 .

[0134] (3)||e||<ξ 2 :

[0135] The dynamics can be redesigned as:

[0136]

[0137] Depend on The Lyapunov function V is defined as 1 have:

[0138]

[0139] From the Lyapunov stability theory, it can be seen that the position tracking error converges to zero exponentially.

[0140] Step 4: Construct a piecewise power reaching law:

[0141] Segmented sliding surface The first-order derivative about e is:

[0142]

[0143] Depend on We can get:

[0144]

[0145] Based on the traditional reaching law and the existing power reaching law, the designed piecewise power reaching law is as follows:

[0146]

[0147]

[0148] Where, 0<u<1, v>1, ε 1 , ε 2 is a positive constant parameter with design and satisfies 0<ε 2 <ε 1 <1, sign(·) represents the sign function, Ξ(·) represents the piecewise power function. 1 >0, which is the gain of the linear term, used to suppress the disturbance of linear growth; ρ 2 >0 is the gain of the piecewise power term, for ρ 2 Ξ(·), yes Satisfy the conditions for sliding mode motion.

[0149] Right now:

[0150] Step 5: According to the designed piecewise sliding surface, the robot dynamics model and joint angle tracking error and the piecewise power reaching law, a fixed-time non-singular terminal sliding mode controller based on the piecewise sliding surface is designed; the designed terminal sliding mode controller is as follows:

[0151]

[0152] Among them, u o represents the terminal sliding mode controller.

[0153] Furthermore, the established terminal sliding mode controller based on the segmented sliding surface is input into the multi-joint robotic arm trajectory system to control the robotic arm, so as to achieve rapid convergence of the joint angle tracking error e of the robotic arm system, and at the same time, the relevant parameters can be adjusted to control the convergence time.

[0154] In this embodiment, the upper bound of the convergence time of the tracking error e of each joint angle of the robotic arm system is expressed as:

[0155]

[0156] Among them, T max is the upper bound of the convergence time of the joint angle tracking error e of the robotic arm system, α and β are the parameters that need to be designed and calculated for the robotic arm system and are both greater than zero, α min and β min are the minimum values ​​of parameters α and β respectively; the upper bound of the convergence time of the tracking error e of each joint angle of the manipulator system is Tmax The angles of each joint of the robotic arm system x 1 It is irrelevant. By adjusting the positive parameters α, β to be designed and calculated and the exponential parameters u, v of the sliding mode components of the segmented sliding surface, the convergence time upper bound T of the tracking error e of each joint angle of the robotic arm system can be controlled. max .

[0157] The method of the present invention is introduced below by taking a two-joint mechanical arm as an example, and the specific implementation method is as follows:

[0158] Step 1: Establish a multi-joint robotic arm dynamics model:

[0159] The dynamic model of the two-degree-of-freedom robotic arm is constructed as follows:

[0160]

[0161] Where, q = [q1, q2]T, and are the joint angles, joint angular velocities and joint angular accelerations of the two-joint robot arm. 2×2 is a symmetric and positive definite inertia matrix, is the Coriolis force matrix, G(q)∈R 2×1 is the gravity vector, τ d ∈R 2×1 represents the bounded external disturbance torque, τ∈R 2 × 1 is the joint input torque.

[0162] The specific representation of the M, C, and G matrices in the kinetic model is as follows:

[0163]

[0164]

[0165]

[0166] and:

[0167] p 1 =(m 1 +m 2 ) 1 2 +m 2 l 2 2 +J 1

[0168] p 2 =m 2 l 1 l 2

[0169] p 3 =ml 2 2

[0170] p 4 =p 3 +J 2

[0171] p 5 =(m 1 +m 2 ) 1 g 1

[0172] p 6 =m 2 l 2 g 1

[0173] Among them, m 1 =0.5, m 2 =1.5,l 1 =1.0,l 2 =0.8, J 1 =J 2 =5.0, g 1 =9.81.

[0174] Step 2: Establish the joint angle and angular velocity tracking error of the robot arm;

[0175] Define the two-degree-of-freedom robot arm joint angle tracking error as e, and the angular velocity tracking error as The specific expression is:

[0176] e=qq d

[0177]

[0178] Where, e=[e 1 , e 2 ] T , q=[q 1 ,q 2 ] T ,q d =[q d1 ,q d2 ] T .

[0179] Given the expected trajectory:

[0180] q d1 =1.25-(7 / 5)exp(-t)+(7 / 20)exp(-4t)

[0181] q d2=1.25+exp(-t)-(1 / 4)exp(-4t)

[0182] Without considering the system modeling error, the external disturbance torques on joints 1 and 2 are respectively:

[0183] τ d =[0.5sin(200πt);0.5sin(200πt)]

[0184] Step 3: Design a segmented sliding surface and analyze the convergence of the joint angle tracking error;

[0185] According to the nonlinear function s (u，v) (·) and sig v (·) properties, a segmented sliding surface is designed as:

[0186]

[0187] Given u = 0.2, v = 2, ξ 1 =0.6,ξ 2 =0.01.

[0188] Step 4: Select the piecewise power reaching law;

[0189] Segmented sliding surface The first-order derivative about e is:

[0190]

[0191] Depend on We can get:

[0192]

[0193] Based on the traditional reaching law and the existing power reaching law, a piecewise power reaching law is designed. The specific form is as follows:

[0194]

[0195] Where, 0<u<1, v>1, ε 1 , ε 2 is a positive constant parameter with design and satisfies 0<ε 2 <ε 1 <1, sign(·) represents the sign function, Ξ(·) represents the piecewise power function. 1 >0, which is the gain of the linear term, used to suppress the disturbance of linear growth; ρ 2 >0 is the gain of the piecewise power term, for ρ 2 Ξ(·), yes Satisfy the conditions for sliding mode motion.

[0196] Step 5: Design a fixed-time non-singular terminal sliding mode controller based on the piecewise sliding surface:

[0197] According to the above formula, the designed terminal sliding mode controller is as follows:

[0198]

[0199] Among them, K 1 , K 2 ∈R n×n is a constant positive definite diagonal gain matrix.

[0200] Further, see Figure 3 and Figure 4 As shown, the joint angle and joint angular velocity tracking curves of the two-degree-of-freedom robot arm are shown. It can be seen that under the action of the controller designed in the present invention, the two joints of the robot arm can track the desired trajectory more quickly and accurately. Figure 5 As shown, the change of the joint angle tracking error of the two-degree-of-freedom robotic arm is shown. It can be seen that under the action of the controller designed in the present invention, the tracking error of each joint angle of the robotic arm is small and the convergence speed is fast.

[0201] In another embodiment, fast non-singular integral terminal sliding mode control (FNITSMC) can also be used, and a fast terminal sliding surface is adopted or an integral term is introduced on the sliding surface. A faster convergence speed can be obtained in the entire sliding stage, and the singularity is avoided by transferring the system state trajectory to a specified area where no singularity occurs in advance, thereby improving the control performance and robustness of the system.

[0202] From the description of the above embodiments, those skilled in the art can know that the present invention provides a design method for a terminal sliding mode controller based on a segmented sliding mode surface. Compared with the prior art solution, the method of the present invention has the following advantages:

[0203] 1. The terminal sliding mode controller designed by the present invention has the characteristics of no singularity, fast convergence, strong robustness and higher precision. It can completely eliminate the singularity problem that occurs in the robot arm control process, facilitate improving the response speed, ensure the operation efficiency of the robot arm, and achieve higher control accuracy at the same time.

[0204] 2. The present invention eliminates the singularity problem by introducing a nonlinear function to design a segmented sliding surface;

[0205] 3. The present invention accelerates the convergence speed of the sliding mode controller by introducing piecewise power terms into the reaching law and optimizing the sliding mode surface;

[0206] 4. The present invention accelerates the convergence speed of the nonlinear terminal sliding mode controller, improves the tracking accuracy and reduces the error by optimizing and improving the sliding surface.

[0207] Embodiment 2:

[0208] The present invention also provides a terminal sliding mode controller design system based on a segmented sliding surface, which is applied to a terminal sliding mode controller design method based on a segmented sliding surface described in the above embodiment 1, designs a terminal sliding mode controller based on a segmented sliding surface, and controls a robotic arm. The system includes:

[0209] A robot arm dynamics model building module is used to build a robot arm dynamics model;

[0210] A tracking error establishment module, used to establish a joint angle tracking error and an angular velocity tracking error of the robotic arm based on the robotic arm dynamics model;

[0211] Segmented sliding surface design module, used to design segmented sliding surface and analyze the convergence of joint angle tracking error during the sliding phase;

[0212] A reaching law construction module, used for constructing a piecewise power reaching law according to the piecewise sliding surface;

[0213] The controller design module is used to design a fixed-time non-singular terminal sliding mode controller based on the mechanical arm dynamics model, the piecewise sliding mode surface, the joint angle tracking error and the piecewise power reaching law.

[0214] An embodiment of the present invention provides a terminal sliding mode controller design system based on a segmented sliding surface, and its implementation principle and technical effects are the same as those of the aforementioned method embodiment. For the sake of brief description, parts not mentioned in this embodiment can be referred to the corresponding contents in the aforementioned method embodiment, which will not be repeated here.

[0215] Embodiment 3:

[0216] Reference Figure 6 As shown, an embodiment of the present invention further provides an electronic device, which may include a processor 10, a memory 11, a communication bus 12 and a communication interface 13, and may also include a computer program stored in the memory 11 and executable on the processor 10, and the processor executes the computer program to implement a terminal sliding mode controller design method based on a segmented sliding surface in the above-mentioned embodiment 1.

[0217] The processor 10 may be composed of an integrated circuit in some embodiments, for example, a single packaged integrated circuit, or a plurality of packaged integrated circuits with the same or different functions, including one or more central processing units (CPUs), microprocessors, digital processing chips, graphics processors, and combinations of various control chips. The processor 10 is the control core of the electronic device, and uses various interfaces and lines to connect various components of the entire electronic device, and executes various functions of the electronic device and processes data by running or executing programs or modules stored in the memory 11, and calling data stored in the memory 11.

[0218] Embodiment 4:

[0219] An embodiment of the present invention also provides a storage medium on which one or more programs readable by a computing device are stored. The one or more programs include instructions. When the instructions are executed by the computing device, the computing device executes a terminal sliding mode controller design method based on a segmented sliding surface in Example 1.

[0220] Examples of computer-readable storage media include: read-only memory (ROM), random-access programmable read-only memory (PROM), electrically erasable programmable read-only memory (EEPROM), random-access memory (RAM), dynamic random-access memory (DRAM), static random-access memory (SRAM), flash memory, non-volatile memory, CD-ROM, DVD-ROM, Blu-ray or optical disk storage, hard disk drive (HDD), solid-state drive (SSD), card-type memory (such as a multimedia card, a secure digital (SD) card, or an extreme digital (XD) card), magnetic tape, floppy disk, magneto-optical data storage system, optical data storage system, hard disk, solid-state disk, and any other system configured to store a computer program and any associated data, data files, and data structures in a non-transitory manner and provide the computer program and any associated data, data files, and data structures to a processor or computer so that the processor or computer can execute the computer program. The computer program in the above-mentioned computer-readable storage medium can be executed in an environment deployed in a computer device such as a client, a host, an agent system, a server, etc. In addition, in one example, the computer program and any associated data, data files, and data structures are distributed on a networked computer system, so that the computer program and any associated data, data files, and data structures are stored, accessed, and executed in a distributed manner by one or more processors or computers.

[0221] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems or computer program products, etc. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0222] It should be noted that the word "comprising" does not exclude the presence of components or steps not listed in the claims. The word "a" or "an" preceding a component does not exclude the presence of a plurality of such components. The invention can be implemented by means of hardware comprising several distinct components, and by means of a suitably programmed computer.

[0223] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0224] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for designing a terminal sliding mode controller based on a segmented sliding surface, wherein the designed terminal sliding mode controller is used to control a robotic arm, and is characterized in that: The method comprises the following steps: S1. Establish a dynamic model of a multi-joint robotic arm; S2. Based on the mechanical arm dynamics model, establish the joint angle tracking error and joint angular velocity tracking error of the mechanical arm; S3, design the segmented sliding surface and analyze the convergence of the joint angle tracking error during the sliding stage; S4. constructing a piecewise power reaching law according to the piecewise sliding surface; S5. Based on the robot arm dynamics model, piecewise sliding surface, joint angle tracking error and piecewise power reaching law, a fixed-time non-singular terminal sliding mode controller is designed.

2. The method for designing a terminal sliding mode controller based on a segmented sliding surface according to claim 1, characterized in that: In step S1, a multi-joint mechanical arm dynamics model with external interference is constructed according to the dynamics principle, and the model expression is: Where q=[q1,q2,…,q n ] T is the joint angle of the robot arm, is the joint angular velocity of the robot arm, is the joint angular acceleration of the robot, n represents the nth joint of the robot; M(q)∈R n ×n is a symmetric and positive definite inertia term, is the Coriolis force and centrifugal force term, G(q)∈R n×1 is the gravity term, τ d ∈R n×1 represents the bounded external disturbance torque generated by the accidental collision with the environment, τ∈R n×1 is the joint input torque.

3. The method for designing a terminal sliding mode controller based on a segmented sliding surface according to claim 2, characterized in that: In step S2, the expressions of the joint angle tracking error and the joint angular velocity tracking error of the robot arm are: e=q-q d Among them, e, They represent joint angle tracking error and angular velocity tracking error, q, Respectively represent the actual joint angle and angular velocity, q d , Represent the desired joint angle and angular velocity respectively.

4. The method for designing a terminal sliding mode controller based on a segmented sliding mode surface according to claim 3, characterized in that: In step S3, before designing the segmented sliding surface, a nonlinear function s is introduced. (u,v) (x) and the nonlinear function sig v (x), the function formula is: sig v (x)=|x| v sgn(x) Among them, 0 <u<1,v> 1 and 0<ξ2<ξ1<1 are four positive constant parameters to be designed; sgn(x) represents the sign function; Define vector S (u,v) (e),Sig v (e)∈R n : S (u,v) (e)=[s (u,v) (e1),…,s (u,v) (have been n )] T Mr v (and)=[sig v (e1),…,sig v (And n )] T Among them, e i Represents the i-th component of vector e, i = 1, 2,…, m.

5. The method for designing a terminal sliding mode controller based on a segmented sliding mode surface according to claim 4, characterized in that: According to the nonlinear function s (u,v) (·) and sig v The properties of (·) are used to design the segmented sliding surface. The designed segmented sliding surface is: Where s represents the segmented sliding surface, K1, K2∈R n×n is a constant positive definite diagonal gain matrix.

6. The method for designing a terminal sliding mode controller based on a segmented sliding mode surface according to claim 5, characterized in that: In the step S4, a piecewise power reaching law is constructed according to the piecewise sliding surface, specifically: Segmented sliding surface The first-order derivative about e is: Depend on have to: In the formula, represents the angular acceleration error of the joint, represents the desired joint angular acceleration; On the basis of the power reaching law, a piecewise power reaching law is constructed, and its specific form is: Where, 0 <u<1,v> 1, ε1 and ε2 are the positive constant parameters to be designed and satisfy 0<ε2<ε1<1; sign(·) represents the sign function, Ξ(·) represents the piecewise power function, ρ1>0 is the gain of the linear term, which is used to suppress the disturbance of linear growth; ρ2>0 is the gain of the piecewise power term.

7. The method for designing a terminal sliding mode controller based on a segmented sliding mode surface according to claim 6, characterized in that: In step S5, the designed terminal sliding mode controller is: Where y0 represents the terminal sliding mode controller.

8. A terminal sliding mode controller design system based on a segmented sliding mode surface, characterized in that: When applied, a terminal sliding mode controller design method based on a segmented sliding mode surface according to any one of claims 1 to 7 is executed to design a terminal sliding mode controller based on a segmented sliding mode surface to control a robotic arm. The system includes: A robot arm dynamics model building module is used to build a robot arm dynamics model; A tracking error establishment module, used to establish a joint angle tracking error and an angular velocity tracking error of the robotic arm based on the robotic arm dynamics model; Segmented sliding surface design module, used to design segmented sliding surface and analyze the convergence of joint angle tracking error during the sliding phase; A reaching law construction module, used for constructing a piecewise power reaching law according to the piecewise sliding surface; The controller design module is used to design a fixed-time non-singular terminal sliding mode controller based on the mechanical arm dynamics model, the piecewise sliding mode surface, the joint angle tracking error and the piecewise power reaching law.

9. An electronic device, characterized in that: It includes a processor and a memory, the memory stores machine executable instructions that can be executed by the processor, and the processor executes the machine executable instructions to implement a terminal sliding mode controller design method based on a segmented sliding surface as described in any one of claims 1-7.

10. A storage medium having stored thereon one or more programs readable by a computing device, characterized in that: The one or more programs include instructions, which, when executed by a computing device, enable the computing device to perform a terminal sliding mode controller design method based on a piecewise sliding surface as described in any one of claims 1-7.

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