Constrained robot arm fixed-time adaptive parameter identification and control method and device

Abstract

The present application relates to a kind of restricted mechanical arm fixed time adaptive parameter identification, control method and device, belong to robot control field, mainly solve the problem that existing technology composite learning adaptive control cannot make mechanical arm system stable in fixed time, and does not consider the problem that mechanical arm joint position tracking error is limited.The present application realizes the constraint to mechanical arm joint position tracking error by constructing the unsymmetrical barrier function independent of initial condition, simultaneously by designing the fixed time control method based on non-singular fast integral terminal sliding mode, so that mechanical arm trajectory tracking error and parameter estimation error can converge to 0 in fixed time, and the appearance of singularity problem is avoided, effectively improve the system control performance, also guarantee the safety of mechanical arm operation process.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of robot control, in particular to a fixed-time adaptive parameter identification and control method and device for a constrained robot arm. BACKGROUND

[0002] A robot arm has the function of imitating human arm movement and can complete various tasks. It is the most widely used automatic mechanical device in the current field of robot technology and is involved in many fields such as industrial manufacturing, agricultural production, medical services, and space exploration.

[0003] In order to accurately control the robot arm, the physical parameters of the robot arm need to be obtained in real time and accurately to construct an accurate dynamic model. However, the robot arm system usually has multiple degrees of freedom and is a typical nonlinear and strongly coupled system. In addition, with the influence of environmental factors and changes in task execution, multiple parameters in the dynamic model of the robot arm will also change. These factors make it difficult to accurately obtain the dynamic model of the robot arm, and the use of an inaccurate robot arm model will seriously affect the control effect of the system.

[0004] Therefore, how to accurately identify the unknown parameters of the robot arm model and improve the control performance of the robot arm system has become a problem to be solved in the current control field. SUMMARY

[0005] To solve the problem of accurately identifying the unknown parameters of the robot arm model and improving the control performance of the robot arm system, the present application provides a fixed-time adaptive parameter identification and control method and device for a constrained robot arm.

[0006] Embodiments of the present application are implemented as follows:

[0007] In a first aspect, the present application provides a fixed-time adaptive parameter identification and control method for a constrained robot arm, which comprises:

[0008] A dynamics model considering the position tracking error of the joints of the robot arm is constructed.

[0009] The position and velocity data of the current joints of the robot arm are obtained, and the position and velocity data are combined with the historical data information of the estimation error of the unknown parameters of the robot arm to design a parameter prediction error.

[0010] A non-singular fast integral terminal sliding mode surface and an auxiliary variable are constructed, and a parameter update law is designed and calculated in combination with the parameter prediction error.

[0011] The parameter estimation value is updated based on the parameter updating law, and a fixed-time control torque value based on a non-singular fast integral terminal sliding mode surface is calculated, so that the manipulator is driven by the control torque to move along the predetermined trajectory, and the joint position tracking error of the manipulator is always limited within the predetermined limit;

[0012] When the system set time is not ended, the next time is obtained as the current time, the joint position and speed data of the manipulator are continuously obtained, and the above steps are repeated.

[0013] In a possible implementation, the dynamic model considering the limited joint position tracking error of the manipulator is constructed by the following steps and methods:

[0014] A dynamic model of the manipulator without considering the limited joint position error is established;

[0015] The dynamic model of the manipulator without considering the limited joint position error is as follows:

[0016]

[0017] In the formula, q(t) = [q1(t), q2(t),... qn(t)] represents the joint position vector of the n-degree-of-freedom manipulator, n represents a positive definite inertia matrix, represents a centrifugal force and Coriolis force matrix, represents viscous friction torque, represents gravity torque, represents control torque, respectively represent the joint position, speed and acceleration of the manipulator;

[0018] An error conversion function is designed;

[0019] In the formula, the error conversion function is designed as follows:

[0020]

[0021] In the formula, e i is the i-th element of the tracking error e, i = 1, 2,..., n, e = q - qd d , q d is the expected trajectory of the joint position of the manipulator, k i and l i are both normal numbers;

[0022] An asymmetric barrier function independent of initial conditions is designed, and the derivative thereof is obtained;

[0023] In the formula, the asymmetric barrier function independent of initial conditions is designed as follows:

[0024] ​

[0025] wherein: φ ai (t) and φ bi (t) are time-varying functions, t is time, and φ ai (t) > 0, φ bi (t) > 0, φ ai (0) = φ bi (0) = k i ;

[0026] The derivative of the asymmetric barrier function is:

[0027]

[0028] wherein:

[0029]

[0030]

[0031] The equation is written in a compact form as:

[0032]

[0033] wherein:

[0034]

[0035]

[0036]

[0037] The error conversion function and the derivative of the asymmetric barrier function independent of initial conditions are substituted into the mechanical arm dynamics model without considering the joint position error constraints to obtain a mechanical arm dynamics model considering the joint position tracking error constraints;

[0038] wherein the mechanical arm dynamics model considering the joint position tracking error constraints is as follows:

[0039]

[0040] wherein:

[0041]

[0042]

[0043]

[0044] wherein: ​an arbitrary auxiliary vector for which the linear parameterization of the dynamic model holds, derivative of ξ, a dynamic regression matrix corresponding to the limited joint position tracking error of the robot arm, a transpose of θ is an unknown parameter vector of the robot arm.

[0045] In a possible implementation, the parameter prediction error is obtained by the following steps and methods:

[0046] constructing an improved excitation matrix;

[0047] wherein the improved excitation matrix is constructed as follows:

[0048]

[0049] wherein: is an improved excitation matrix, Φ(t) is an excitation matrix, T e is a time upper boundary for which the interval excitation condition holds;

[0050] designing a parameter prediction error according to the improved excitation matrix;

[0051] wherein the parameter prediction error is designed as follows:

[0052]

[0053] wherein: ε(t) is a parameter prediction error, is an unknown parameter estimation error, defined as θ is an estimated value of the unknown parameter vector θ of the robot arm.

[0054] In a possible implementation, the improved excitation matrix is obtained based on integral of a regression matrix of dynamics of a robot arm model, and the regression matrix is obtained by linear parameterization processing of a dynamic model of the robot arm.

[0055] In a possible implementation, the non-singular fast integral terminal sliding mode surface is calculated by the following formula:

[0056]

[0057] wherein s is a non-singular fast integral terminal sliding mode surface, λ1, λ2, λ3, λ4, α, α1, β, β1 are all controller parameters, wherein: λ1, λ2, λ3, 0 < α < 1, -1 < β < 0, α1 = 2α / (1-α), β1 = 2β / (1-β).

[0058] In one possible implementation, the auxiliary variable is constructed as shown in the following equation:

[0059]

[0060] in, These are the auxiliary variables that were constructed.

[0061] In one possible implementation, the parameter update law is calculated by the following formula:

[0062]

[0063]

[0064] in, sign(·) is the standard sign function, Γ, K1, The adaptive gain matrix is ​​typically a positive definite diagonal matrix. γ1 and γ2 are controller parameters satisfying 0 < γ1 < 1, γ2 > 1. P is the projection operator. for The norm of the radius c θ spherical range This is set as the bound of the unknown parameter vector of the robotic arm. This bound can be calculated by the user based on the rough information of the robotic arm model parameters obtained in advance. This is the dynamic regression matrix corresponding to the constrained robotic arm.

[0065] In one possible implementation, the fixed-time control torque is calculated by the following formula:

[0066]

[0067] Where τ is the control torque, K3, This is the controller gain matrix, which is typically set as a positive definite diagonal matrix.

[0068] Secondly, this application provides a device for identifying and controlling adaptive parameters of a constrained robotic arm with a fixed time, the device comprising:

[0069] Modeling module: Used to build dynamic models that take into account the limitations of joint position tracking errors in robotic arms;

[0070] The processing and calculation module is used to acquire the current position and velocity data of the robotic arm joints, and combine the position and velocity data with historical data information of the estimation error of unknown parameters of the robotic arm to calculate the parameter prediction error; it is used to construct the non-singular fast integral terminal sliding surface and auxiliary variables, and calculate the parameter update law based on the parameter prediction error; it is used to update the parameter estimate based on the parameter update law, and then calculate the fixed-time control torque value based on the non-singular fast integral terminal sliding surface.

[0071] a control module configured to control the torque-driven robot arm to move along a predetermined trajectory and ensure that a joint position tracking error of the robot arm is always limited within a predetermined range;

[0072] a timing module configured to obtain a next time as a current time when a system set time is not ended, and return the processing and calculation module.

[0073] The technical scheme provided in the application can achieve at least the following beneficial effects:

[0074] The adaptive parameter identification and control method and device for a limited robot arm provided in the application, based on the existing composite learning control theory, realizes the constraint of the joint position tracking error of the robot arm by constructing an asymmetric barrier function independent of initial conditions, and designs a fixed-time adaptive control method based on a non-singular fast integral terminal sliding mode, in combination with a parameter update law, so that the parameter estimation error of the robot arm model and the trajectory tracking error can both converge to 0 in a fixed time under weak interval excitation conditions, and no singular problem occurs, thereby quickly and accurately controlling the movement of the robot arm and effectively improving the control performance of the system. BRIEF DESCRIPTION OF DRAWINGS

[0075] In order to more clearly illustrate the technical scheme in the embodiments of the application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0076] Figure 1 is a flowchart of an adaptive parameter identification and control method according to an example embodiment of the application;

[0077] Figure 2 is a flowchart of how to construct a dynamics model considering the limited joint position tracking error of the robot arm according to an example embodiment of the application;

[0078] Figure 3 is a flowchart of calculating a parameter prediction error according to an example embodiment of the application;

[0079] Figure 4 is a flowchart of constructing an improved excitation matrix according to an example embodiment of the application;

[0080] Figure 5 is a flowchart of calculating a parameter update law according to an example embodiment of the application;

[0081] Figure 6is a flowchart of a process of controlling the robot arm to move along a predetermined trajectory according to the parameter updating law shown in an example embodiment of the present application;

[0082] Figure 7 is a diagram showing the effect of unknown parameter estimation of the robot arm in the tracking control mode shown in an example embodiment of the present application;

[0083] Figure 8 is a diagram showing the convergence of variables s, e and zeta in the tracking control mode shown in an example embodiment of the present application;

[0084] Figure 9 is a diagram showing the comparison of error results between the present application and the composite learning control method shown in an example embodiment of the present application;

[0085] Figure 10 is a diagram showing the comparison of unknown parameter estimation values between the present application and the composite learning control method shown in an example embodiment of the present application;

[0086] Figure 11 is a diagram showing the adaptive parameter identification and control device shown in an example embodiment of the present application. DETAILED DESCRIPTION

[0087] In order to make the objects, implementation manners and advantages of the present application clearer, the following will clearly and completely describe the example implementation manners of the present application with reference to the drawings in the example embodiments of the present application. Obviously, the described example embodiments are only some of the embodiments of the present application but not all the embodiments of the present application. It should be understood that the specific embodiments described herein are only used to explain the present application and not intended to limit the present application.

[0088] It should be noted that the brief description of the terms in the present application is only for the convenience of understanding the following described embodiments and is not intended to limit the implementation manners of the present application. Unless otherwise specified, these terms should be understood according to their ordinary and general meanings.

[0089] The terms "first", "second", "third", etc. in the specification and claims and the above drawings are used to distinguish similar or similar objects or entities and do not necessarily mean to limit the specific order or sequence, unless otherwise specified. It should be understood that the terms used in this way can be interchanged under appropriate circumstances.

[0090] The terms "include" and "have" and any variations thereof are intended to cover but not exclusive inclusion, for example, a product or device including a series of components does not have to be limited to all the components clearly listed, but can include other components not clearly listed or inherent to these products or devices.

[0091] For the convenience of describing the technical solutions of the application, first, some symbols involved in the present application are explained.

[0092] In the present application, is a real number, is a positive real number, is an n-dimensional real vector, is an n*n real matrix, is an m*n real matrix, is an m-dimensional real vector.

[0093] Before explaining the limited robot fixed-time adaptive parameter identification and control method and device provided by the embodiments of the present application, the application scenarios and implementation environments of the embodiments of the present application are introduced.

[0094] The robot has the function of imitating human arm movement and can complete various tasks. It is the most widely used automatic mechanical device in the current robot technology field, involving industrial manufacturing, agricultural production, medical services, space exploration and many other fields.

[0095] In order to accurately control the robot, the physical parameters of the robot need to be obtained in real time and accurately to construct its accurate dynamic model. However, the robot system usually contains multiple degrees of freedom and is a typical nonlinear and strongly coupled system. In addition, with the influence of environmental factors and the change of task execution, multiple parameters in the dynamic model of the robot will also change. These factors all lead to the difficulty of accurately obtaining the dynamic model of the robot, and the use of inaccurate robot model will seriously affect the system control effect.

[0096] Therefore, how to accurately identify the unknown parameters of the robot model and improve the control performance of the robot system has become a problem to be solved in the current control field.

[0097] Based on this, the present application provides a limited robot fixed-time adaptive parameter identification and control method and device, which considers the limited joint position tracking error of the robot and ensures that the robot system can be stable within a fixed time. Based on the existing composite learning control theory, the method realizes the constraint of the joint position tracking error of the robot by constructing an asymmetric barrier function independent of the initial condition, and designs a fixed-time adaptive control method based on a non-singular fast integral terminal sliding mode, so that the trajectory tracking error and unknown parameter estimation error of the robot system can converge to 0 within a fixed time, and the singularity problem does not occur, effectively improving the control performance of the system.

[0098] Next, the technical solutions of the present application and how the technical solutions solve the above technical problems will be described in detail through embodiments and in conjunction with the drawings. The embodiments can be combined with each other, and the same or similar concepts or processes can not be described again in some embodiments. Obviously, the described embodiments are part of the embodiments of the present application, not all.

[0099] Figure 1 is a flowchart of an adaptive parameter identification and control method shown in an exemplary embodiment of the present application, Figure 2 is a flowchart of how to construct a dynamics model considering the limited joint position tracking error of a robot arm.

[0100] In one exemplary embodiment, as Figure 1 shown, a limited robot arm fixed-time adaptive parameter identification and control method is provided. In this embodiment, the method can include the following steps:

[0101] Step 100, constructing a dynamics model considering the limited joint position tracking error of a robot arm, as Figure 2 shown, further includes the following steps:

[0102] Step 110, establishing a robot arm dynamics model without considering the limited joint position error.

[0103] Wherein, the robot arm dynamics model without considering the limited joint position error is as follows:

[0104]

[0105] In the formula, q(t) = [q1(t), q2(t),... qn(t)] represents the joint position vector of an n-degree-of-freedom robot arm, n represents a positive definite inertia matrix, represents a centrifugal force and Coriolis force matrix, represents viscous friction torque, represents gravity torque, represents control torque, represent the joint position, velocity and acceleration of the robot arm, respectively.

[0106] It has the following properties:

[0107] Property 1: is a positive definite symmetric matrix, satisfying m1||ψ|| 2 ≤ψ T M(q)ψ≤m2||ψ|| 2 , ​For any vector, ||ψ|| is the norm of ψ, and m1 and m2 are normal numbers.

[0108] Property 2: is a skew-symmetric matrix.

[0109] Property 3: The left side of the robot dynamics model (1) can be written as follows:

[0110]

[0111] In the formula: is an arbitrary auxiliary vector that satisfies formula (2), is the derivative of ξ, is a dynamic regression matrix, is the transpose of , and is an unknown parameter vector of the robot model.

[0112] According to Property 3, the left side of the robot dynamics model (1) can be linearly parameterized, that is, it can be written as the product of the transpose of the regression matrix and the unknown parameter vector θ of the model, where Each parameter in can be measured or calculated, and only the unknown parameter vector θ is unknown.

[0113] Step 120, design an error conversion function.

[0114] The error conversion function is as follows:

[0115]

[0116] In the formula: e i is the i-th element of the tracking error e, i = 1, 2,..., n, k i and l i are normal numbers. From formula (3), the error conversion function has the following properties:

[0117] 1) For any η(e i ) ∈ (-k i , k i );

[0118] 2) For any η(e i ) is a strictly monotonically increasing function;

[0119] 3) When e i → -∞, η(e i ) → -k i , and when e i → ∞, η(e i)→k i ;

[0120] 4)

[0121] 5) The inverse function of the error conversion function (3) is:

[0122]

[0123] It can be seen that: for any η i ∈(-k,k), formula (4) is also a strictly monotonic increasing function.

[0124] Step 130, design an asymmetric barrier function independent of the initial condition, and derive it.

[0125] Wherein, the designed asymmetric barrier function does not need to limit the initial error condition of the system, and can realize global control performance, and the asymmetric barrier function independent of the initial condition is as follows:

[0126]

[0127] In the formula: φ ai (t) and φ bi (t) are time-varying functions, which satisfy φ ai (t)>0, φ bi (t)>0, φ ai (0)=φ bi (0)=k i If φ ai (t)=φ bi (t), formula (5) is called a symmetric barrier function independent of the initial condition.

[0128] It can be seen from formula (5) that: when and only when η(e i )→φ ai (t) or η(e i )→-φ bi (t), ζ i →∞, that is, if ζ i is bounded, for any e i (0), then:

[0129] -φ bi (t)<η i (e i )<φ ai (t) (6)

[0130] Further, according to the strictly monotonic increasing property of formula (4), for any e i (0), the following can be met:

[0131] -Ψbi (t) < e i <Ψ ai (t) (7)

[0132] From the above analysis, if the asymmetric barrier function ζ i is bounded, the tracking error e i can be guaranteed to be limited in a predetermined asymmetric time-varying region, which is independent of the initial value e i (0). Therefore, the control method based on the barrier function will have global control performance.

[0133] Taking the derivative of equation (3) and equation (5) with respect to time t, we have:

[0134]

[0135] Wherein:

[0136]

[0137]

[0138] Write equation (8) in a compact form:

[0139]

[0140] In the formula:

[0141]

[0142]

[0143]

[0144] According to equation (9), when equation (6) is established, μ 1i > 0, and further μ1> 0.

[0145] Step 140, substituting the error conversion function and the derivative of the asymmetric barrier function independent of the initial condition into the dynamics model of the robot arm without considering the limitation of joint position error, to obtain the dynamics model of the robot arm considering the limitation of joint position tracking error.

[0146] Substituting equation (11) into the dynamics model (1) of the robot arm, we have:

[0147]

[0148] Multiply the left and right ends of equation (15) by We have:

[0149]

[0150] wherein:

[0151]

[0152]

[0153]

[0154] According to properties 1-3, the constrained robot arm model (16) has the following properties:

[0155] Property 4: is a positive definite symmetric matrix, and satisfies a1||ψ||2 2 ≤ψ T H(q,μ1)ψ≤a2||ψ|| 2 , is an arbitrary vector, ||ψ|| is the norm of ψ, and a1 and a2 are normal numbers.

[0156] Property 5: is a skew-symmetric matrix.

[0157] Property 6: The left side of the constrained robot arm dynamics model (16) can be written in the following form:

[0158]

[0159] In equation (20), is a dynamic regression matrix corresponding to the constrained robot arm joint position tracking error, is the transpose of .

[0160] Figure 3 is a flowchart illustrating a process of calculating a parameter prediction error according to an example embodiment of the present application, Figure 4 is a flowchart illustrating a process of constructing an improved excitation matrix according to an example embodiment of the present application.

[0161] Step 200, position and velocity data of the current robot arm joint are acquired, and the position and velocity data are combined with historical data information of the robot arm unknown parameter estimation error to design a parameter prediction error, as shown in Figure 3 The process further includes the following steps:

[0162] Step 210, an improved excitation matrix is constructed.

[0163] The improved excitation matrix is obtained based on integration of a dynamic regression matrix of the robot arm model, and the regression matrix is obtained by linear parameterization processing of the robot arm dynamics model, as shown in Figure 4 The construction of the improved excitation matrix further includes the following steps:

[0164] Step 211, linear parameterization is performed on the robot arm dynamics model (1).

[0165] When , formula (2) can be written as:

[0166]

[0167] Substitute (21) into (1) to get:

[0168]

[0169] Step 212, define the excitation matrix.

[0170] First, the definitions of the continuous excitation condition and the interval excitation condition are introduced.

[0171] Continuous excitation condition definition: for any time t>0, if there exists a positive number such that

[0172] , then the matrix is said to satisfy the continuous excitation condition.

[0173] Interval excitation condition definition: there exists a positive number such that , then the matrix is said to satisfy the interval excitation condition.

[0174] Multiply both sides of (22) by and integrate over the time interval [t-t d , t] to get:

[0175]

[0176] Multiply both sides of (23) by a fixed unknown parameter vector θ and substitute it into formula (22) to get:

[0177]

[0178] In the formula: Φ(t) is the excitation matrix.

[0179] Step 213, design an improved excitation matrix.

[0180] In the traditional adaptive control method, in order to ensure that the parameter estimation error of the robot arm model can converge to 0, the robot arm regression matrix must satisfy the continuous excitation condition, which is difficult to achieve in reality. Therefore, in order to weaken the excitation condition, an improved excitation matrix in the form of segmentation is designed as follows:

[0181]

[0182] wherein: To improve the excitation matrix, when the matrix is not satisfied, the interval excitation condition is not satisfied. Once the matrix is satisfied, the interval excitation condition is satisfied, i.e., there exists a positive number such that is established, then for any t≥T e at some time, is established. Compared with the excitation matrix, the improved excitation matrix weakens the system excitation condition and improves the feasibility of accurately identifying unknown parameters of the system model.

[0183] Step 220, designing a parameter prediction error according to the improved excitation matrix.

[0184] wherein, for the convenience of subsequent design of the parameter update law, the following parameter prediction error is constructed:

[0185]

[0186] Substituting equation (25) into equation (26) can obtain:

[0187]

[0188] wherein: ε(t) is the defined prediction error, is the estimated value of the unknown parameter vector θ, is the unknown parameter estimation error, which is defined as:

[0189] Figure 5 is a flowchart for calculating the parameter update law shown in an example embodiment of the present application.

[0190] Step 300, constructing a non-singular fast integral terminal sliding mode surface and an auxiliary variable, combining the parameter prediction error to design and calculate the parameter update law, as shown in Figure 5 , including the following steps:

[0191] Step 310: constructing a non-singular fast integral terminal sliding mode surface.

[0192]

[0193] wherein: s is a terminal sliding mode surface, λ1, λ2, λ3, λ4, α, α1, β, β1 are all controller parameters, wherein: λ1, λ2, λ3, 0<α<1, -1<β<0, α1=2α / (1-α), β1=2β / (1-β).

[0194] Step 320: defining an auxiliary variable.

[0195] where the auxiliary variable is defined as follows:

[0196]

[0197] After the derivative of the sliding surface s with respect to time t is taken, the equation is multiplied by H(q, μ1) on both sides and substituted into equation (16). Through equation (29) and property 6, the following equation can be obtained:

[0198]

[0199] where: is introduced as an auxiliary variable the corresponding limited robot dynamic regression matrix, is the derivative of

[0200] Step 330, design the parameter update law.

[0201] where the parameter update law is designed as follows:

[0202]

[0203]

[0204] where: sign(·) is the standard sign function, Γ, K1, is an adaptive gain matrix, which is usually taken as a positive definite diagonal matrix, γ1 and γ2 are controller parameters, which satisfy 0 < γ1 < 1 and γ2 > 1, P is a projection operator, which can be obtained by equation (32), is the norm of a spherical range with a radius of cθ is set as the bound of the unknown parameter vector of the robot, which can be calculated by the user according to the rough information of the pre-obtained robot model parameters, such as the length of the robot arm not exceeding l, the mass of the robot not exceeding m, etc. Through the design of the parameter update law, the estimation value of the unknown parameter can be continuously updated, and finally it is equal to the true value of the unknown parameter θ, that is, the estimation error of the unknown parameter of the model converges to 0.

[0205] Step 340, calculate the parameter update law according to the designed parameter update law calculation formula.

[0206] Figure 6 is a flowchart of controlling the robot to move along the predetermined trajectory based on the parameter update law according to an exemplary embodiment of the present application.

[0207] ​Step 400, updating the parameter estimation value based on the parameter update law, and then calculating the fixed-time control torque value based on the non-singular fast integral terminal sliding mode surface, so as to drive the robot arm to move along the predetermined trajectory by the control torque and ensure that the joint position tracking error of the robot arm is always limited within the predetermined limit. Figure 7 The method further comprises the following steps:

[0208] Step 410, updating the parameter estimation value according to the parameter update law.

[0209] The parameter update law is the change rate of the unknown parameter vector, which can be calculated by the following formula:

[0210]

[0211] In the formula: is the parameter update law obtained by real-time calculation according to formula (31) after b-1 time steps, is the updated unknown parameter vector estimation value after b time steps, is the unknown parameter vector estimation value at the previous time, is the initial estimation value of the unknown parameter vector set by the user, b = 1, 2,..., p, p is a positive integer, and Δt b is the time step, which can be set by oneself, and is taken as 1ms in the following experiment.

[0212] Step 420, designing a robot arm fixed-time controller based on a non-singular fast integral terminal sliding mode.

[0213] The robot arm fixed-time controller based on the non-singular fast integral terminal sliding mode is designed as follows:

[0214]

[0215] Substituting formula (34) into formula (30) can obtain the closed-loop dynamic model of the robot arm system:

[0216]

[0217] In the formula: is the controller gain matrix, which is generally set as a positive definite diagonal matrix.

[0218] Step 430, calculating the control torque value according to the designed robot arm fixed-time controller, and then controlling the robot arm to move along the predetermined trajectory and ensuring that the joint position tracking error of the robot arm is always limited within the predetermined limit.

[0219] Compared with the traditional exponential stability controller, the fixed-time controller can significantly improve the system stability speed. Through the fixed-time controller, real-time control of the motion of the mechanical arm is realized, so that the actual motion trajectory of the mechanical arm can quickly and accurately track the expected trajectory within a fixed time, and the unknown parameter estimation value can also converge to its true value within a fixed time by combining the parameter update law.

[0220] Step 500: When the system set time is not over, the next time is obtained as the current time, and the step 200 is returned.

[0221] Wherein, the fixed-time controller τ and the parameter update law designed by the application If there is a time T e > 0, the interval excitation condition is established, that is, there is a normal number So that Θ(T e ) ≥ σI is established, then the unknown parameter estimation error And the trajectory tracking error e(t) of the mechanical arm system can converge to 0 in a limited time, and the trajectory tracking error will be limited within the predetermined limit.

[0222] For the fixed-time stability of the above system, the Lyapunov function can be designed for analysis and verification, and the specific process is as follows:

[0223] First, the Lyapunov candidate function is designed:

[0224]

[0225] Derive V with respect to time t, combine formula (34), property 4 and property 5 to obtain:

[0226]

[0227] According to the projection operator property: if Then And can ensure that the following formula is established:

[0228]

[0229] Substitute formula (38) into formula (37) to obtain:

[0230]

[0231] According to the inequality property and combining formula (27), the last two terms of the above formula can be written as follows:

[0232]

[0233] In the formula: k1=λ min (K1), Substitute (40) into (39) and use inequality properties to obtain:

[0234]

[0235] where k3= λ min (K3),

[0236] When the system meets the interval excitation condition during operation, i.e., there exists such that When the interval t∈[T e -t d ,T e ] satisfies then from equation (27) we can obtain:

[0237]

[0238] Substitute (42) into (41) and use inequality properties to obtain:

[0239]

[0240] where

[0241] According to the finite time stability theory, we can obtain that s and can converge to 0 within a fixed time, and the convergence time Further, we can obtain that ζ can converge to 0 within a fixed time, and the convergence time T2=T1+T s . From equation (5), we can obtain that when ζ i =0, η i (e i ) =0, thus we can deduce that e i =0, i=1,...n, and finally we can obtain that the tracking error e can converge to 0 within a fixed time T2, and the trajectory tracking error of the manipulator will be always limited within the pre-set asymmetric bound range.

[0242] To verify the effectiveness of the proposed method, the following tracking control mode experiments are performed:

[0243] Select joint 1 and joint 2 of DENSO manipulator (model: VP-6242G) to form a two-DOF manipulator, and the gear tooth ratio of the two joints is 160:1 and 120:1 respectively, and the angular coordinate resolution is 3×10 -7 rad and 4×10 -7 rad respectively, and the sampling time interval is set to 1ms. The unknown parameter vector of the two-DOF manipulator is θ=[θ1, θ2,..., θ8] T , wherein: θ3 = m1l c1 + m2l1, θ4 = m2l c2 , θ5 = k v1 , θ6 = k v2 θ7 = F f1 , θ8 = F f2 . In the above formulas, I1 and I2 are the rotational inertia of the two arms of the robot, m1 and m2 are the masses of the two arms, l1 and l2 are the lengths of the two arms, l c1 and l c2 are the lengths from the centers of mass of the two arms to the axes, k v1 and k v2 are the viscous friction coefficients of the two arms, F f1 and F f2 are the Coulomb frictions of the two arms.

[0244] The system state and parameters are initialized as follows:

[0245] According to the inverse dynamics model, the desired trajectory of the robot joints is set as:

[0246]

[0247] where x d1 = 0.5 + 0.2cos(πt), x d2 = 0.5 + 0.2sin(πt). The tracking error constraint functions φ ai and φ bi of joint 1 and joint 2 are set as φ ai (t) = 1.97exp(-0.6t) + 0.03, φ bi (t) = 1.97exp(-0.8t) + 0.03, k i = 2, l i = 1, i = 1, 2. The controller parameters are set as follows: K1 = 9 x 10 -3 I, K2 = 8 x 10 -3 I, K3 = 10I, K4 = 10I, Γ = 0.1I, γ1 = 0.6, γ2 = 1.5 λ1 = λ2 = λ3 = λ4 = 40, α = 0.5, β = -0.25, α1 = 2, β2 = -0.4, σ = 0.05, t d = 1.5s, T e = 1.7s, q(0) = [3π / 10, π / 8], α3 = 5, and the initial values of the remaining parameters are all set to 0.

[0248] Figure 7 is an unknown parameter estimation effect diagram of a robot in a tracking control mode according to an example embodiment of the present application,Figure 8 is a convergence effect diagram of variables s, e and ζ in the tracking control mode according to an example embodiment of the present application.

[0249] The estimation effect of unknown parameters of the mechanical arm is as shown in Figure 7 The convergence curves of variables s, e and ζ are as shown in Figure 8 Figure 7 It can be seen from that the designed controller and parameter updating law can make the estimation value of the unknown parameter vector

[0250] Figure 9 is a comparison diagram of errors of the present application and the composite learning control method according to an example embodiment of the present application, Figure 10 is a comparison diagram of estimation values of unknown parameters of the present application and the composite learning control method according to an example embodiment of the present application.

[0251] To further highlight the superiority of the control method proposed in the present application, the control effect of the method is compared with that of the composite learning adaptive control method, as shown in Figure 9 and Figure 10 The selection of parameters of the two methods is consistent during the experiment. It can be seen from the comparison curves that the control method proposed in the present application can make the trajectory tracking error and the estimation error of unknown parameters of the mechanical arm converge to 0 faster, and at the same time, the trajectory tracking error of the mechanical arm can be limited in the pre-set asymmetric limit range, effectively ensuring the safety and reliability of the operation process of the mechanical arm system.

[0252] It should be understood that although each step in the flowchart involved in the above embodiment is displayed in sequence as indicated, these steps are not necessarily executed in sequence as indicated. Unless explicitly stated herein, the execution of these steps is not strictly limited in sequence, and these steps can be executed in other sequences. Moreover, at least part of the steps in the flowchart involved in the above embodiment can include multiple steps or stages, which are not necessarily executed at the same time, but can be executed at different times, and the execution sequence of these steps or stages is not necessarily sequential, but can be executed in rotation or alternation with at least part of other steps or steps or stages in other steps.

[0253] Corresponding to the foregoing embodiment of the limited mechanical arm fixed-time adaptive parameter identification and control method, the same technical concept is adopted, and an embodiment of a limited mechanical arm fixed-time adaptive parameter identification and control device is also provided. ​

[0254] Figure 11 is a schematic diagram of an adaptive parameter identification and control device shown in an example embodiment of the present application.

[0255] In an example embodiment, as shown in Figure 11 the parameter identification and control device comprises:

[0256] a modeling module 1 for constructing a dynamic model considering the limitation of the joint position tracking error of the robot arm;

[0257] a processing and calculation module 2 for obtaining the position and velocity data of the current joint of the robot arm, combining the position and velocity data with the historical data information of the estimation error of the unknown parameters of the robot arm, and calculating the parameter prediction error; constructing a non-singular fast integral terminal sliding mode surface and an auxiliary variable, combining the parameter prediction error, and calculating a parameter update law; updating the parameter estimation value based on the parameter update law, and further calculating a fixed-time control torque value based on the non-singular fast integral terminal sliding mode surface;

[0258] a control module 3 for controlling the robot arm to move according to a predetermined trajectory through the control torque, and ensuring that the joint position tracking error of the robot arm is always limited within a predetermined limit;

[0259] a timing module 4 for obtaining the next time as the current time when the system set time is not over, and returning to the processing and calculation module.

[0260] For specific limitations of the adaptive parameter identification and control device for a limited robot arm, please refer to the limitations of the adaptive parameter identification and control method for a limited robot arm described above, which will not be repeated here. Each module in the adaptive parameter identification and control device for a limited robot arm described above can be realized by software, hardware, or a combination thereof, in whole or in part. The above modules can be embedded in or independent of the processor in the computer device in hardware form, or stored in the memory in the computer device in software form, so as to be called and executed by the processor to perform the operations corresponding to each module.

[0261] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a non-volatile computer readable storage medium, and when executed, can include the processes of the above-mentioned embodiment methods. Any reference to memory, storage, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory or optical memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration but not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0262] Any combination of the technical features of the above embodiments can be made. In order to make the description simple, all possible combinations of the technical features in the above embodiments are not described, but as long as the combination of the technical features does not exist, it should be considered as the scope of the present application.

[0263] The above embodiments only express several implementation manners of the present application, and the description is more specific and detailed, but it should not be understood as a limitation on the scope of the patent. It should be pointed out that for those skilled in the art, without departing from the concept of the present application, some modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the patent of the present application should be subject to the appended claims.

Claims

1. A method for fixed-time adaptive parameter identification and control of a constrained robot, characterized in that, The method comprises: a dynamic model considering that a mechanical arm joint position tracking error is limited is constructed; current mechanical arm joint position and speed data are acquired, and the position and speed data are combined with historical data information of mechanical arm unknown parameter estimation error to design a parameter prediction error; a non-singular fast integral terminal sliding mode surface and an auxiliary variable are constructed, and a parameter update law is designed and calculated in combination with the parameter prediction error; a parameter estimation value is updated based on the parameter update law, and a fixed time control torque value based on the non-singular fast integral terminal sliding mode surface is calculated, so that the mechanical arm is driven to move along a predetermined trajectory through the control torque, and it is ensured that the mechanical arm joint position tracking error is always limited within a predetermined limit; when the system set time is not ended, the next time is the current time, the mechanical arm joint position and speed data are continuously acquired, and the above steps are repeated; the dynamic model considering that the mechanical arm joint position tracking error is limited is constructed by the following steps and methods: a mechanical arm dynamic model without considering that a joint position error is limited is established; the mechanical arm dynamic model without considering that the joint position error is limited is as follows: In the formula: represents the n-degree-of-freedom robot arm joint position vector, represents the positive definite inertia matrix, represents the centrifugal force and Coriolis force matrix, represents the viscous friction torque, represents the gravity torque, represents the control torque, respectively represent the robot arm joint position, velocity and acceleration; an error conversion function is designed; the error conversion function is designed as follows: wherein: is the tracking error e the first i element, is the mechanical arm joint position desired trajectory, and are both normal numbers; an asymmetric barrier function independent of initial conditions is designed, and derivation is performed thereon; the asymmetric barrier function independent of initial conditions is designed as follows: wherein: and are time-varying functions, t is time, satisfying ; derivation of the asymmetric barrier function is as follows: wherein: will be written as in compact form as: in the formula: the derivative of the error conversion function and the asymmetric barrier function independent of initial conditions is substituted into the mechanical arm dynamic model without considering that the joint position error is limited, to obtain a mechanical arm dynamic model considering that the joint position tracking error is limited; the mechanical arm dynamic model considering that the joint position tracking error is limited is as follows: in the formula: wherein: an arbitrary auxiliary vector for which the linear parameterization of the dynamics model holds, the derivative of the transpose of a dynamic regression matrix corresponding to the joint position tracking error of the robot arm after the restriction, the transpose of the transpose of an unknown parameter vector of the robot arm; the non-singular fast integral terminal sliding mode surface is calculated as follows: wherein s is a non-singular fast integral terminal sliding surface, are controller parameters, wherein: ; the fixed time control torque is calculated as follows: wherein, is the control torque, is the controller gain matrix, typically set as a positive definite diagonal matrix.

2. The method of claim 1, wherein, the designed asymmetric barrier function does not need to limit the initial error conditions of the system, and can achieve global control performance.

3. The method of claim 1, wherein the parameter prediction error is obtained by the following steps and methods: an improved excitation matrix is constructed; the improved excitation matrix is constructed as follows: wherein: to improve the excitation matrix, to improve the excitation matrix, is the time upper bound for the interval excitation condition to hold. a parameter prediction error is designed according to the improved excitation matrix; the parameter prediction error is designed as follows: where: is the parameter prediction error, is the unknown parameter estimation error defined as , is the estimate of the robot unknown parameter vector .

4. The method of claim 3, wherein the fixed-time adaptive parameter identification and control method for constrained robot arms is characterized by, the improved excitation matrix is obtained based on integral of a regression matrix of a mechanical arm model dynamics, and the regression matrix is obtained by linear parameterization processing of a mechanical arm dynamic model.

5. The method of claim 1, wherein the auxiliary variable is constructed as follows: wherein is the constructed auxiliary variable.

6. The fixed-time adaptive parameter identification and control method for constrained robot arms of claim 1, wherein, the parameter update law is calculated as follows: wherein , is the standard sign function, is an adaptive gain matrix, usually taken as a positive definite diagonal matrix, and are controller parameters satisfying , P is a projection operator, is the norm of a spherical range with radius is set as the bound of the unknown parameter vector of the robot arm, which can be calculated by the user according to the rough information of the model parameters of the robot arm obtained in advance, is the dynamic regression matrix corresponding to the constrained robot arm.

7. A constrained robot arm fixed-time adaptive parameter identification and control device, the device is used to implement the constrained robot arm fixed-time adaptive parameter identification and control method according to any one of claims 1 to 6, characterized in that, The device comprises: a modeling module: used for constructing a dynamic model considering that a mechanical arm joint position tracking error is limited; The processing and calculation module is used for obtaining position and speed data of current joints of the robot arm, combining the position and speed data with historical data information of unknown parameter estimation error of the robot arm, calculating parameter prediction error, constructing a non-singular fast integral terminal sliding mode surface and an auxiliary variable, combining the parameter prediction error, and calculating a parameter update law; the parameter update law is used for updating parameter estimation value, and then a fixed time control torque value based on the non-singular fast integral terminal sliding mode surface is calculated; The control module is used for controlling the robot arm to move according to a predetermined trajectory by a control torque, and ensuring that a joint position tracking error of the robot arm is always limited within a predetermined limit; The timing module is used for obtaining next time as current time when a system set time is not ended, and returning the processing and calculation module.

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