A high-precision trajectory control method for prescribed performance of a manipulator based on an improved hypertorsion expansion state observer

Abstract

The present invention discloses a method for high-precision trajectory control of a manipulator with specified performance based on an improved hypertorsion expansion state observer. The method comprises the following steps: establishing a dynamic model of an n-joint manipulator; re-describing the dynamic model of the n-joint manipulator as a dynamic model of the manipulator based on total disturbance; designing an improved hypertorsion expansion state observer to estimate the total disturbance in the dynamic model of the manipulator based on total disturbance; and constructing a recursive integral sliding mode controller based on funnel error transformation according to an equivalent control law, a switching control law, and a total disturbance estimate to achieve trajectory tracking of the manipulator. The present invention can effectively improve the convergence speed of the system, effectively suppress chattering in the system, and have good anti-interference performance.

Description

Technical Field

[0001] The present invention relates to a high-precision trajectory control method for a manipulator with prescribed performance based on an improved supertorsion expansion state observer, and belongs to the technical field of manipulator trajectory tracking. Background Art

[0002] Robotic arms are now widely used in various fields such as industry, medicine, and aviation. However, the robotic arm itself has characteristics such as strong coupling, nonlinearity, and uncertainty of some internal parameters. During operation, it is also affected by external disturbances such as time-varying disturbances and sudden disturbances. These problems will affect the control speed and accuracy of the robotic arm. Therefore, how to achieve fast and high-precision trajectory tracking control of the robotic arm system under the influence of these problems remains a huge challenge. Many scholars have proposed and improved various advanced control methods to achieve the desired control effect, such as fuzzy control, anti-disturbance control, adaptive control, model predictive control, sliding mode control, etc. Among them, sliding mode control provides a high-quality control solution for robot trajectory tracking control due to its inherent robustness and simple implementation.

[0003] Sliding mode control design involves both sliding surface design and reaching law design. Traditional linear sliding mode control suffers from uncertain convergence time, leading scholars to propose terminal sliding mode control, which can achieve system stability within a finite time. Furthermore, to address the potential singularity issues often associated with terminal sliding mode control, patent application CN117506908A discloses a non-singular terminal sliding mode control scheme for robotic arm trajectory control. This scheme avoids potential singularities by rationally adjusting the state variables of the sliding surface. However, its convergence rate slows as the system converges near an equilibrium point. To address the shortcomings of non-singular terminal sliding mode control, patent application CN117762020A discloses a fast non-singular terminal sliding mode control scheme, enhancing the rapidity of tracking error convergence and control accuracy. Furthermore, to address chattering issues that can arise in the designed sliding surface, patent application CN117826589A discloses an improved integral fast non-singular terminal sliding mode control scheme. By employing a saturation function as the switching function, this scheme ensures that the designed control law is continuous and smooth, effectively addressing chattering.

[0004] The above control method can improve the performance of the robot system, but it is still inevitably affected by the uncertainty of its internal parameters and external unknown disturbances. In order to deal with these unknown parameters, scholars have proposed various disturbance compensation strategies, among which the observer-based compensation strategy is widely used. Patent application CN113359447A designs an extended state observer to perform asymptotic estimation of multi-source disturbances. Patent application CN117970794A designs a nonlinear disturbance observer to realize the estimation of external disturbances and uncertainties of the system. However, the above observers lack the ability to suppress fast time-varying disturbances, so the design of observers for estimating time-varying disturbances and sudden disturbances is also particularly important. Summary of the Invention

[0005] The present invention provides a high-precision trajectory control method for a robotic arm with prescribed performance based on an improved super-torsion expansion state observer. By combining a disturbance observer, a new sliding surface and error conversion, the method can effectively suppress the system's chattering while ensuring rapid system convergence and has excellent anti-disturbance performance.

[0006] The technical solution of the present invention is:

[0007] A method for high-precision trajectory control of a manipulator with prescribed performance based on an improved hypertorsion expansion state observer comprises the following steps:

[0008] S1. Establish n Dynamic model of the joint robot arm; n The dynamic model of the joint manipulator is re-described as a dynamic model of the manipulator based on total disturbance;

[0009] S2. Design an improved hypertorsion expansion state observer to estimate the total disturbance in the dynamic model of the manipulator based on the total disturbance;

[0010] S3. According to the equivalent control law, switching control law and total disturbance estimation value, a recursive integral sliding mode controller based on funnel error transformation is constructed to realize the trajectory tracking of the robotic arm.

[0011] Furthermore, the dynamic model of the manipulator based on the total disturbance is expressed as:

[0012]

[0013] Among them, M0(q), G0(q) is M(q), The deterministic part of G(q); M(q) is the positive definite mass inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) represents the gravity matrix; τ is the control input torque; d is the total disturbance; q, and Represent the position, velocity and acceleration vectors of the robot arm respectively.

[0014] Furthermore, the S2 specifically includes:

[0015] Transforming the dynamic model of the manipulator based on the total disturbance to obtain a transformed dynamic model of the manipulator based on the total disturbance;

[0016] By introducing generalized momentum p to change the transformed dynamic model of the manipulator based on total disturbance, a dynamic model of the manipulator containing generalized momentum is obtained;

[0017] Introducing the intermediate variable τ into the manipulator dynamics model containing generalized momentum p , we get the transformed dynamic model of the manipulator containing generalized momentum;

[0018] An improved supertorsion expansion state observer is designed based on the transformed manipulator dynamics model containing generalized momentum to obtain the estimated values ​​of generalized momentum and total disturbance.

[0019] Furthermore, define is the estimated value of the generalized momentum p, is the estimated value of the total disturbance d, then the improved supertorsion expansion state observer is designed as:

[0020]

[0021] in, They are The first derivative of ω1 = 2ω0 and ω2 = ω0 2 is the parameter to be designed, ω0 is the bandwidth of the supertorsion expansion state observer; M0(q) is the deterministic part of M(q), where M(q) is the positive definite mass inertia matrix and q represents the position of the manipulator; is the estimation error of p, the nonlinear term Designed to:

[0022]

[0023] in,

[0024] Furthermore, the S3 specifically includes: defining the position tracking error and tracking error constraints; constructing a transformation function; defining the performance funnel boundary based on the transformation function and the tracking error constraints; constructing a non-smooth funnel error transformation based on the position tracking error and the performance funnel boundary; defining a non-singular terminal sliding mode function based on the non-smooth funnel error transformation; proposing a recursive integral sliding mode surface based on the non-singular terminal sliding mode function; setting the first-order derivative of the recursive integral sliding mode surface to zero to obtain an equivalent control law in the absence of total disturbance; designing a switching control law; constructing a recursive integral sliding mode controller based on the funnel error transformation based on the equivalent control law, the switching control law, and the total disturbance estimate.

[0025] Furthermore, the non-smooth funnel error transformation z(t) is specifically:

[0026]

[0027] Where k(t) is the performance funnel boundary; e(t) is the position tracking error.

[0028] Furthermore, by setting the first-order derivative of the recursive integral sliding surface to zero, we can obtain the equivalent control law u without total disturbance: eq for:

[0029]

[0030] Design switching control law u sw for:

[0031] u sw =-M0(q)Λ -1 [K4s+K5sig γ (s)]

[0032] Among them, M0(q), G0(q) is M(q), G(q) determines the part; M(q) is the positive mass inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) represents the gravity matrix; q, and Represent the position, velocity and acceleration vector of the robot arm respectively; q d is the desired position; q d The second derivative of is the first derivative of φ, k(t) is the performance funnel boundary, is the first-order derivative of k(t); e is the position tracking error, is the first derivative of e; α∈(0.5, 1); K1, K2, K3, K4, K5 are positive definite diagonal matrices; z is the non-smooth funnel error transformation; s is the recursive integral sliding surface; σ I is an intermediate variable; 0<γ<1, β>1.

[0033] Furthermore, the recursive integral sliding mode controller u based on funnel error transformation is designed as:

[0034]

[0035] Where u eq is the equivalent control law; u sw is the switching control law; is the estimated value of the total disturbance d.

[0036] The beneficial effects of the present invention are:

[0037] For a multi-degree-of-freedom serial manipulator system, the present invention designs a high-precision trajectory control method for the specified performance of the manipulator based on an improved hypertorque expansion state observer. Based on hypertorque technology and robot dynamics ideas, this method designs a hypertorque expansion state observer to estimate the total disturbance composed of external disturbances and internal uncertain parameters. The designed observer has only one adjustable parameter; the proposed non-smooth funnel error transformation can constrain the tracking error within a pre-designed range; simulation also further illustrates that the specified performance control method based on the new hypertorque expansion state observer and recursive terminal sliding surface proposed in the present invention can effectively reduce the system's convergence time and steady-state error, and effectively suppress the chattering phenomenon, while ensuring the convergence speed and control accuracy while also enhancing the robustness of the entire closed-loop system. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a control flow diagram of the present invention;

[0039] Figure 2 It is a schematic diagram of the position tracking effect of each joint of the two-degree-of-freedom manipulator according to the present invention under the composite signal;

[0040] Figure 3 It is a schematic diagram of the position tracking error convergence effect of each joint of the two-degree-of-freedom manipulator according to the present invention under the composite signal;

[0041] Figure 4 Schematic diagram of the control input effects of the joints of the robotic arm involved in the present invention;

[0042] Figure 5 This is a schematic diagram of the observation effect of the improved super-torsion expansion state observer involved in the present invention;

[0043] Figure 6This is a schematic diagram of the observation error effect of the improved super-torsion expansion state observer involved in the present invention. DETAILED DESCRIPTION

[0044] 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 with reference to the accompanying drawings. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other in any way.

[0045] Please refer to Figure 1-6 The present invention discloses a high-precision trajectory control method for a manipulator with specified performance based on an improved super-torsion expansion state observer, the method comprising the following steps:

[0046] S1. Establish a dynamic model of an n-joint robotic arm and initialize the initial conditions, sampling time, and parameters of the robotic arm system. The process of establishing the dynamic model of an n-joint robotic arm is as follows:

[0047] S1.1, let the desired n-joint serial robot end pose information be P, P∈R 4×4 , the end position information P is solved by the inverse kinematics of the manipulator into the expected position q of each joint d ,q d ∈R n That is q d =[q 1d ,q 2d ,…,q dn ] T , R n Represents an n-dimensional matrix; R 4×4 Indicates that the dimension of the matrix is ​​4×4;

[0048] S1.2. Establish the dynamic model of the n-joint serial robot arm:

[0049]

[0050] Among them, q, and Represent the position, velocity and acceleration vector of the manipulator respectively, M(q) is the positive mass inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) represents the gravity matrix, τ d represents the external disturbance, and τ is the control input torque.

[0051] In practical applications, due to factors such as modeling errors and physical parameter perturbations, the dynamic model of the n-joint serial robot arm always has uncertainty, so the following formula holds true:

[0052]

[0053] Among them, M0(q), G0(q) is M(q), The determining part of G(q), ΔM(q), ΔG(q) is M(q), The uncertainty of G(q).

[0054] The external disturbance τ d The sum of the uncertainty terms of the system is defined as the total disturbance d:

[0055]

[0056] Then, the dynamic model of the manipulator can be rewritten as the dynamic model of the manipulator based on the total disturbance:

[0057]

[0058] S2. Design an improved supertorsion expansion state observer as follows:

[0059] S2.1. Establishing the state space equation of the robotic arm

[0060] Define the state variable x1=q, Then the state space equation of the robotic arm can be expressed as:

[0061]

[0062] Where F(x1, x2) = -M0 -1 (x1)[C0(x1,x2)x2+G0(x1)].

[0063] In order to further design the observer, we define a new state variable x3 = M0 -1 (x1)d, then the state space equation of the manipulator can be transformed into:

[0064]

[0065] S2.2. Construction of the Improved Supertorsion Expansion State Observer STESO

[0066] In actual control, the angular velocity of the manipulator can be directly measured, but the angular acceleration is difficult to measure. Therefore, the observer design should avoid using the angular acceleration signal. In order to accurately estimate rapidly changing disturbances and improve the anti-interference ability of the manipulator system, a second-order hypertorsion extended state observer is designed in combination with hypertorsion technology as follows:

[0067]

[0068] in, is the estimated value of the state variable x2, express The first derivative of is the estimated value of the state variable x3, express The first derivative of , ; represents the estimation error of the state variable x2; ω1 = 2ω0 and ω2 = ω0 2 is the parameter to be designed, ω0 is the bandwidth of the supertorsion expansion state observer, which is used to adjust the parameters of the observer. and Designed to:

[0069]

[0070] Where,

[0071] In this way, the estimated value of the total disturbance d of the system is It can be expressed as:

[0072]

[0073] The above-mentioned STESO is designed by combining super-torsion technology. It only needs to select a suitable bandwidth ω0 to accurately estimate the total disturbance d of the system. It has the advantages of accurate observation and convenient parameter adjustment. However, in the process of designing the observer, it is necessary to calculate the inverse of the system inertia matrix M0 -1 (x1), involves the matrix inversion problem, which will bring a heavy computational burden to the multi-degree-of-freedom manipulator. Therefore, in order to avoid calculating M0 -1 (x1), the present invention designs an improved super-torsion expansion state observer STESO with a new arrangement form by rearranging equation (4) into a transformation equation with different state variables. The specific design method is as follows:

[0074] First, the dynamic model of the manipulator based on the total disturbance corresponding to equation (4) is transformed to obtain the transformed dynamic model of the manipulator based on the total disturbance, which is specifically:

[0075]

[0076] in,

[0077] Next, we change the left side of equation (10) by introducing the generalized momentum p and define the generalized momentum Transform Equation (10) to obtain the dynamic model of the manipulator containing generalized momentum, specifically:

[0078]

[0079] Furthermore, we introduce intermediate variables The transformed dynamic model of the manipulator containing generalized momentum can be obtained, specifically:

[0080]

[0081] In this way, the dynamic model of the rearranged robotic arm containing the new generalized momentum is designed.

[0082] definition is the estimated value of p, is the estimated value of d, then the improved supertorsion expansion state observer STESO can be designed as:

[0083]

[0084] in, is the estimation error of p, the nonlinear term Designed to:

[0085]

[0086] The improved supertorsion extended state observer (STESO) designed in this invention, as shown in Equation (13), introduces generalized momentum p. This allows for accurate and rapid estimation of the system's total disturbance without the need to calculate the inverse inertia matrix. Compared to the second-order supertorsion extended state observer shown in Equation (7), this simplifies the calculation process while ensuring observation performance, thereby improving its practical application value. Furthermore, the improved supertorsion extended state observer (STESO) uses a bandwidth-based parameter tuning method, which facilitates fair comparison with the traditional ESO.

[0087] The estimation error is defined as: Then, the estimation error system can be expressed as:

[0088]

[0089] Where, represents the estimation error of d, express The first derivative of express The first derivative of ;

[0090] Next, we analyze the stability of the estimation error system shown in equation (15). Construct the Lyapunov function V0:

[0091] V0=ζ T Hζ (16)

[0092] Where H is a positive definite symmetric matrix, Then the time derivative of ζ can be expressed as:

[0093]

[0094] in, represents the first-order derivative of d,

[0095] Pick Where θ> 0. If appropriate matrices R and S are selected, it can be guaranteed that Δ(ζ, γ)≥0 holds.

[0096] Through (16) and (17), the derivative of V0 can be obtained as:

[0097]

[0098] By selecting a suitable positive definite symmetric matrix H and coefficient κ, the following inequality holds:

[0099]

[0100] Then, (18) can be further transformed into:

[0101]

[0102] By V0=ζ T Hζ T You can get:

[0103] λ min {H}||ζ|| 2 ≤ζ T Hζ≤λ max {H}||ζ|| 2 (twenty one)

[0104] Among them, λ min {H} and λ max {H} are the minimum and maximum eigenvalues ​​of the matrix H, respectively, so we can get:

[0105]

[0106] Therefore (22) can be written as:

[0107]

[0108] According to the finite time lemma, we can determine that the estimation error system (15) is finite time stable. And the convergence time T DO satisfy:

[0109]

[0110] The above results indicate that the improved STESO of the present invention is stable for a limited time.

[0111] S3. Design of recursive integral sliding mode controller based on funnel error transformation, as follows:

[0112] S3.1. Design of a new non-smooth funnel error transformation

[0113] Define the position tracking error as:

[0114] e(t)=qq d (25)

[0115] Correspondingly, the velocity error and acceleration error are:

[0116]

[0117] From (4) and (26), the error dynamics after transformation can be obtained as:

[0118]

[0119] Furthermore, the control target of the manipulator can be converted into the control target of the tracking error, so the tracking error constraint is established, that is, the tracking error satisfies:

[0120] |e(t)|<ε,t≥T1 (28)

[0121] Among them, T1>0 and ε>0 are predetermined by the designer to quantify the convergence time and accuracy, respectively.

[0122] Based on the dynamic model of an n-joint serial manipulator, a novel non-smooth funnel surface error transformation is proposed, and a sliding mode controller based on the disturbance error transformation is used to complete the manipulator trajectory tracking. The specific steps are as follows:

[0123] First, construct a transformation function ξ(t) following the following rules:

[0124]

[0125] Select a transformation function that meets the above conditions:

[0126]

[0127] Furthermore, based on the transformation function and tracking error constraints, the performance funnel boundary k(t) is defined as:

[0128] k(t)=k0ξ(t)+ε (31)

[0129] Where k0 is a positive constant; ε is a parameter in the tracking error constraint;

[0130] On this basis, the non-smooth funnel error transformation z(t) is constructed based on the position tracking error and the performance funnel boundary:

[0131]

[0132] Taking the derivative of (32), we can get the first-order derivative of z(t):

[0133]

[0134] Among them, e is a function of time, that is,

[0135] Further deriving (33), we can get the second-order derivative of z(t):

[0136]

[0137] In order to avoid the potential singularity of Equation (32), when When it will cause Then Defined as:

[0138]

[0139] S3.2. Design of recursive integral sliding surface

[0140] Define a fast non-singular terminal sliding mode function σ:

[0141]

[0142] in, is the first derivative of z, z is a function of time, i.e. z(t); K1, K2 are positive definite diagonal matrices, β>1 is the parameter to be designed, sig β (·)=|·| β sign(·).

[0143] Next, based on the non-singular terminal sliding mode function, a recursive integral sliding mode surface s is proposed:

[0144]

[0145] Among them, K3 is a positive definite diagonal matrix, p1>q1>0 is a positive odd number; σ I is an intermediate variable.

[0146] Due to the nested structure of the recursive integral sliding surface, the proof of its stability can be divided into two stages:

[0147] The first stage: Prove that when s = 0, the sliding mode function σ can converge to zero in a finite time.

[0148] When s = 0, σ = -K3σ I , which shows that σ and σ I The convergence time of is the same. Through (37), the integral term can be equivalent to:

[0149]

[0150] Define the Lyapunov function Then the time derivative of V1 is:

[0151]

[0152] in, k 3i represents the i-th diagonal element of K3. According to the finite time theorem, when s=0, σ I Can converge to 0 in a finite time, σ I The convergence time satisfies:

[0153]

[0154] The second stage: Prove that when σ=0 in (36), the error transformation z can be I Converges to zero. When σ=0, (36) can be transformed into Define the Lyapunov function Then the time derivative of V2 is:

[0155]

[0156] Among them, k 1i represents the i-th diagonal element of K1, k 2i represents the i-th diagonal element of K2, z i represents the i-th element of z; According to the finite time theorem, the error transformation z can converge to 0 in a finite time, and the convergence time satisfies:

[0157]

[0158] In order to reduce the arrival time and improve the response speed of the system, the integral term σ I The initial conditions are designed to be:

[0159] σ I (0) = -K3 -1 σ(0) (43)

[0160] Where σ(0) represents the non-singular terminal sliding mode function at t=0; σ is a function of time, i.e., σ(t).

[0161] Substituting (43) into (37), we can obtain s(0) = 0, which means that under the condition that the initial time is 0, the system can be forced to start on the sliding surface, thereby reducing the arrival time and improving the transient performance of the system.

[0162] S3.3. Design of a recursive integral sliding mode controller based on funnel error transformation

[0163] First, let the first derivative of s be It can be obtained that in the absence of total disturbance, the equivalent control law u eq for:

[0164]

[0165] Furthermore, the switching control law u is designed sw for:

[0166] u sw =-M0(q)Λ -1 [K4s+K5sig γ (s)] (45)

[0167] Among them, K4 and K5 are positive definite diagonal matrices, 0<γ<1.

[0168] Therefore, the recursive integral sliding mode controller u based on funnel error transformation is designed as:

[0169]

[0170] where u eq and u sw Designed by (44)(45), The improved STESO designed above is used for estimation compensation.

[0171] The recursive integral sliding mode controller based on the funnel error transformation designed above is used as the input torque of the manipulator to realize the system position q to the desired position q d tracking to form a closed-loop system.

[0172] Then we analyze the stability of the entire closed-loop system and define the Lyapunov function:

[0173]

[0174] Taking the derivative of V3, we can get:

[0175]

[0176] Among them, k 4i represents the i-th diagonal element of K4, k 5i represents the i-th diagonal element of K5.

[0177] Since 0<γ<1, We can further obtain:

[0178]

[0179] Among them, L1>2n -1 λ min (K4), λ min (K4) represents the minimum eigenvalue of the diagonal matrix K4.

[0180] Before the improved STESO converges, the sliding surfaces s, d, and p will not escape in a finite time. And the above also proves that the error system (15) is finite time stable. It can be seen that when the improved STESO converges, can be reduced to:

[0181]

[0182] Among them, L3>2n -1 λ min (K4), According to the finite time stability theorem, it can be obtained that the sliding surface converges to zero in a finite time, and the convergence time satisfies:

[0183]

[0184] Based on the above, it can be determined that when s converges to zero, the error transform z will also converge to zero in a finite time.

[0185] Next, we prove that when e(0)<k(0), the tracking error e(t) can always be constrained within the performance funnel boundary k(t).

[0186] From (32), we can get the function of e(t) with respect to z(t):

[0187]

[0188] Since 0.5<α<1, we can get Therefore, it can be deduced that:

[0189]

[0190] From (52) and (53), it can be deduced that |e(t)| < k(t) holds true at any time t > 0. Therefore, it can be proved that the error transformation z(t) based on the non-smooth funnel surface can ensure that the position tracking error e(t) can always be constrained within the performance funnel boundary. Therefore, it can be proved that the entire closed-loop system is finite-time stable.

[0191] Example 2:

[0192] In order to verify the feasibility of the method described in Example 1, this example provides a control simulation experiment of the above control method on a two-degree-of-freedom robotic arm, and the specific parameters are set as follows:

[0193] The dynamic model of the two-degree-of-freedom manipulator is established as:

[0194]

[0195] Through modeling, the parameters of the two-degree-of-freedom manipulator are selected as follows: l1=l2=0.25m is the length of the link, m1=3.9kg is the mass of link 1, m2=5kg is the mass of joint 2 between links 1 and 2, m3=2.7kg is the mass of link 2, and m4=1.5kg is the mass of the end effector. The system matrix M(q) is G(q) is defined as:

[0196]

[0197] G(q)=0

[0198] The parameter selection is The variable is defined as c2=cos(q 12 ), s2=sin(q 12 ),q 11 ,q 12 Represent the actual positions of joints 1 and 2 respectively (joint 1 is the head end of link 1). The system uncertainty is defined as ΔM(q) = 0.2M(q), ΔG(q)=0.

[0199] The initial conditions of the robotic arm system are designed to be q = [0.2, 0.2] T ; The expected trajectory of the system is designed to be q d =[2sin(2t)+0.5sin(t),3sin(t)+sin(0.5t)] T ; External disturbance τ d=[2sin(0.5πt),2cos(0.5πt)] T The basic sampling time is set to 0.0001s.

[0200] The specific parameter designs of the control method of the present invention are as follows: the improved STESO design parameter is ω0=25; the non-smooth funnel error transformation parameters are selected as: T1=1, k0=0.6, ε=0.02, α=0.9; the sliding surface parameters are designed as: K1=diag{1,1}, K2=diag{0.5,0.5}, K3=diag{5,5}, β=1.5, p1=3, q1=5; the controller parameters are designed as: K4=diag{20,20}, K5=diag{5,5}, γ=0.7.

[0201] Substituting the above parameters into the dynamic model of the controller and the manipulator of the present invention, the simulation results are as follows: the position tracking response curve and the position tracking error response curve of the manipulator link 1 and 2 are as follows: Figure 2 and Figure 3 As shown; the control input response curves of the robot arm links 1 and 2 are as follows Figure 4 The improved STESO observation results and errors are shown in Figure 5 and Figure 6 shown.

[0202] pass Figure 2 and Figure 3 It can be seen that the high-precision trajectory control method for a robotic arm with specified performance based on the improved super-torsion expansion state observer proposed in the present invention still has good tracking performance in the presence of external disturbances and uncertain parameters within the system. At the same time, it can be seen that the tracking response speed is fast and the tracking error is small, indicating that the control method of the present invention has good control performance and anti-interference ability.

[0203] pass Figure 4 It can be seen that the control input torque of the robotic arm is smooth, which shows that the control method proposed in the present invention can effectively suppress chattering.

[0204] from Figure 5 and Figure 6 It can be seen that the estimation error of the improved supertorsion expansion state observer designed in the present invention can converge in a very short time and remain in a very small range, indicating that the observer of the present invention has good observation performance.

[0205] In summary, the high-precision trajectory control method for the specified performance of the robotic arm based on the improved super-torque expansion state observer can effectively improve the convergence speed of the system, effectively suppress the chattering phenomenon in the system, and has good anti-interference ability.

[0206] The specific embodiments of the present invention are described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made within the knowledge of ordinary technicians in this field without departing from the scope of the present invention.

Claims

1. A high-precision trajectory control method for a manipulator with specified performance based on an improved hypertorsion expansion state observer, characterized in that: The following steps are involved: S1. Establish the dynamic model of the n-joint robotic arm; The dynamic model of the n-joint manipulator is re-described as a dynamic model of the manipulator based on total disturbance; S2. Design an improved hypertorsion expansion state observer to estimate the total disturbance in the dynamic model of the manipulator based on the total disturbance; S3. Based on the equivalent control law, switching control law, and total disturbance estimation, a recursive integral sliding mode controller based on funnel error transformation is constructed to achieve trajectory tracking of the robotic arm. Said S2 specifically includes: Transforming the dynamic model of the manipulator based on the total disturbance to obtain a transformed dynamic model of the manipulator based on the total disturbance; By introducing generalized momentum p to change the transformed dynamic model of the manipulator based on total disturbance, a dynamic model of the manipulator containing generalized momentum is obtained; Introducing the intermediate variable τ into the manipulator dynamics model containing generalized momentum p , we get the transformed dynamic model of the manipulator containing generalized momentum; An improved supertorsion expansion state observer is designed based on the transformed manipulator dynamics model containing generalized momentum to obtain the estimated values ​​of generalized momentum and total disturbance. definition is the estimated value of the generalized momentum p, is the estimated value of the total disturbance d, then the improved supertorsion expansion state observer is designed as: in, They are The first derivative of ω1 = 2ω0 and ω2 = ω0 2 is the parameter to be designed, ω0 is the bandwidth of the supertorsion expansion state observer; M0(q) is the deterministic part of M(q), where M(q) is the positive definite mass inertia matrix and q represents the position of the manipulator; is the estimation error of p, the nonlinear term Designed to: in, The S3 specifically includes: Define position tracking error and tracking error constraints; Construct a transformation function; Define the performance funnel boundary based on the transformation function and tracking error constraints; Construct a non-smooth funnel error transform based on position tracking error and performance funnel boundary; Based on the non-smooth funnel error transformation, a non-singular terminal sliding mode function is defined; Based on the non-singular terminal sliding mode function, a recursive integral sliding mode surface is proposed; By setting the first-order derivative of the recursive integral sliding surface to zero, we can obtain the equivalent control law without total disturbance. Design switching control laws; According to the equivalent control law, switching control law and total disturbance estimation, a recursive integral sliding mode controller based on funnel error transformation is constructed; The non-smooth funnel error transformation z(t) is specifically: Where k(t) is the performance funnel boundary; e(t) is the position tracking error; Let the first-order derivative of the recursive integral sliding surface be zero, and the equivalent control law u is obtained without total disturbance eq for: Design switching control law u sw for: u sw =-M0(q)Λ -1 [K4s+K5sig γ (s)] Among them, M0(q), G0(q) is M(q), G(q) determines the part; M(q) is the positive mass inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) represents the gravity matrix; q, and Represent the position, velocity and acceleration vector of the robot arm respectively; q d is the desired position; q d The second derivative of is the first derivative of φ, k(t) is the performance funnel boundary, is the first-order derivative of k(t); e is the position tracking error, is the first derivative of e; α∈(0.5,1); K1, K2, K3, K4, K5 are positive definite diagonal matrices; z is the non-smooth funnel error transformation; s is the recursive integral sliding surface; σ I is an intermediate variable; 0<γ<1, β>1.

2. The method for high-precision trajectory control of a manipulator with specified performance based on an improved super-torque expansion state observer according to claim 1, characterized in that: The dynamic model of the manipulator based on total disturbance is expressed as: Among them, M0(q), G0(q) is M(q), The deterministic part of G(q); M(q) is the positive definite mass inertia matrix, is the Coriolis force and centrifugal force matrix, G(q) represents the gravity matrix; τ is the control input torque; d is the total disturbance; q, and Represent the position, velocity and acceleration vectors of the robot arm respectively.

3. The method for high-precision trajectory control of a manipulator with specified performance based on an improved super-torque expansion state observer according to claim 1, characterized in that: The recursive integral sliding mode controller u based on funnel error transformation is designed as follows: Where u eq is the equivalent control law; u sw is the switching control law; is the estimated value of the total disturbance d.

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