Adaptive Robust Control Method for Hydraulic Manipulator Based on Nonlinear State Observation

Abstract

The present invention discloses an adaptive robust control method for a hydraulic manipulator based on non - linear state observation. The parameter estimation value of the dynamic parameters is input into the intermediate conversion state quantity model to output the intermediate conversion state quantity. The non - linear state observer performs observation to output the observed state and obtains the estimated value of the joint angular velocity. The estimated value of the joint angular velocity and the target trajectory are input, and the control signal of the spool displacement is output to control the operation of the multi - joint hydraulic manipulator. The tracking error is obtained and output to the adaptive robust control law. The above steps are repeated while the non - linear state observer is self - updated, and finally, the adaptive robust control is realized. The method of the present invention realizes the real - time observation of the unmeasurable state based on the uncertainty of the model parameters, solves the situation where the feedback state is unmeasurable due to sensor limitations in actual situations, and while ensuring the overall stability of the control system and the observation system, reduces the tracking error at the end of the manipulator and improves the control performance.

Description

Technical Field

[0001] The present invention relates to a hydraulic manipulator adaptive robust control method, and particularly to a hydraulic manipulator adaptive robust control method based on non-linear state observation. Background Art

[0002] Hydraulic manipulators are usually applied to harsh operation tasks such as heavy loads. However, with the development of industry and the continuous progress of human exploration, the complexity of the operation tasks of hydraulic manipulators has been increasing continuously, and the requirements for operation accuracy have also been rising. The traditional proportional-integral-differential (PID) control gradually fails to meet the high control performance requirements because it does not consider factors such as uncertain parameters of the manipulator dynamics model. In this case, developing a full-state feedback controller based on the dynamics model of a multi-joint hydraulic manipulator is an effective solution. On the other hand, the working conditions of multi-joint hydraulic manipulators have become increasingly harsh. In most practical applications, for safety and reliability considerations, hydraulic manipulators are only equipped with position sensors with low accuracy. This results in large noise in the measurement signals and the inability to perform other state measurements, especially speed measurements. The current common method for obtaining speed signals is to differentiate the position signal and use a low-pass filter. However, the presence of the low-pass filter seriously affects the closed-loop bandwidth of the system, thus limiting the control performance of multi-joint hydraulic manipulators. Therefore, existing controllers are difficult to comprehensively consider problems such as uncertain parameters of the multi-joint hydraulic manipulator dynamics model and unmeasurable states in a harsh and complex operation environment, resulting in difficulty in ensuring good control accuracy at the end of the manipulator and affecting the operation performance in specific scenarios. Summary of the Invention

[0003] In order to solve the problems in the background art, the present invention provides a hydraulic manipulator adaptive robust control method based on non-linear state observation, which improves the end control accuracy under the conditions of uncertain parameters of the multi-joint hydraulic manipulator dynamics model and unmeasurable feedback states, and while ensuring the overall stability of the control system and the observation system, reduces the end tracking error of the manipulator and enhances the control performance.

[0004] The technical solution adopted by the present invention is as follows:

[0005] The hydraulic manipulator adaptive robust control method of the present invention includes the following steps:

[0006] Step 1: Comprehensively considering the hydraulic characteristics and multi-degree-of-freedom coupling characteristics, establish a non-linear dynamics model of a multi-joint hydraulic manipulator under the constraint of the dynamics model; design an intermediate conversion state quantity model for the unmeasurable states of the multi-joint hydraulic manipulator and its non-linear state space, and establish a non-linear state observer using the non-linear state observation method according to the non-linear state space.

[0007] Step 2: Input the parameter estimation values of the dynamic parameters of the non-linear dynamic model into the intermediate conversion state quantity model. The intermediate conversion state quantity model outputs the intermediate conversion state quantity. The non-linear state observer observes the intermediate conversion state quantity and outputs the observed state of the intermediate conversion state quantity. An estimated value of the joint angular velocity of the multi-joint hydraulic manipulator is obtained based on the observed state of the intermediate conversion state quantity.

[0008] Step 3: Design an adaptive robust control law using the adaptive robust control method based on the non-linear dynamic model and the non-linear state observer.

[0009] Step 4: The non-linear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator to the adaptive robust control law. At the same time, the target trajectory of the multi-joint hydraulic manipulator is input into the adaptive robust control law. The adaptive robust control law outputs a control signal for the spool displacement of the multi-joint hydraulic manipulator to control the operation of the multi-joint hydraulic manipulator. The tracking error is calculated based on the target trajectory of the multi-joint hydraulic manipulator and the joint angles actually output during operation and output to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation values of the dynamic parameters of the non-linear dynamic model to the intermediate conversion state quantity model and repeats Step 2 and Step 4. At the same time, the non-linear state observer performs self-update, ultimately achieving the adaptive robust control of the multi-joint hydraulic manipulator.

[0010] In the above-mentioned Step 1, the established non-linear dynamic model of the multi-joint hydraulic manipulator is specifically as follows:

[0011] a) Link dynamics model:

[0012]

[0013] τ j =J j (q)P L

[0014] P L =A i P i -A o P o

[0015]

[0016] where q, and respectively represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, q, n represents the number of joints of the multi-joint hydraulic manipulator; M j (), C j () and G j( ) represent the inertia dynamics matrix, Coriolis force matrix, and gravity matrix of the multi-joint hydraulic manipulator, respectively, \(M\) j ( ), \(C\) j ( ), \(G\) j () ∈ ℝ n×n ; \(τ\) j represents the driving torque of each joint of the multi-joint hydraulic manipulator, \(τ\) j ∈ ℝ n ; \(J\) j () represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic manipulator; \(P\) L represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, \(P\) L ∈ ℝ n ; \(A\) i and \(A\) o respectively represent the oil inlet chamber and oil return chamber contact areas of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, \(A\) i , \(A\) o ∈ ℝ n×n ; \(P\) i and \(P\) o respectively represent the oil inlet chamber and oil return chamber oil pressures of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, \(P\) i , \(P\) o ∈ ℝ n ; \(l\) represents the elongation of the hydraulic cylinder push rod of each joint of the multi-joint hydraulic manipulator, \(l ∈ ℝ\) n ; The dynamics matrix is skew-symmetric.

[0017] By setting the dynamic parameters \(θ\) of the appropriate link dynamics model m , the link dynamics model can be linearized into the following form:

[0018]

[0019] where, represents the regression matrix of the dynamic parameter \(θ\) of the link dynamics model m .

[0020] b) Considering the hydraulic drive characteristics, a hydraulic dynamics model is established on the premise of assuming no leakage of the hydraulic cylinder:

[0021]

[0022] \(V\) i = \(V\) hi + \(A\) i diag[\(l\)]

[0023] \(V\) o = \(V\) ho - \(A\) o diag[\(l\)]

[0024]

[0025] Among them, V i and V o respectively represent the volumes of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator. V i and V o ∈R n×n ; β e represents the bulk modulus of the hydraulic oil; V hi and V ho respectively represent the volumes of the oil inlet chamber and the oil return chamber of the respective hydraulic cylinders of the respective drive devices in the initial case where the push rod elongation l = 0 of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator; diag[·] represents a diagonal matrix with · as the main element; Q i and Q o respectively represent the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator. Q id and Q od respectively represent the preset ideal flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator. Q id and Q od ∈R n , and respectively represent the calculable flow rate differences of the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator, and respectively represent the non-calculable flow rate differences of the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator, and respectively characterize the flow rate differences between the actual flow rate and the ideal flow rate; k qi and k qo respectively represent the flow rate gain constants of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator; x v represents the spool displacement of the hydraulic control valve of the respective joints of the multi-joint hydraulic manipulator; g1() represents the non-linear conversion function between the oil inlet pressure P i of the oil inlet chamber of the hydraulic cylinder of the respective joints of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve, and g2() represents the non-linear conversion function between the oil return pressure P o of the oil return chamber of the hydraulic cylinder of the respective joints of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve. g1() and g2() ∈R n×n .

[0026] Specifically, g1() and g2() are as follows:

[0027]

[0028] Among them, P s is the supply pressure of the hydraulic pump, and P r is the reference pressure of the hydraulic return oil tank.

[0029] By setting the dynamic parameter θ p of the appropriate hydraulic dynamic model, the hydraulic dynamic model can be linearized into the following form:

[0030]

[0031] Among them, represents the regression matrix of the dynamic parameter θ p of the hydraulic dynamic model.

[0032] The constraints of the dynamic model are specifically as follows:

[0033] |Δ j |≤δ j

[0034] θ∈{θ:θ min ≤θ≤θ max}

[0035] Among them, Δ j represents the uncertain nonlinearity and interference during the movement of the multi-joint hydraulic manipulator, and Δ j ∈R n ; δ j represents the preset constant vector; θ max and θ min respectively represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model, and θ = [θ m ; θ p .

[0036] The spool displacement x v of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator is specifically as follows:

[0037]

[0038] Among them, Q L represents the equivalent flow rate of the hydraulic cylinder chamber, and Q L ∈R n .

[0039] In the first step mentioned above, the intermediate conversion state quantity model of the unmeasurable state of the designed multi-joint hydraulic manipulator is specifically as follows:

[0040] s = [s1; s2; s3]

[0041] s1 = q

[0042]

[0043] Among them, s represents the intermediate conversion state quantity, and s1, s2, and s3 respectively represent the first, second, and third state quantities of the intermediate conversion state quantity s; q and respectively represent the joint angle and joint angular velocity of the multi-joint hydraulic manipulator; and respectively represent the first and second elements of the link dynamic parameter θ of the link dynamics model m ; M j and C j respectively represent the inertia dynamics matrix and Coriolis force matrix of the multi-joint hydraulic manipulator, and I represents the identity matrix; f1 and f2 respectively represent the simplified first and second equal matrixes of the intermediate conversion state quantity s; θ represents the dynamic parameter of the nonlinear dynamics model, represents the parameter estimation value of the dynamic parameter θ of the nonlinear dynamics model, represents the parameter adaptive error of the dynamic parameter θ of the nonlinear dynamics model.

[0044] The joint angular velocity of the multi-joint hydraulic manipulator is the unmeasurable state of the multi-joint hydraulic manipulator.

[0045] In the first step mentioned above, the nonlinear state space is specifically as follows:

[0046]

[0047] Among them, and respectively represent the differentials of the first state quantity s1, the second state quantity s2, and the third state quantity s3 of the intermediate conversion state quantity s; represents the third element of the link dynamic parameter θ of the link dynamics model m ; Δ j represents the uncertain nonlinearity and interference during the movement of the multi-joint hydraulic manipulator; and respectively represent the first and second elements of the hydraulic dynamic parameter θ of the hydraulic dynamics model p ; f3, f4, and f5 respectively represent the simplified third, fourth, and fifth equal matrixes of the intermediate conversion state quantity s; u v represents the control voltage actually output by the adaptive robust control law, u v = k v x v , u v ∈R n , xv denotes the spool displacement of the hydraulic control valve for each joint of the multi-joint hydraulic manipulator, k v denotes the conversion ratio coefficient.

[0048] The simplified first to fifth equal matrices of the intermediate conversion state quantity s are specifically as follows:

[0049] f1 = J j P L

[0050]

[0051] f3 = J j V i -1 A i

[0052] f4 = J j V o -1 A o

[0053] f5 = J j (V i -1 A i k qi g1 + V o -1 A o k qo g2)k v

[0054] In the first step described above, the nonlinear state observer is specifically as follows:

[0055]

[0056] Among them, denotes the observed state of the intermediate conversion state quantity s, and respectively denote the observed values of the first intermediate conversion state quantity s1, the second intermediate conversion state quantity s2, and the third intermediate conversion state quantity s3 of the joint angular velocity of the multi-joint hydraulic manipulator; and respectively denote the second and third elements of the first observer coefficient ε1 in the first observer coefficient matrix ε i of the nonlinear state observer, and respectively denote the second and third elements of the second observer coefficient ε2 in the first observer coefficient matrix ε i of the nonlinear state observer, and respectively represent the first observer coefficient matrix ε of the nonlinear state observer i the second and third elements of the third observer coefficient ε3 in i = 1, 2, 3; and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i the second and third elements of the first observer coefficient φ1 in and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i the second and third elements of the second observer coefficient φ2 in and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i the second and third elements of the third observer coefficient φ3 in the first and second observer coefficient matrices are related to the uncertain dynamic model parameters θ m and θ p ; and respectively represent the observed values of the first, second, and third elements of the link dynamic parameter θ m of the link dynamic model; and respectively represent the observed values of the first and second elements of the hydraulic dynamic parameter θ p of the hydraulic dynamic model; v2 and v3 respectively represent the second and third observer adaptive characterization parameters; n represents the number of joints of the multi-joint hydraulic manipulator.

[0057] Regarding the observed state of the intermediate conversion state quantity s the third observer adaptive characterization parameter v3 in is used as the estimated value of the joint angular velocity

[0058] In the third step described above, the designed adaptive robust control law is specifically as follows:

[0059] a) First-order adaptive robust control law v 3d :

[0060] v 3d = v 3da + v 3dr + v 3ds

[0061]

[0062] wherein, v 3da represents the first-order adaptive model compensation control law, v 3drrepresents a first-order linear robust control law, v 3ds represents a first-order nonlinear robust control law; z2 represents the angle conversion error of the multi-joint hydraulic manipulator, z1 and respectively represent the joint angle tracking error and its differential of the multi-joint hydraulic manipulator, z1 = q - q d , q d represents the control target value of each joint angle of the multi-joint hydraulic manipulator, that is, the target trajectory of the multi-joint hydraulic manipulator. The establishment purpose of the angle conversion error z2 is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is less than or equal to zero, so that the overall nonlinear robust controller maintains stability; k1 and k2 respectively represent the first and second gain positive definite diagonal matrices. k1 and k2 ensure that the differential of the Lyapunov control function of the first-order adaptive robust control law in the nonlinear robust controller is less than or equal to zero, so that the entire nonlinear robust controller maintains stability; and respectively represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator; θ 1min represents the minimum value of the model parameter θ1 of the nonlinear dynamic model of the multi-joint hydraulic manipulator; the first-order nonlinear robust control law v 3ds is divided into two parts, v 3ds1 and v 3ds2 respectively represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v 3d ; represents the link dynamic parameter θ of the link dynamic model m of the first element; represents the second parameter regression matrix; represents the link dynamic parameter θ of the link dynamic model m of the parameter adaptive error; and ∈2 respectively represent the first, second and third preset design parameters; z ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ ob represents the observer error integration.

[0063] Considering that there are still uncertain nonlinear factors in the nonlinear dynamic model of the link manipulator, it is necessary to compensate for this part of the influencing factors. As the uncertainty compensation parameter, the first-order nonlinear robust control law v 3ds cannot be written as a specific formula expression. The first-order nonlinear robust control law v 3ds that meets the conditions can ensure the first-order adaptive robust control law v 3dIt can maintain good control performance in the presence of parameter uncertainties and uncertain non - linearities.

[0064] The first - order adaptive robust control law \(v\) 3d is calculated as follows:

[0065] The joint - angle tracking error \(z_1\) of the multi - joint hydraulic manipulator is as follows:

[0066] \(z_1 = q-\hat{q}\) d

[0067] where \(q\) represents the actual measured value of each joint angle of the multi - joint hydraulic manipulator.

[0068] The angle conversion error \(z_2\) of the multi - joint hydraulic manipulator is as follows:

[0069]

[0070] Differentiating the above formula, we can get the following form:

[0071]

[0072] where represents the differential of the angle conversion error \(z_2\) of the multi - joint hydraulic manipulator; represents the second - order differential of the joint - angle tracking error \(z_1\) of the multi - joint hydraulic manipulator.

[0073] The unmeasurable velocity state and the acceleration state can be expressed in the following form:

[0074]

[0075] Combining the above formulas, we can obtain the following equation:

[0076]

[0077] Because only \(v_3\) in the above formula contains the high - order term \(Q\) of the non - linear dynamic model of the link manipulator L , so based on the idea of order reduction, using the backstepping method, a first - order adaptive robust control law \(v\) 3d is proposed as the linear robust control law of the multi - joint hydraulic manipulator, which can reduce the joint - angle tracking error while ensuring the transient performance of the system.

[0078] b) Based on the first - order adaptive robust control law \(v\) 3d , use the backstepping method to establish the second - order adaptive robust control law \(Q\) Ld :

[0079] \(Q\) Ld \(=Q\) Lda \(+\Delta Q\)Ldr +Q Lds

[0080]

[0081] Q Ldr =-k 3r z3

[0082] Q Lds =Q Lds1 +Q Lds2

[0083]

[0084] where Q Lda represents the second-order adaptive model compensation control law, Q Ldr represents the second-order linear robust control law, Q Lds represents the second-order nonlinear robust control law; ω2 and ω3 respectively represent the preset proportional balance constants of the first-order adaptive robust control law v 3d and the second-order adaptive robust control law Q Ld ; represents the estimated value of the angle conversion error z2 of the multi-joint hydraulic manipulator; k ob1 represents the first-order observer gain; v1 represents the first observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v 3d ; k 3r represents the third gain positive definite diagonal matrix to ensure the stability of the designed controller; z3 represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z3 = v3 - v 3d ; the second-order nonlinear robust control law Q Lds is divided into two parts, Q Lds1 and Q Lds2 represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of the second-order nonlinear robust control law Q Lds respectively; represents the third parameter regression matrix; represents the parameter adaptive error of the dynamic parameter θ of the nonlinear dynamic model; and ∈3 respectively represent the fourth, fifth, and sixth preset design parameters.

[0085] Take the second-order adaptive robust control law Q Ld as the nonlinear robust control law of the multi-joint hydraulic manipulator. The calculation process of the second-order adaptive robust control law Q Ld is as follows:

[0086] The equivalent flow tracking error z3 of the multi-joint hydraulic manipulator is as follows:

[0087] z3 = v3 - v 3d

[0088] Differentiating both sides of the above equation gives the following:

[0089]

[0090] where, represents the differential of the equivalent flow tracking error z3 of the multi-joint hydraulic manipulator, represents the differential of the third observer adaptive characterization parameter v3; represents the differential of the first-order adaptive robust control law v 3d .

[0091] According to the design result of the first-order adaptive robust control law v 3d and the properties of the observer, v 3d is a function of the joint angle q, time t, observer parameters η, φ1, φ2, φ3, and the parameter estimation value . Therefore, the differential form of the first-order adaptive robust control law v 3d is as follows:

[0092]

[0093] where, v 3dc and represent the computable part of v 3d and its differential respectively, v 3du and represent the non-computable part of v 3d and its differential respectively; η and represent the observer parameters of the nonlinear state observer and their differentials respectively; and represent the parameter estimation value of the dynamic parameter θ of the nonlinear dynamic model and its differential respectively.

[0094] is the linear regression matrix, specifically as follows:

[0095]

[0096] Construct the auxiliary positive semi-definite matrix V as:

[0097]

[0098] Differentiating both sides of the above equation and substituting the first-order adaptive robust control law v 3d gives the following form:

[0099]

[0100] Among them, represents the differential of the auxiliary positive semi - definite matrix V.

[0101] Based on the above formula, a second - order adaptive robust control law Q Ld is proposed to reduce the tracking error of each joint angle while ensuring the transient performance of the system.

[0102] c) Considering the model parameter uncertainty in the overall dynamic model of the hydraulic manipulator, a parameter adaptive law is constructed for compensation. The parameter adaptive law:

[0103]

[0104] Among them, represents the differential of the estimated value of the link dynamic parameter θ m of the link dynamic model; τ2 and τ3 represent the first - order and second - order model parameter adaptive reference values respectively; represents the differential of the estimated value of the dynamic parameter θ of the non - linear dynamic model; represents the parameter estimated value of the dynamic parameter θ of the non - linear dynamic model of the adaptive mapping function; Γ c represents the parameter adaptive gain coefficient matrix, Γ c =[Γ m ; Γ p , Γ m and Γ p represent the first and second elements of the parameter adaptive gain coefficient matrix Γ c respectively.

[0105] The parameter estimated value of the dynamic parameter θ of the non - linear dynamic model of the adaptive mapping function is specifically as follows:

[0106]

[0107] Among them, x represents the input parameter of the adaptive mapping function.

[0108] The second parameter regression matrix is specifically as follows:

[0109]

[0110] Among them, k e represents the tracking error gain parameter.

[0111] The third parameter regression matrix is specifically as follows:

[0112]

[0113] Among them, represents the estimated value of the model parameter θ1 of the nonlinear dynamic model of the multi-joint hydraulic manipulator; represents the linear regression matrix.

[0114] The said linear regression matrix is specifically as follows:

[0115]

[0116] In the said step 4, the nonlinear state observer performs self-update, specifically, for the first observer coefficient matrix ε of the nonlinear state observer i , the second observer coefficient matrix φ i and the observer adaptive characterization parameter matrix v are self-updated at their respective self-update rates, specifically as follows:

[0117]

[0118] where, v = [v1; v2; v3]; and respectively represent the self-update rates of the first observer coefficient ε1, the second observer coefficient ε2, and the third observer coefficient ε3 in the first observer coefficient matrix ε of the nonlinear state observer i ; A ob and K ob respectively represent the first and second gain coefficient matrices of the nonlinear state observer; y and y ob respectively represent the theoretical and actual outputs of the observer; e1, e2, and e3 respectively represent the first, second, and third dimension characterization parameters, e1 = [1; 0; 0], e2 = [0; 1; 0], e3 = [0; 0; 1]; represents the self-update rate of the observer adaptive characterization parameter matrix v; Q L represents the equivalent flow rate of the hydraulic cylinder chamber; and respectively represent the self-update rates of the first observer coefficient φ1, the second observer coefficient φ2, and the third observer coefficient φ3 in the second observer coefficient matrix φ of the nonlinear state observer i .

[0119] The first gain coefficient matrix A ob and the second gain coefficient matrix K ob of the said nonlinear state observer are specifically as follows:

[0120]

[0121] Λ = Λ T > 0

[0122] Among them, respectively represent the 1st, 2nd, …, i-th, …, n-th elements in the first gain coefficient matrix A ob ; respectively represent the 1st, 2nd, …, i-th, …, n-th elements in the second gain coefficient matrix K ob ; and respectively represent the first, second, and third gain parameters of the observer; Λ represents a positive semi - definite matrix; I represents an identity matrix.

[0123] The beneficial effects of the present invention are as follows:

[0124] 1. By constructing the intermediate state observable and designing the non - linear state observer, the present invention realizes the real - time observation of the unmeasurable state based on the uncertain model parameters of the multi - joint hydraulic manipulator, and solves the problem of the unmeasurable feedback state caused by sensor limitations in actual situations.

[0125] 2. The present invention proposes an adaptive robust control method for the multi - joint hydraulic manipulator based on the unmeasurable state observation value. While ensuring the overall stability of the control system and the observation system, it reduces the tracking error at the end of the manipulator and improves the control performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0126] Figure 1 is the system block diagram of the method of the present invention;

[0127] Figure 2 is the hydraulic drive system diagram of the multi - joint hydraulic manipulator of the present invention;

[0128] Figure 3 is the structure diagram of the manipulator control object instance of the present invention;

[0129] Figure 4 is the diagram of the hydraulic manipulator joint angle sensor signal and the differential filtering result used in the present invention;

[0130] Figure 5 is the comparison diagram of the control effects between the adaptive robust controller for the multi - joint hydraulic manipulator based on non - linear state observation designed in the present invention and the traditional PID controller; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0131] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the drawings and embodiments. The specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0132] Such as Figure 1As shown in the figure, the adaptive robust control method for the hydraulic manipulator of the present invention includes the following steps:

[0133] Step 1: Considering the hydraulic characteristics and multi-degree-of-freedom coupling characteristics comprehensively, establish a nonlinear dynamic model of the multi-joint hydraulic manipulator under the constraint of the dynamic model; design an intermediate conversion state quantity model and its nonlinear state space for the unmeasurable state of the multi-joint hydraulic manipulator, and establish a nonlinear state observer according to the nonlinear state space using the nonlinear state observation method.

[0134] In Step 1, the specific nonlinear dynamic model of the multi-joint hydraulic manipulator established is as follows:

[0135] a) Link dynamics model:

[0136]

[0137] τ j =J j (q)P L

[0138] P L =A i P i -A o P o

[0139]

[0140] Among them, q, and respectively represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, q, n represents the number of joints of the multi-joint hydraulic manipulator; M j (), C j () and G j () respectively represent the inertial dynamics matrix, Coriolis force matrix and gravity matrix of the multi-joint hydraulic manipulator, M j (), C j (), G j ()∈R n×n ; τ j represents the driving torque of each joint of the multi-joint hydraulic manipulator, τ j ∈R n ; J j () represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic manipulator; P L represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, P L ∈R n ; A i and A orespectively represent the contact areas of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, A i 、A o ∈R n×n ;P i and P o respectively represent the oil pressures of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, P i 、P o ∈R n ;l represents the elongation of the push rod of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, l ∈ R n ;The dynamic matrix is skew-symmetric.

[0141] By setting the dynamic parameters θ m of the appropriate link dynamic model, the link dynamic model can be linearized into the following form:

[0142]

[0143] Among them, represents the regression matrix of the dynamic parameter θ m of the link dynamic model.

[0144] b) Considering the hydraulic drive characteristics, a hydraulic dynamic model is established on the premise of assuming no leakage of the hydraulic cylinder:

[0145]

[0146] V i =V hi +A i diag[l]

[0147] V o =V ho -A o diag[l]

[0148]

[0149] Among them, V i and V o respectively represent the volumes of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, V i 、V o ∈R n×n ;β e represents the bulk modulus of the hydraulic oil; V hi and V ho respectively represent the volumes of the oil inlet chamber and the oil return chamber of each hydraulic cylinder of each drive device in the initial case where the elongation l of the push rod of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator is 0; diag[·] represents a diagonal matrix with · as the main element; Qi and Q o respectively represent the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator. Q id and Q od respectively represent the preset ideal flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator. Q id 、Q od ∈R n ,Q iΔ and Q oΔ respectively represent the calculable flow rate differences between the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator, and respectively represent the incalculable flow rate differences between the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator, and respectively characterize the flow rate differences between the actual flow rate and the ideal flow rate; k qi and k qo respectively represent the flow rate gain constants of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of the respective joints of the multi-joint hydraulic manipulator; x v represents the spool displacement of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator; g1() represents the oil inlet pressure P i of the oil inlet chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve, and g2() represents the oil return pressure P o of the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve, g1(), g2() ∈ R n×n .

[0150] g1() and g2() are specifically as follows:

[0151]

[0152] Among them, P s is the supply pressure of the hydraulic pump, and P r is the reference pressure of the hydraulic oil return tank.

[0153] By setting the dynamic parameters θ p of the appropriate hydraulic dynamics model, the hydraulic dynamics model can be linearized into the following form:

[0154]

[0155] Among them, represents the regression matrix of the dynamic parameters θ p of the hydraulic dynamics model.

[0156] The constraints of the dynamic model are as follows:

[0157] |Δ j |≤δ j

[0158] θ∈{θ:θ min ≤θ≤θ max}

[0159] Among them, Δ j represents the uncertain nonlinearity and interference during the movement of the multi-joint hydraulic manipulator. Δ j ∈R n ; δ j represents a preset constant vector; θ max and θ min respectively represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model. θ = [θ m ; θ p .

[0160] The spool displacement x v of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator is as follows:

[0161] x v =(V i -1 A i k qi g1+V o -1 A o k qo g2) -1 Q L

[0162]

[0163] Among them, Q L represents the equivalent flow rate of the hydraulic cylinder chamber. Q L ∈R n .

[0164] In step one, the intermediate conversion state quantity model of the unmeasurable state of the designed multi-joint hydraulic manipulator is as follows:

[0165] s = [s1; s2; s3]

[0166] s1 = q

[0167]

[0168] Among them, s represents the intermediate conversion state quantity, and s1, s2, and s3 respectively represent the first, second, and third state quantities of the intermediate conversion state quantity s; q and respectively represent the joint angles and joint angular velocities of the multi-joint hydraulic manipulator; and respectively represent the first and second elements of the link dynamic parameter θ of the link dynamic model m ; M j and C j respectively represent the inertia dynamic matrix and Coriolis force matrix of the multi-joint hydraulic manipulator, I represents the identity matrix; f1 and f2 respectively represent the simplified first and second equal matrices of the intermediate conversion state quantity s; θ represents the dynamic parameter of the non-linear dynamic model, represents the parameter estimate value of the dynamic parameter θ of the non-linear dynamic model, represents the parameter adaptive error of the dynamic parameter θ of the non-linear dynamic model.

[0169] The joint angular velocity of the multi-joint hydraulic manipulator is the unmeasurable state of the multi-joint hydraulic manipulator.

[0170] In step one, the non-linear state space is as follows:

[0171]

[0172] where, and respectively represent the differentials of the first state quantity s1, the second state quantity s2, and the third state quantity s3 of the intermediate conversion state quantity s; represents the third element of the link dynamic parameter θ of the link dynamic model m ; Δ j represents the uncertain non-linearity and interference during the movement of the multi-joint hydraulic manipulator; and respectively represent the first and second elements of the hydraulic dynamic parameter θ of the hydraulic dynamic model p ; f3, f4, and f5 respectively represent the simplified third, fourth, and fifth equal matrices of the intermediate conversion state quantity s; u v represents the control voltage actually output by the adaptive robust control law, u v = k v x v , u v ∈R n , x v represents the spool displacement of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator, k v represents the conversion ratio coefficient.

[0173] The simplified first-fifth equal matrices of the intermediate conversion state quantity s are as follows:

[0174] f1 = J j P L

[0175]

[0176] f3 = J j V i -1 A i

[0177] f4 = J j V o -1 A o

[0178] f5 = J j (V i -1 A i k qi g1 + V o -1 A o k qo g2)0k v

[0179] In step one, the nonlinear state observer is as follows:

[0180]

[0181] Among them, represents the observed state of the intermediate conversion state quantity s, and respectively represent the observed values of the first intermediate conversion state quantity s1, the second intermediate conversion state quantity s2, and the third intermediate conversion state quantity s3 of the joint angular velocity of the multi-joint hydraulic manipulator; and respectively represent the second and third elements of the first observer coefficient ε1 in the first observer coefficient matrix ε i of the nonlinear state observer, and respectively represent the second and third elements of the second observer coefficient ε2 in the first observer coefficient matrix ε i of the nonlinear state observer, and respectively represent the second and third elements of the third observer coefficient ε3 in the first observer coefficient matrix ε i of the nonlinear state observer, i = 1, 2, 3; and respectively represent the second observer coefficient matrix φ iThe second and third elements of the first observer coefficient φ1 in and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i The second and third elements of the second observer coefficient φ2 in and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i The second and third elements of the third observer coefficient φ3 in The first and second observer coefficient matrices are related to the uncertain dynamic model parameters θ m and θ p ; and respectively represent the observed values of the first, second, and third elements of the link dynamic parameter θ of the link dynamic model m ; and respectively represent the observed values of the first and second elements of the hydraulic dynamic parameter θ of the hydraulic dynamic model; v2 and v3 respectively represent the second and third observer adaptive characterization parameters; n represents the number of joints of the multi-joint hydraulic manipulator. p Take the third observer adaptive characterization parameter v3 in the observed state of the intermediate conversion state quantity s as the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator

[0182] Step 2: Input the parameter estimation value of the dynamic parameter of the nonlinear dynamic model into the intermediate conversion state quantity model. The intermediate conversion state quantity model outputs the intermediate conversion state quantity. The nonlinear state observer observes the intermediate conversion state quantity and outputs the observed state of the intermediate conversion state quantity. Obtain the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator according to the observed state of the intermediate conversion state quantity. of the multi-joint hydraulic manipulator

[0183] Step 3: Design an adaptive robust control law using the adaptive robust control method according to the nonlinear dynamic model and the nonlinear state observer.

[0184] In Step 3, the designed adaptive robust control law is specifically as follows:

[0185] a) First-order adaptive robust control law v

[0186] : 3d

[0187] v 3d = v 3da + v 3dr + v 3ds

[0188] ​​

[0189] Among them, v 3da represents the first-order adaptive model compensation control law, and v 3dr represents the first-order linear robust control law, and v 3ds represents the first-order nonlinear robust control law; z2 represents the angle conversion error of the multi-joint hydraulic manipulator, z1 and respectively represent the joint angle tracking error and its differential of the multi-joint hydraulic manipulator, z1 = q - q d , q d represents the control target value of each joint angle of the multi-joint hydraulic manipulator, that is, the target trajectory of the multi-joint hydraulic manipulator. The purpose of establishing the angle conversion error z2 is also to ensure that the differential of the Lyapunov control function of the first nonlinear robust control law is less than or equal to zero, so that the overall nonlinear robust controller maintains stability; k1 and k2 respectively represent the first and second gain positive definite diagonal matrices, and k1 and k2 ensure that the differential of the Lyapunov control function of the first-order adaptive robust control law in the nonlinear robust controller is less than or equal to zero, so that the entire nonlinear robust controller maintains stability; and respectively represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator; θ 1min represents the minimum value of the model parameter θ1 of the nonlinear dynamic model of the multi-joint hydraulic manipulator; the first-order nonlinear robust control law v 3ds is divided into two parts, v 3ds1 and v 3ds2 respectively represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v 3d ; represents the link dynamic parameter θ m of the link dynamic model; the first element of represents the second parameter regression matrix; represents the parameter adaptive error of the link dynamic parameter θ m of the link dynamic model; and ∈2 respectively represent the first, second, and third preset design parameters; z ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ ob represents the observer error integration.

[0190] Considering that there are still uncertain nonlinear factors in the nonlinear dynamic model of the link manipulator, it is necessary to compensate for these influencing factors. As the uncertainty compensation parameter, the first-order nonlinear robust control law v 3dsIt cannot be written as a specific formula. The first-order nonlinear robust control law v that satisfies the conditions 3ds can ensure the first-order adaptive robust control law v 3d to maintain good control performance in the presence of parameter uncertainties and uncertain non-linearities.

[0191] The first-order adaptive robust control law v 3d is calculated as follows:

[0192] The joint angle tracking error z1 of the multi-joint hydraulic manipulator is as follows:

[0193] z1 = q - q d

[0194] where q represents the actual measured value of each joint angle of the multi-joint hydraulic manipulator.

[0195] The angle conversion error z2 of the multi-joint hydraulic manipulator is as follows:

[0196]

[0197] Differentiating the above equation gives the following form:

[0198]

[0199] where represents the differential of the angle conversion error z2 of the multi-joint hydraulic manipulator; represents the second-order differential of the joint angle tracking error z1 of the multi-joint hydraulic manipulator.

[0200] The unmeasurable velocity state and the acceleration state can be expressed in the following form:

[0201]

[0202] Combining the above formulas gives the following equation:

[0203]

[0204] Since only v3 in the above equation contains the high-order term Q of the non-linear dynamics model of the link manipulator L , based on the idea of order reduction, an inversion establishment method is adopted to propose the first-order adaptive robust control law v 3d as the linear robust control law of the multi-joint hydraulic manipulator, which reduces the joint angle tracking error while ensuring the transient performance of the system.

[0205] b) Based on the first-order adaptive robust control law v 3d , use the inversion establishment method to establish the second-order adaptive robust control law QLd :

[0206] Q Ld =Q Lda +Q Ldr +Q Lds

[0207]

[0208] Q Ldr =-k 3r z3

[0209] Q Lds =Q Lds1 +Q Lds2

[0210]

[0211] Among them, Q Lda represents the second-order adaptive model compensation control law, Q Ldr represents the second-order linear robust control law, Q Lds represents the second-order nonlinear robust control law; ω2 and ω3 respectively represent the first-order adaptive robust control law v 3d and the preset proportional balance constant of the second-order adaptive robust control law Q Ld ; represents the estimated value of the angle conversion error z2 of the multi-joint hydraulic manipulator; k ob1 represents the first-order observer gain; v1 represents the first-order observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v 3d ; k 3r represents the third gain positive definite diagonal matrix to ensure the stability of the designed controller; z3 represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z3 = v3 - v 3d ; The second-order nonlinear robust control law Q Lds is divided into two parts, Q Lds1 and Q Lds2 respectively represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of the second-order nonlinear robust control law Q Lds ; represents the third parameter regression matrix; represents the parameter adaptive error of the dynamic parameter θ of the nonlinear dynamic model; and ∈3 respectively represent the fourth, fifth, and sixth preset design parameters.

[0212] Take the second-order adaptive robust control law Q Ld as the nonlinear robust control law of the multi-joint hydraulic manipulator. The second-order adaptive robust control law Q LdThe calculation process is as follows:

[0213] The equivalent flow tracking error z3 of the multi-joint hydraulic manipulator is as follows:

[0214] z3 = v3 - v 3d

[0215] Differentiating both sides of the above equation gives the following:

[0216]

[0217] where, represents the differential of the equivalent flow tracking error z3 of the multi-joint hydraulic manipulator, represents the differential of the third observer adaptive characterization parameter v3; represents the first-order adaptive robust control law v 3d of the differential.

[0218] According to the design result of the first-order adaptive robust control law v 3d and the observer property, v 3d is a function of the joint angle q, time t, observer parameters η, φ1, φ2, φ3, and the parameter estimate value , so the differential form of the first-order adaptive robust control law v 3d is as follows:

[0219]

[0220] where, v 3dc and respectively represent the computable part of v 3d and its differential, v 3du and respectively represent the non-computable part of v 3d and its differential; η and respectively represent the observer parameters of the nonlinear state observer and their differentials; and respectively represent the parameter estimates of the dynamic parameter θ of the nonlinear dynamic model and their differentials.

[0221] is the linear regression matrix, which is as follows:

[0222]

[0223] Establish the auxiliary positive semi-definite matrix V as:

[0224]

[0225] Differentiating both sides of the above equation and substituting the first-order adaptive robust control law v 3dSubstituting it in, we can get the following form:

[0226]

[0227] where, denotes the differential of the auxiliary positive semi - definite matrix V.

[0228] Based on the above equation, a second - order adaptive robust control law Q Ld is proposed to reduce the tracking error of each joint angle while ensuring the transient performance of the system.

[0229] c) Considering the model parameter uncertainty in the overall dynamic model of the hydraulic manipulator, a parameter adaptive law is constructed for compensation. The parameter adaptive law:

[0230]

[0231] where, denotes the differential of the estimated value of the link dynamic parameter θ m of the link dynamic model; τ2 and τ3 represent the first - order and second - order model parameter adaptive reference values respectively; denotes the differential of the estimated value of the dynamic parameter θ of the non - linear dynamic model; denotes the parameter estimated value of the dynamic parameter θ of the non - linear dynamic model of the adaptive mapping function; Γ c denotes the parameter adaptive gain coefficient matrix, Γ c =[Γ m ; Γ p , Γ m and Γ p represent the first and second elements of the parameter adaptive gain coefficient matrix Γ c respectively.

[0232] The adaptive mapping function of the parameter estimated value of the dynamic parameter θ of the non - linear dynamic model is specifically as follows:

[0233]

[0234] where, x represents the input parameter of the adaptive mapping function.

[0235] The second parameter regression matrix is specifically as follows:

[0236]

[0237] where, k e denotes the tracking error gain parameter.

[0238] The third parameter regression matrix The details are as follows:

[0239]

[0240] Among them, represents the estimated value of the model parameter θ1 of the nonlinear dynamic model of the multi-joint hydraulic manipulator; represents the linear regression matrix.

[0241] Linear regression matrix The details are as follows:

[0242]

[0243] Step 4: The nonlinear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator to the adaptive robust control law, and at the same time inputs the target trajectory of the multi-joint hydraulic manipulator into the adaptive robust control law. The adaptive robust control law outputs the control signal of the spool displacement of the multi-joint hydraulic manipulator to control the operation of the multi-joint hydraulic manipulator. The tracking error is calculated through the target trajectory of the multi-joint hydraulic manipulator and the joint angle actually output during operation and output to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation value of the dynamic parameter of the nonlinear dynamic model to the intermediate conversion state quantity model and repeats steps 2 and 4. At the same time, the nonlinear state observer performs self-update, and finally realizes the adaptive robust control of the multi-joint hydraulic manipulator.

[0244] In step 4, the nonlinear state observer performs self-update, specifically for the first observer coefficient matrix ε i of the nonlinear state observer, the second observer coefficient matrix φ i and the observer adaptive characterization parameter matrix v are self-updated at their respective self-update rates, and the details are as follows:

[0245]

[0246] Among them, v = [v1; v2; v3]; and respectively represent the self-update rates of the first observer coefficient ε1, the second observer coefficient ε2, and the third observer coefficient ε3 in the first observer coefficient matrix ε i of the nonlinear state observer; A ob and K ob respectively represent the first and second gain coefficient matrices of the nonlinear state observer; y and y ob respectively represent the theoretical and actual outputs of the observer; e1, e2, and e3 respectively represent the first, second, and third dimension characterization parameters, e1 = [1; 0; 0], e2 = [0; 1; 0], e3 = [0; 0; 1]; represents the self-update rate of the observer adaptive representation parameter matrix v; Q L represents the equivalent flow rate of the hydraulic cylinder chamber; and respectively represent the second observer coefficient matrix φ of the nonlinear state observer i the self-update rates of the first observer coefficient φ1, the second observer coefficient φ2, and the third observer coefficient φ3 in

[0247] the first gain coefficient matrix A of the nonlinear state observer ob and the second gain coefficient matrix K ob are specifically as follows:

[0248]

[0249]

[0250] wherein, respectively represent the 1st, 2nd,..., i,..., nth elements in the first gain coefficient matrix A ob ; respectively represent the 1st, 2nd,..., i,..., nth elements in the second gain coefficient matrix K ob ; and respectively represent the first, second, and third gain parameters of the observer; Λ represents a positive semi-definite matrix; I represents an identity matrix.

[0251] Such as Figure 2 and Figure 3As shown in the figure, the underwater multi-degree-of-freedom hydraulic manipulator includes a multi-degree-of-freedom manipulator linkage mechanism and a hydraulic system. There are a total of n degrees-of-freedom joints on the multi-degree-of-freedom manipulator linkage mechanism. The hydraulic system mainly includes an oil tank, a hydraulic pump, a total supply oil pressure sensor, a total return oil pressure sensor, and n driving devices. Each driving device is hinged to a corresponding degree-of-freedom joint of the multi-degree-of-freedom manipulator linkage mechanism. The hydraulic oil in the oil tank flows through the hydraulic pump and then into each driving device, thereby driving the movement of each degree-of-freedom joint of the multi-degree-of-freedom manipulator linkage mechanism. The hydraulic oil then flows back to the oil tank through each driving device. The total supply oil pressure flowing out of the oil tank is detected by the total supply oil pressure sensor, that is, the supply pressure of the hydraulic pump. The total return oil pressure flowing back to the oil tank is detected by the total return oil pressure sensor, that is, the reference pressure of the entire hydraulic system. The hydraulic system also includes a check valve, two filters, and a safety circuit. The hydraulic oil in the oil tank flows through the total supply oil passage, through the hydraulic pump, and then flows out through the check valve, and then flows into each driving device through a filter. A safety circuit is also provided between the supply oil pressure sensor and the oil tank to ensure the safety of the entire hydraulic system. The hydraulic oil in each driving device flows back to the oil tank through the total return oil passage and through another filter. The total supply oil pressure sensor is arranged on the total supply oil passage of the oil tank between the check valve and one filter, and the total return oil pressure sensor is arranged on the total return oil passage between another filter and several driving devices. Each driving device includes a hydraulic cylinder, a hydraulic valve, a supply oil pressure sensor, and a return oil pressure sensor. The push rod of the hydraulic cylinder is hinged to a corresponding degree-of-freedom joint of the multi-degree-of-freedom manipulator linkage mechanism. The supply oil pressure and return oil pressure of the hydraulic oil flowing into and out of each driving device are detected by their respective supply oil pressure sensors and return oil pressure sensors. The hydraulic valve of the driving device is arranged on the supply oil passage where the hydraulic oil flows into the hydraulic cylinder and the return oil passage where the hydraulic oil flows out of the hydraulic cylinder. The supply oil pressure sensor is arranged on the supply oil passage between the hydraulic valve and the hydraulic cylinder, and the return oil pressure sensor is arranged on the return oil passage between the hydraulic valve and the hydraulic cylinder. Among them, A i and A o are the areas of the oil inlet chamber and the oil return chamber of each hydraulic cylinder of each driving device respectively, are the areas of the oil inlet chambers of the 1st, 2nd, 3rd, …, nth hydraulic cylinders respectively, are the areas of the oil return chambers of the 1st, 2nd, 3rd, …, nth hydraulic cylinders respectively; are the displacement amounts of the valve cores of the 1st, 2nd, 3rd, …, nth hydraulic valves respectively; are the supply oil pressures of the hydraulic oil flowing into the 1st, 2nd, 3rd, …, nth driving devices respectively, are the outlet oil pressures of the hydraulic oil flowing out of the 1st, 2nd, 3rd, …, nth driving devices respectively; They are the actual flow rates of the oil inlet chambers of the 1st, 2nd, 3rd, …, nth hydraulic cylinders respectively. They are the actual flow rates of the oil return chambers of the 1st, 2nd, 3rd, …, nth hydraulic cylinders respectively.

[0252] Experiments on the control method of the present invention were carried out on a multi-degree-of-freedom hydraulic manipulator without a speed sensor, and compared with a PID controller to verify the control effect of the control method proposed by the present invention. During the verification, in the designed obARC controller, the controller gain parameters were selected as shown in Table 1. The reason why some adaptive parameters in Γ are zero is that in practical applications, some parameters can be uniquely determined by known parameters and have less uncertainty. Therefore, in order to improve the controller efficiency, only the parameters with greater uncertainty can be adaptively adjusted.

[0253] Table 1 Selection of controller parameters

[0254]

[0255] The sensing accuracy of the angle sensor of the multi-joint hydraulic manipulator and the differential filtering results are as Figure 4 shown. Figure 4 In it, the original signal and the filtered speed signal both refer to the left vertical coordinate, and the filtered angle signal refers to the right vertical coordinate. It can be seen from Figure 4 that the first subfigure is the original signal diagram, the second subfigure is the differential filtering signal result diagram when the passband frequency w c of the filter is 10 rad / s, the third subfigure is the differential filtering signal result diagram when the passband frequency w c of the filter is 30 rad / s, and the fourth subfigure is the differential filtering signal result diagram when the passband frequency w c of the filter is 50 rad / s, indicating that the accuracy of the angle sensor of this multi-joint hydraulic manipulator is relatively low, and differential filtering will introduce additional signal lag, thus limiting the control accuracy.

[0256] The experimental results of the multi-joint hydraulic manipulator are as Figure 5 shown. In Figure 5 the first subfigure is the tracking experimental results of obARC and PID, the second subfigure is the control error of the PID controller, and the third subfigure is the control error of the obARC controller. It can be seen from the control effect subfigures that the adaptive robust controller of the multi-joint hydraulic manipulator based on non-linear state observation designed by the present invention can accurately and smoothly track the target trajectory curve under the conditions of uncertain dynamic model parameters and unmeasurable feedback states. At the same time, the control tracking error curve shows that the angle tracking errors of each joint remain zero at steady state (the angular velocity and acceleration remain unchanged) during the whole movement process.

[0257] Compared with the traditional PID controller, the joint tracking error is significantly reduced and the transient response time is greatly shortened, which reflects that the adaptive robust control method for multi-joint hydraulic manipulators based on non-linear state observation designed by the present invention has more excellent transient response performance and better robustness. It can effectively compensate for the influence of the uncertainty of the dynamic model parameters of the hydraulic manipulator and the unmeasurability of some states on the control accuracy of the end of the manipulator. While ensuring the stability of the control system, it reduces the tracking error at the end of the manipulator and improves the control performance.

[0258] The present invention belongs to the field of motion control of multi-joint hydraulic manipulators. Specifically, it is a motion control method for multi-joint hydraulic manipulators in complex operating environments where physical signals such as motion speed are unmeasurable. The present invention comprehensively considers factors such as parameter uncertainty and multi-joint coupling, and establishes a non-linear dynamic model of an underwater multi-joint hydraulic manipulator. Then, a non-linear observer is designed to obtain intermediate state variables related to the unmeasurable states. Then, based on the observed values of the intermediate state variables, an adaptive robust controller for multi-joint hydraulic manipulators is designed. The proposed adaptive robust control method for multi-joint hydraulic manipulators based on non-linear state observation, obARC, can effectively improve the end control accuracy in the case of uncertain dynamic model parameters of multi-joint hydraulic manipulators and unmeasurable feedback states. While ensuring the overall stability of the control system and the observation system, it reduces the tracking error at the end of the manipulator, enhances the control performance, can achieve state observation in the case of unmeasurable non-linear states such as motion speed, and ensure the stability of the control system, reduce the tracking error of the end motion of the multi-joint hydraulic manipulator, improve the control accuracy of the end actuator of the manipulator, thereby improving the working performance of the manipulator in more severe operating environments.

[0259] The above content is only the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention fall within the protection scope of the claims of the present invention.

Claims

1. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation, characterized in that: The method includes the following steps: Step 1: Establish a nonlinear dynamic model of a multi-joint hydraulic manipulator under dynamic model constraints; design an intermediate conversion state quantity model for the unmeasurable states of the multi-joint hydraulic manipulator and its nonlinear state space, and establish a nonlinear state observer using the nonlinear state observation method according to the nonlinear state space; Step 2: Input the parameter estimation values of the dynamic parameters of the nonlinear dynamic model into the intermediate conversion state quantity model. The intermediate conversion state quantity model outputs the intermediate conversion state quantity. The nonlinear state observer observes the intermediate conversion state quantity and outputs the observed state of the intermediate conversion state quantity. An estimated value of the joint angular velocity of the multi-joint hydraulic manipulator is obtained according to the observed state of the intermediate conversion state quantity; Step 3: Design an adaptive robust control law using the adaptive robust control method according to the nonlinear dynamic model and the nonlinear state observer; Step 4: The nonlinear state space outputs the estimated value of the joint angular velocity of the multi-joint hydraulic manipulator to the adaptive robust control law. At the same time, the target trajectory of the multi-joint hydraulic manipulator is input into the adaptive robust control law. The adaptive robust control law outputs a control signal for the spool displacement of the multi-joint hydraulic manipulator to control the operation of the multi-joint hydraulic manipulator. The tracking error is calculated from the target trajectory of the multi-joint hydraulic manipulator and the joint angles actually output during operation and output to the adaptive robust control law. The adaptive robust control law outputs the parameter estimation values of the dynamic parameters of the nonlinear dynamic model to the intermediate conversion state quantity model and repeats Steps 2 and 4. At the same time, the nonlinear state observer performs self-update, and finally realizes continuous adaptive robust control of the multi-joint hydraulic manipulator.

2. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 1, characterized in that: In the above Step 1, the established nonlinear dynamic model of the multi-joint hydraulic manipulator is specifically as follows: a) Link dynamics model: τ j = J j (q)P L P L = A i P i - A o P o Among them, q, and respectively represent the joint angle, joint angular velocity and joint angular acceleration of the multi-joint hydraulic manipulator, n represents the number of joints of the multi-joint hydraulic manipulator; M j ( ), C j ( ) and G j ( ) respectively represent the inertia dynamics matrix, Coriolis force matrix and gravity matrix of the multi-joint hydraulic manipulator, M j ( ), C j ( ), G j ( )R n×n ; τ j represents the driving torque of each joint of the multi-joint hydraulic manipulator, τ j ∈R n ; J j ( ) represents the multi-joint motion coupling characterization matrix of each joint of the multi-joint hydraulic manipulator; P L represents the equivalent thrust of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, P L ∈R n ; A i and A o respectively represent the contact areas of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, A i , A o ∈R n×n ; P i and P o respectively represent the oil pressures of the oil inlet chamber and the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, P i , P o ∈R n ; l represents the elongation of the push rod of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator, l ∈ R n ; b) Hydraulic dynamics model: V i = V hi + A i diag[l] V o = V ho - A o diag[l] Among them, V i and V o respectively represent the volumes of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator. V i and V o ∈R n×n ; β e represents the bulk modulus of the hydraulic oil; V hi and V ho respectively represent the volumes of the oil inlet chamber and the oil return chamber of each hydraulic cylinder of each drive device in the initial case where the push rod elongation l = 0 of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator; diag[·] represents a diagonal matrix with · as the main element; Q i and Q o respectively represent the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator. Q id and Q od respectively represent the preset ideal flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator. Q id and Q od ∈R n , and respectively represent the calculable flow rate differences of the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator, and respectively represent the incalculable flow rate differences of the actual flow rates of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator; k qi and k qo respectively represent the flow rate gain constants of the oil inlet chamber and the oil return chamber of the hydraulic cylinders of each joint of the multi-joint hydraulic manipulator; x v represents the spool displacement of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator; g1( ) represents the non-linear conversion function between the oil inlet pressure P i of the oil inlet chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve. g2( ) represents the non-linear conversion function between the oil return pressure P o of the oil return chamber of the hydraulic cylinder of each joint of the multi-joint hydraulic manipulator and the spool displacement x v of the hydraulic control valve. g1( ), g2( ) ∈R n×n ; The specific dynamic model constraints are as follows: |Δ j |≤δ j θ ∈ {θ: θ min ≤ θ ≤ θ max} where, Δ j represents the uncertain nonlinearity and disturbances during the movement of the multi-joint hydraulic manipulator, Δ j ∈R n ; δ j represents a preset constant vector; θ max and θ min respectively represent the upper and lower bounds of the dynamic parameter θ of the nonlinear dynamic model, θ = [θ m ; θ p ; The spool displacement x of the hydraulic control valve for each joint of the multi-joint hydraulic manipulator described above v is as follows: Among them, Q L represents the equivalent flow rate of the hydraulic cylinder chamber, Q L ∈R n .

3. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 2, characterized in that: In the above Step 1, the designed intermediate conversion state quantity model for the unmeasurable states of the multi-joint hydraulic manipulator is specifically as follows: s = [s1; s2; s3] s1 = q where s represents the intermediate conversion state variable, and s1, s2, and s3 represent the first, second, and third state variables of the intermediate conversion state variable s respectively; q and represent the joint angle and joint angular velocity of the multi-joint hydraulic manipulator respectively; and represent the first and second elements of the link dynamic parameter θ of the link dynamics model, m respectively; M j and C j represent the inertia dynamics matrix and the Coriolis force matrix of the multi-joint hydraulic manipulator respectively, I represents the identity matrix; f1 and f2 represent the first and second equal matrixes of the intermediate conversion state variable s respectively; θ represents the dynamic parameter of the nonlinear dynamics model, represents the parameter estimation value of the dynamic parameter θ of the nonlinear dynamics model, represents the parameter adaptive error of the dynamic parameter θ of the nonlinear dynamics model; The joint angular velocity of a multi-joint hydraulic manipulator is the unmeasurable state of the multi-joint hydraulic manipulator.

4. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 2, characterized in that: In the above Step 1, the nonlinear state space is specifically as follows: Among them, and respectively represent the differentials of the first state quantity s1, the second state quantity s2, and the third state quantity s3 of the intermediate conversion state quantity s; represents the third element of the link dynamic parameter θ m of the link dynamic model, Δ j represents the uncertain nonlinearity and interference during the movement of the multi-joint hydraulic manipulator; and respectively represent the first and second elements of the hydraulic dynamic parameter θ p of the hydraulic dynamic model, f3, f4, and f5 respectively represent the third, fourth, and fifth equal matrixes of the intermediate conversion state quantity s; u v represents the control voltage actually output by the adaptive robust control law, u v = k v x v , u v ∈R n , x v represents the spool displacement of the hydraulic control valve of each joint of the multi-joint hydraulic manipulator, and k v represents the conversion ratio coefficient; The first-fifth equal quantity matrix of the intermediate conversion state quantity s is specifically as follows:

5. The adaptive robust control method for a hydraulic manipulator based on nonlinear state observation according to claim 2, characterized in that: In the above Step 1, the nonlinear state observer is specifically as follows: Among them, represents the observed state of the intermediate conversion state quantity s, and respectively represent the observed values of the first intermediate conversion state quantity s1, the second intermediate conversion state quantity s2, and the third intermediate conversion state quantity s3 of the joint angular velocity of the multi-joint hydraulic manipulator; and respectively represent the second and third elements of the first observer coefficient ε i in the first observer coefficient matrix ε of the nonlinear state observer, and respectively represent the second and third elements of the second observer coefficient ε2 i in the first observer coefficient matrix ε of the nonlinear state observer, and respectively represent the second and third elements of the third observer coefficient ε3 i in the first observer coefficient matrix ε of the nonlinear state observer, and respectively represent the second and third elements of the first observer coefficient φ i in the second observer coefficient matrix φ of the nonlinear state observer, and respectively represent the second and third elements of the second observer coefficient φ2 i in the second observer coefficient matrix φ of the nonlinear state observer, and respectively represent the second and third elements of the third observer coefficient φ3 i in the second observer coefficient matrix φ of the nonlinear state observer, and respectively represent the observed values of the first, second, and third elements of the link dynamic parameter θ m of the link dynamics model; and respectively represent the observed values of the first and second elements of the hydraulic dynamic parameter θ p of the hydraulic dynamics model; v2 and v3 respectively represent the second and third observer adaptive characterization parameters; n represents the number of joints of the multi-joint hydraulic manipulator; The observed state of the intermediate conversion state quantity s in which the third observer adaptive representation parameter v3 is used as the joint angular velocity of the multi-joint hydraulic manipulator estimated value 6. A hydraulic manipulator adaptive robust control method based on non-linear state observation according to claim 4, characterized in that: In the above Step 3, the designed adaptive robust control law is specifically as follows: a) First-order adaptive robust control law v 3d : v 3d = v 3da + v 3dr + v 3ds v 3ds = v 3ds1 + v 3ds2 Among them, v 3da represents the first-order adaptive model compensation control law, v 3dr represents the first-order linear robust control law, v 3ds represents the first-order nonlinear robust control law; z2 represents the angle conversion error of the multi-joint hydraulic manipulator, z1 and respectively represent the joint angle tracking error and its differential of the multi-joint hydraulic manipulator, z1 = q - q d , q d represents the control target value of each joint angle of the multi-joint hydraulic manipulator, that is, the target trajectory of the multi-joint hydraulic manipulator; k1 and k2 respectively represent the first and second gain positive definite diagonal matrices; and respectively represent the control target values of the angular velocity and acceleration of each joint of the multi-joint hydraulic manipulator; θ 1min represents the minimum value of the model parameter θ1 of the nonlinear dynamic model of the multi-joint hydraulic manipulator; v 3ds1 and v 3ds2 respectively represent the first-order parameter nonlinear robust control law and the first-order observation nonlinear robust control law of the first-order nonlinear robust control law v 3d ; represents the first element of the link dynamic parameter θ m of the link dynamic model; represents the second parameter regression matrix; represents the parameter adaptive error of the link dynamic parameter θ m of the link dynamic model; and ∈2 respectively represent the first, second and third preset design parameters; z ob represents the observer error of the nonlinear state observer, represents the observed state of the intermediate conversion state quantity s; δ ob represents the observer error integration; b) Second-order adaptive robust control law Q Ld : Q Ld = Q Lda + Q Ldr + Q Lds Q Ldr = -k 3r z3 Q Lds = Q Lds1 + Q Lds2 Among them, Q Lda represents the second-order adaptive model compensation control law, and Q Ldr represents the second-order linear robust control law, and Q Lds represents the second-order nonlinear robust control law; ω2 and ω3 respectively represent the preset proportional balance constants of the first-order adaptive robust control law v 3d and the second-order adaptive robust control law Q Ld ; represents the estimated value of the angle conversion error z2 of the multi-joint hydraulic manipulator; k ob1 represents the first-order observer gain; v1 represents the first observer adaptive characterization parameter; represents the differential of the computable part of the first-order adaptive robust control law v 3d ; k 3r represents the third gain positive definite diagonal matrix; z3 represents the equivalent flow tracking error of the multi-joint hydraulic manipulator, z3 = v3 - v 3d ; Q Lds1 and Q Lds2 respectively represent the second-order parameter nonlinear robust control law and the second-order observation nonlinear robust control law of the second-order nonlinear robust control law Q Lds ; represents the third parameter regression matrix; represents the parameter adaptive error of the dynamic parameter θ of the nonlinear dynamic model; and ∈3 respectively represent the fourth, fifth, and sixth preset design parameters; c) Parameter adaptive law: Among them, represents the differential of the estimated value of the connecting rod dynamic parameter θ of the connecting rod dynamic model m ; τ2 and τ3 respectively represent the first-order and second-order model parameter adaptive reference values; represents the differential of the estimated value of the dynamic parameter θ of the nonlinear dynamic model; represents the parameter estimated value of the dynamic parameter θ of the nonlinear dynamic model of the adaptive mapping function; Γ c represents the parameter adaptive gain coefficient matrix, Γ c = [Γ m ; Γ p , Γ m and Γ p respectively represent the first and second elements of the parameter adaptive gain coefficient matrix Γ c .

7. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 6, characterized in that: The parameter estimated value of the kinetic parameter θ of the described non-linear kinetic model The specific form of the adaptive mapping function is as follows: Where x represents the input parameter of the adaptive mapping function.

8. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 6, characterized in that: The second parameter regression matrix described above Specifically as follows: where k e represents the tracking error gain parameter; The third parameter regression matrix described above Specifically as follows: wherein, denotes the estimated value of the model parameter θ1 of the non-linear dynamic model of the multi-joint hydraulic robotic arm; denotes the linear regression matrix; The linear regression matrix described above Specifically as follows:

9. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 5, characterized in that: In the fourth step described above, the nonlinear state observer performs self-update, specifically for the first observer coefficient matrix ε of the nonlinear state observer i , the second observer coefficient matrix φ i and the observer adaptive characterization parameter matrix v are self-updated at their respective self-update rates, specifically as follows: where, v = [v1; v2; v3]; and respectively represent the self - update rates of the first observer coefficient ε1, the second observer coefficient ε2, and the third observer coefficient ε3 in the first observer coefficient matrix ε of the non - linear state observer; A i in ob and K ob respectively represent the first and second gain coefficient matrices of the non - linear state observer; y and y ob respectively represent the theoretical and actual outputs of the observer; e1, e2, and e3 respectively represent the first, second, and third - dimension characterization parameters, e1 = [1; 0; 0], e2 = [0; 1; 0], e3 = [0; 0; 1]; represents the self - update rate of the observer adaptive characterization parameter matrix v; Q L represents the equivalent flow rate of the hydraulic cylinder chamber; and respectively represent the second observer coefficient matrix φ i in the self - update rates of the first observer coefficient φ1, the second observer coefficient φ2, and the third observer coefficient φ3.

10. An adaptive robust control method for a hydraulic manipulator based on non-linear state observation according to claim 9, characterized in that: The first gain coefficient matrix A of the described non-linear state observer ob and the second gain coefficient matrix K ob are specifically as follows: Λ = Λ T > 0 Among them, respectively represent the 1st, 2nd, …, i-th, …, n-th elements in the first gain coefficient matrix A ob ; respectively represent the 1st, 2nd, …, i-th, …, n-th elements in the second gain coefficient matrix K ob ; and respectively represent the first, second, and third gain parameters of the observer; Λ represents a positive semi-definite matrix; I represents an identity matrix.

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