Motion control method of hydraulic manipulator based on low-pressure bulk elastic modulus compensation

Abstract

The present invention discloses a method for controlling the motion of a hydraulic manipulator based on low-pressure bulk modulus compensation. The method comprises: establishing a dynamic linearization model of a multi-degree-of-freedom hydraulic manipulator including an effective bulk modulus; designing an adaptive robust controller using a backstepping method; inputting the desired joint angle into the adaptive robust controller; and simultaneously performing online adaptive parameter updates. The adaptive robust controller processes and outputs a virtual control flow of the multi-degree-of-freedom hydraulic manipulator; static mapping is performed to obtain a valve port control voltage, thereby controlling the hydraulic valve; and the multi-degree-of-freedom hydraulic manipulator outputs the actual control flow, actual joint control torque, and actual joint angle to the adaptive robust controller in real time, thereby achieving closed-loop motion control of the multi-degree-of-freedom hydraulic manipulator. The method of the present invention can achieve high-precision motion tracking performance for the hydraulic manipulator while maintaining a stable low pressure.

Description

Technical Field

[0001] The present invention relates to a hydraulic manipulator motion control method, and relates to the field of multi-degree-of-freedom hydraulic manipulator motion control, and in particular to a hydraulic manipulator motion control method based on low-pressure bulk elastic modulus compensation. Background Art

[0002] Hydraulic manipulators are in high demand for applications in construction, underwater operations, and various other scenarios. Control accuracy is a key factor in determining the success rate of these tasks and is currently a research focus. Model-based control methods, such as virtual decomposition control, robust integral control with error sign, and adaptive robust control, have achieved promising results. Furthermore, the energy efficiency of hydraulic manipulators has attracted significant attention in recent years due to environmental and economic considerations. Energy losses primarily fall into three categories: mechanical and volumetric losses in the pump, and throttling losses in the valve. Typically, the pump in a hydraulic manipulator operates at a constant speed, so reducing throttling losses is a primary strategy for optimizing energy efficiency. Specifically, this is achieved by minimizing the pressure loss as the fluid passes through the throttle valve. However, existing methods inherently require maintaining the backpressure chamber pressure of the hydraulic cylinder at a low level, which can make it difficult to balance control performance and energy efficiency. In hydraulic system control research, the effective bulk modulus is often treated as a constant or lumped parameter, given that the systems typically operate at high pressure. However, this approximation does not address the low-pressure conditions necessary for various energy-efficient control methods. Most methods for purging air from hydraulic systems are complex and cannot completely remove all air. The compression characteristics of hydraulic oil mixed with air change significantly. In particular, the effective bulk modulus at different pressures can vary several times. This is why most energy-saving research often neglects control accuracy or relies solely on simulation verification. Therefore, as a key parameter in control, further mechanism modeling and control compensation are essential. Summary of the Invention

[0003] In order to solve the problems existing in the background technology, the present invention provides a hydraulic manipulator motion control method based on low-pressure bulk elastic modulus compensation.

[0004] The technical solution adopted in the present invention is:

[0005] The hydraulic manipulator motion control method based on low-pressure bulk elastic modulus compensation of the present invention comprises:

[0006] In the first step, a dynamic linearization model of a multi-degree-of-freedom hydraulic manipulator including an improved effective bulk elastic modulus is established.

[0007] In the second step, based on the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator, the backstepping method is used to design an adaptive robust controller for the multi-degree-of-freedom hydraulic manipulator. The desired joint angles of the multi-degree-of-freedom hydraulic manipulator are input into the adaptive robust controller for processing. At the same time, the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The virtual control flow is statically mapped to obtain the valve port control voltage, and then the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator is controlled. The online parameter adaptive method is designed based on the exchange lemma and the least squares method.

[0008] In the third step, the multi-degree-of-freedom hydraulic manipulator outputs the actual control flow, actual joint control torque and actual joint angle in real time and feeds back the state to the adaptive robust controller to realize the closed-loop control of the motion of the multi-degree-of-freedom hydraulic manipulator.

[0009] In the first step, the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator is as follows:

[0010]

[0011] ∈{i,o}

[0012]

[0013]

[0014] Where M( ), C( ) and G( ) represent the mass matrix, Coriolis term and gravity term respectively; q, and They represent the actual joint angle, actual joint angular velocity and actual joint angular acceleration of the multi-degree-of-freedom hydraulic manipulator; τ represents the actual joint control torque of the multi-degree-of-freedom hydraulic manipulator; f F represents the Stribeck friction torque of the friction model; Δ F represents the lumped modeling error; represents a function that transforms vector ·1 into a diagonal matrix, where ·1 represents the vector to be processed; f v and f s Denote the Coulomb friction coefficient and the viscous friction coefficient, respectively, f c represents the difference between the static friction coefficient and the viscous friction coefficient, (f c +f s ) represents the static friction coefficient; S f Represents the approximate value of the symbol Sign function; e f represents the Stribeck overall coefficient of the friction model; represents the Stribeck velocity threshold of the friction model; Jh ( ) represents the non-singular joint Jacobian matrix; A i and A o They represent the piston areas of the rodless and rod-end chambers of the cylinder of the multi-DOF hydraulic manipulator, respectively. i and p o Represent the chamber pressure of the rodless chamber and the rod chamber respectively, and Denote the derivatives of the chamber pressure of the rodless chamber and the rod chamber, V i and V o are the compressible volumes of the rodless and rod-containing cavities, β ei and β eo are the effective bulk elastic moduli of the rodless cavity and the rod cavity, Q i and Q o Represent the actual control flow of the rodless cavity and the rod cavity respectively, and They represent the flow modeling errors of the rodless cavity and the rod cavity, respectively, and k qi and k qo Respectively represent the flow gain coefficient of the valve port with and without rod cavity, h i and h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, u vi and u vo Represent the valve port control voltage of the hydraulic valve with and without rod chamber respectively; S(·2) represents the selection function of vector ·2, ·2 represents the vector to be processed; β e· represents the effective bulk elastic modulus of the rodless or rod-containing cavity, θ β· and represents the effective bulk elastic modulus β of the rodless cavity or the rod cavity, respectively e· The polynomial fitting part and infinitesimal residual term of Indicates that the ratio of the pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power of the multi-order term, θ βi and θ βo are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively. e· The polynomial fitting part of and are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively. e· The infinitesimal residual term of and represents the effective bulk elastic modulus β of the rodless cavity or the rod cavity, respectively e· The polynomial fitting part θ β· The linear regression matrix and coefficient matrix of and are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively.e· The polynomial fitting part θ β· The coefficient matrix of p s and p r They represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator respectively; and Represent the lumped modeling error Δ F The nominal value and bounded deviation value of ; and denote the nominal value and bounded deviation value of the chamber flow rate of the rodless cavity, and They represent the nominal value and bounded deviation value of the chamber flow rate of the rod chamber respectively; φ F represents the control torque regression matrix; Θ F The parameter matrix representing the control torque of the multi-degree-of-freedom hydraulic manipulator, θ1, θ2, θ3, and θ4 respectively represent the first, second, third, and fourth torque parameters in the parameter matrix of the control torque, and θ1, θ2, θ3, and θ4 are the viscous friction coefficient, Coulomb friction coefficient, static friction coefficient, and modeling error nominal values ​​of the multi-degree-of-freedom hydraulic manipulator, respectively. and I represents the parameter matrix of the rodless cavity and the rod cavity, θ5 and θ6 represent the fifth and sixth torque parameters of the parameter matrix of the rodless cavity and the rod cavity, respectively. θ5 and θ6 are the nominal values ​​of the nonlinear modeling error of the rodless cavity or the rod cavity of the multi-degree-of-freedom hydraulic manipulator. n Represents the n-dimensional identity matrix.

[0015] In the second step, the adaptive robust controller of the multi-degree-of-freedom hydraulic manipulator is specifically as follows:

[0016] Q id =Q ida1 +Q ids1 +Q ida2 +Q ids2 +Q ids3

[0017]

[0018] Q od =Q oda1 +Q ods1 +Q oda2 +Q ods2 +Q ods3

[0019]

[0020] z1=qq d

[0021]

[0022] z3=τ-τ d

[0023]

[0024] τ d =τ da1 +τ ds1 +τ da2 +τ ds2

[0025]

[0026] z pi =p i -p id ,z po =p o -p od

[0027]

[0028] Among them, Q id , Q ida1 , Q ids1 , Q ids2 , Q ida2 and Q ids3 They represent the virtual control flow of the rodless cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity respectively; id and They represent the desired chamber pressure of the rodless chamber and its derivative respectively; φ χi The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rodless cavity, and are the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity; k Qis1 and k Qis2 They represent the virtual control flow Q of the rodless cavity respectively id The linear feedback gain matrix and nonlinear robust feedback gain matrix of z pi represents the pressure tracking error of the rodless cavity; z2 and Denote the quasi-sliding modulus and its derivative respectively; d Qi and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate of the rodless cavity, and They represent the low-frequency part of the total uncertainty of the chamber flow rate of the rodless cavity dQi The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty of the chamber flow rate based on the rodless cavity. Qi Estimated value of The discontinuous projection function of γ Qi Indicates the virtual control flow Q of the rodless cavity id The update coefficient of the fast dynamic compensation term; d QiM The low-frequency part d represents the lumped uncertainty of the chamber flow rate of the rodless cavity. Qi The maximum value of η Qi Represents the first infinitesimal quantity; Q od , Q oda1 , Q ods1 , Q ods2 , Q oda2 and Q ods3 They represent the virtual control flow of the rod cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the sixth torque parameter θ6 of the parameter matrix of the rod cavity respectively; od and They represent the desired pressure of the rod chamber and its derivative respectively; φ χo The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rod cavity, and They represent the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rod cavity; d Qo and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate in the rod cavity, and They represent the low-frequency part of the total uncertainty of the chamber flow rate in the rod cavity, d Qo The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty of the chamber flow rate based on the rod cavity. Qo Estimated value of The discontinuous projection function of γ Qo Indicates the virtual control flow Q of the rod cavity od The update coefficient of the fast dynamic compensation term; z po Indicates the pressure tracking error of the rod cavity; d QoM The low-frequency part d represents the lumped uncertainty of the chamber flow rate in the rod cavity. Qo The maximum value of k Qos1 and k Qos2 They represent the virtual control flow Q of the rod cavity respectively od The linear feedback gain matrix and the nonlinear robust feedback gain matrix of ηQo represents the second infinitesimal quantity; z1 and They represent the angle tracking error and its derivative of the multi-DOF hydraulic manipulator, q d represents the desired joint angle of the multi-degree-of-freedom hydraulic manipulator, k1 represents the positive definite diagonal matrix of the sliding mode coefficient, q eq 、 and They represent the joint angle modulus value and its derivative and second-order derivative of the multi-degree-of-freedom hydraulic manipulator; z3 represents the torque tracking error of the multi-degree-of-freedom hydraulic manipulator; τ d , τ da1 , τ ds1 , τ da2 and τ ds2 They represent the joint desired control torque of the multi-DOF hydraulic manipulator and its feedforward compensation term, linear feedback term, fast dynamic compensation term and nonlinear robust feedback term respectively; and The parameter matrices Θ represent the control torque of the multi-degree-of-freedom hydraulic manipulator. F The estimated value and estimation bias of k Fs1 and k Fs2 They represent the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The linear feedback gain matrix and the nonlinear robust feedback gain matrix; d F and denote the low-frequency and high-frequency parts of the lumped uncertainty of rigid body dynamics, respectively. and They represent the low-frequency part of the lumped uncertainty of rigid body dynamics d F The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty based on rigid body dynamics d F Estimated value of The discontinuous projection function of γ F represents the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The update coefficient of the fast dynamic compensation term; d FM The low-frequency part of the lumped uncertainty representing the rigid body dynamics d F The maximum value of η F represents the third infinitesimal quantity; Indicates the back pressure chamber pressure p c The integrated function of .

[0029] The actual control flow output in real time by the multi-degree-of-freedom hydraulic manipulator is used as the virtual control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

[0030] In the second step, the parameters are updated online adaptively as follows:

[0031]

[0032] ∈{i,o}

[0033]

[0034] in, and represent the derivatives of the desired chamber pressure for the rodless and rod-containing chambers, respectively; represents the generalized momentum regression matrix; u F1 Represents the first torque voltage input, Indicates the second torque voltage input u F2 The derivative of and are the derivatives of the regression matrices of the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively; u Qi and u Qo Respectively represent the voltage input of the rodless cavity and the rod cavity; is the auxiliary voltage filter variable ξ of the rodless cavity or the rod cavity · The derivative of λ · Indicates the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o Respectively represent the cutoff frequency of the first-order filter without rod cavity and with rod cavity; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; Auxiliary linear matrix filter variable ψ representing the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the rodless cavity or the rod cavity; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the rodless cavity or the rod cavity in the system; Φ · represents the linear regression matrix after the reorganization of the rodless cavity or the rod cavity; It represents the estimation error of the lumped parameters of the rodless cavity or the rod cavity; Represents the recursive least squares coefficient Γ of the rodless cavity or the rod cavity · The derivative of ι · Indicates the forgetting factor of the rodless cavity or the rod cavity; and ρ ·M They represent the upper bound and maximum value of the recursive least squares coefficients of the rodless cavity or the rod cavity, respectively.

[0035] The parameters of the adaptive robust controller are adaptively updated online, and the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator in the adaptive robust controller is updated using the obtained parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator. The estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller are updated respectively using the obtained parameter matrices of the rodless cavity and the rod cavity.

[0036] In the second step, the virtual control flow Q of the rodless cavity is id and the virtual control flow Q of the rod cavity od After static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained vi And the valve port control voltage u of the hydraulic valve with rod cavity vo , and then control the hydraulic valve of the multi-degree-of-freedom hydraulic robotic arm.

[0037] The present invention first takes into account the need for the hydraulic cylinder to maintain a lower back pressure chamber pressure to save energy, and proposes a low-pressure maintenance control method while ensuring motion accuracy. By constructing an improved effective bulk elastic modulus model, the dynamics of the effective bulk elastic modulus of the gas-liquid mixture under low pressure is accurately described to balance the feasibility of the control design and the accuracy of the model description. In addition, an improved internal parameter online adaptive method of the effective bulk elastic modulus model is designed based on X-swapping and least squares method. The method shows good convergence, and the final fitting results are highly consistent with the standard model. Finally, an expected pressure update algorithm and an adaptive robust controller are also developed, and experiments are carried out on a load-port independent hydraulic manipulator to verify the low-pressure stability maintenance capability and high-precision motion tracking performance of the proposed method.

[0038] The beneficial effects of the present invention are:

[0039] The method of the present invention can achieve high-precision motion tracking performance in a hydraulic mechanical arm while maintaining a stable low pressure. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a motion control block diagram of the method of the present invention;

[0041] Figure 2 : is a reference trajectory curve and its tracking error curve diagram in the experimental setting group 1 and the experimental setting group 2 when the present invention is specifically implemented, wherein, Figure 2 (a) is the reference trajectory curve diagram of experimental setting group 1 and experimental setting group 2. Figure 2 (b) is the tracking error curve of experimental setting group 1 and experimental setting group 2;

[0042] Figure 3is a comparison graph of the reference pressure trajectory in the controller C1 designed by the present invention and the pressure tracking error in the experimental setting group 1 and the experimental setting group 2 during specific implementation, wherein, Figure 3 (a) is the reference pressure trajectory curve of the rod cavity and rodless cavity of experimental setting group 1 and experimental setting group 2. Figure 3 (b) is the pressure tracking error curve of the rodless cavity of experimental setting group 1 and experimental setting group 2. Figure 3 (c) is a graph of the pressure tracking error of the rod cavity in experimental setup group 1 and experimental setup group 2;

[0043] Figure 4 : This is a diagram showing the internal parameter estimation results of the effective bulk elastic modulus of the rodless cavity and the rod cavity in the controller C1 designed by the present invention and the experimental setting group 1 during specific implementation, wherein: Figure 4 (a) is the result of internal parameter estimation of the effective bulk elastic modulus of the rodless cavity. Figure 4 (b) is the result of internal parameter estimation of the effective bulk elastic modulus of the rod cavity;

[0044] Figure 5 1 is a diagram of the fitting results of the pressure obtained by the controller C1 in the experimental setting group 1 during the specific implementation of the present invention;

[0045] Figure 6 is a tracking error diagram for each dimension in Cartesian space in experimental setup group 3 during the specific implementation of the present invention, wherein, Figure 6 (a) is the tracking error diagram of each controller in the x direction, Figure 6 (b) is the tracking error diagram of each controller in the y direction, Figure 6 (c) is the tracking error diagram of each controller in the z direction. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0047] like Figure 1 As shown, the hydraulic manipulator motion control method based on low-pressure bulk elastic modulus compensation of the present invention is as follows:

[0048] The first step is to establish a dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator including the improved effective bulk elastic modulus as follows:

[0049]

[0050] ∈{i,o}

[0051]

[0052]

[0053] Where M( ), C( ) and G( ) represent the mass matrix, Coriolis term and gravity term respectively; q, and They represent the actual joint angle, actual joint angular velocity and actual joint angular acceleration of the multi-degree-of-freedom hydraulic manipulator; τ represents the actual joint control torque of the multi-degree-of-freedom hydraulic manipulator; f F represents the Stribeck friction torque of the friction model; Δ F represents the lumped modeling error; represents a function that transforms vector ·1 into a diagonal matrix, where ·1 represents the vector to be processed; f v and f s Denote the Coulomb friction coefficient and the viscous friction coefficient, respectively, f c represents the difference between the static friction coefficient and the viscous friction coefficient, (f c +f s ) represents the static friction coefficient; S f Represents the approximate value of the symbol Sign function; e f represents the Stribeck overall coefficient of the friction model; represents the Stribeck velocity threshold of the friction model; J h ( ) represents the non-singular joint Jacobian matrix; A i and A o They represent the piston areas of the rodless and rod-end chambers of the cylinder of the multi-DOF hydraulic manipulator, respectively. i and p o Represent the chamber pressure of the rodless chamber and the rod chamber respectively, and Denote the derivatives of the chamber pressure of the rodless chamber and the rod chamber, V i and V o are the compressible volumes of the rodless and rod-containing cavities, β ei and β eo are the effective bulk elastic moduli of the rodless cavity and the rod cavity, Q i and Q o Represent the actual control flow of the rodless cavity and the rod cavity respectively, and They represent the flow modeling errors of the rodless cavity and the rod cavity, respectively, and k qi and k qo Respectively represent the flow gain coefficient of the valve port with and without rod cavity, h iand h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, u vi and u vo Represent the valve port control voltage of the hydraulic valve with and without rod chamber respectively; S(·2) represents the selection function of vector ·2, ·2 represents the vector to be processed; β e· represents the effective bulk elastic modulus of the rodless or rod-containing cavity, θ β· and represents the effective bulk elastic modulus β of the rodless cavity or the rod cavity, respectively e· The polynomial fitting part and infinitesimal residual term of Indicates that the ratio of the pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power of the multi-order term, θ βi and θ βo are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively. e· The polynomial fitting part of and are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively. e· The infinitesimal residual term of and represents the effective bulk elastic modulus β of the rodless cavity or the rod cavity, respectively e· The polynomial fitting part θ β· The linear regression matrix and coefficient matrix of and are the effective bulk elastic modulus β of the rodless cavity and the rod cavity, respectively. e· The polynomial fitting part θ β· The coefficient matrix of p s and p r They represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator respectively; and Represent the lumped modeling error Δ F The nominal value and bounded deviation value of ; and denote the nominal value and bounded deviation value of the chamber flow rate of the rodless cavity, and They represent the nominal value and bounded deviation value of the chamber flow rate of the rod chamber respectively; φ F represents the control torque regression matrix; Θ F The parameter matrix representing the control torque of the multi-degree-of-freedom hydraulic manipulator, θ1, θ2, θ3, and θ4 respectively represent the first, second, third, and fourth torque parameters in the parameter matrix of the control torque, and θ1, θ2, θ3, and θ4 are the viscous friction coefficient, Coulomb friction coefficient, static friction coefficient, and modeling error nominal values ​​of the multi-degree-of-freedom hydraulic manipulator, respectively. and I represents the parameter matrix of the rodless cavity and the rod cavity, θ5 and θ6 represent the fifth and sixth torque parameters of the parameter matrix of the rodless cavity and the rod cavity, respectively. θ5 and θ6 are the nominal values ​​of the nonlinear modeling error of the rodless cavity or the rod cavity of the multi-degree-of-freedom hydraulic manipulator. n Represents the n-dimensional identity matrix.

[0054] In the second step, based on the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator, the backstepping method is used to design an adaptive robust controller for the multi-degree-of-freedom hydraulic manipulator. The desired joint angles of the multi-degree-of-freedom hydraulic manipulator are input into the adaptive robust controller for processing. At the same time, the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The virtual control flow is statically mapped to obtain the valve port control voltage, and then the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator is controlled. The online parameter adaptive method is designed based on the exchange lemma and the least squares method.

[0055] The adaptive robust controller of the multi-degree-of-freedom hydraulic manipulator is as follows:

[0056] Q id =Q ida1 +Q ids1 +Q ida2 +Q ids2 +Q ids3

[0057]

[0058] Q od =Q oda1 +Q ods1 +Q oda2 +Q ods2 +Q ods3

[0059]

[0060]

[0061] z1=qq d

[0062]

[0063] z3=τ-τ d

[0064]

[0065] τ d =τ da1 +τ ds1 +τ da2 +τds2

[0066]

[0067] z pi =p i -p id ,z po =p o -p od

[0068]

[0069]

[0070] Among them, Q id , Q ida1 , Q ids1 , Q ids2 , Q ida2 and Q ids3 They represent the virtual control flow of the rodless cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity respectively; id and They represent the desired chamber pressure of the rodless chamber and its derivative respectively; φ χi The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rodless cavity, and are the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity; k Qis1 and k Qis2 They represent the virtual control flow Q of the rodless cavity respectively id The linear feedback gain matrix and nonlinear robust feedback gain matrix of z pi represents the pressure tracking error of the rodless cavity; z2 and Denote the quasi-sliding modulus and its derivative respectively; d Qi and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate of the rodless cavity, and They represent the low-frequency part of the total uncertainty of the chamber flow rate of the rodless cavity d Qi The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty of the chamber flow rate based on the rodless cavity. Qi Estimated value of The discontinuous projection function of γ Qi Indicates the virtual control flow Q of the rodless cavityid The update coefficient of the fast dynamic compensation term; d QiM The low-frequency part d represents the lumped uncertainty of the chamber flow rate of the rodless cavity. Qi The maximum value of η Qi Represents the first infinitesimal quantity; Q od , Q oda1 , Q ods1 , Q ods2 , Q oda2 and Q ods3 They represent the virtual control flow of the rod cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the sixth torque parameter θ6 of the parameter matrix of the rod cavity respectively; od and They represent the desired pressure of the rod chamber and its derivative respectively; φ χo The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rod cavity, and They represent the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rod cavity; d Qo and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate in the rod cavity, and They represent the low-frequency part of the total uncertainty of the chamber flow rate in the rod cavity, d Qo The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty of the chamber flow rate based on the rod cavity. Qo Estimated value of The discontinuous projection function of γ Qo Indicates the virtual control flow Q of the rod cavity od The update coefficient of the fast dynamic compensation term; z po Indicates the pressure tracking error of the rod cavity; d QoM The low-frequency part d represents the lumped uncertainty of the chamber flow rate in the rod cavity. Qo The maximum value of k Qos1 and k Qos2 They represent the virtual control flow Q of the rod cavity respectively od The linear feedback gain matrix and the nonlinear robust feedback gain matrix of η Qo represents the second infinitesimal quantity; z1 and They represent the angle tracking error and its derivative of the multi-degree-of-freedom hydraulic manipulator, q d represents the desired joint angle of the multi-degree-of-freedom hydraulic manipulator, k1 represents the positive definite diagonal matrix of the sliding mode coefficient, q eq、 and They represent the joint angle modulus value and its derivative and second-order derivative of the multi-degree-of-freedom hydraulic manipulator; z3 represents the torque tracking error of the multi-degree-of-freedom hydraulic manipulator; τ d , τ da1 , τ ds1 , τ da2 and τ ds2 They represent the joint desired control torque of the multi-DOF hydraulic manipulator and its feedforward compensation term, linear feedback term, fast dynamic compensation term and nonlinear robust feedback term respectively; and The parameter matrices Θ represent the control torque of the multi-degree-of-freedom hydraulic manipulator. F The estimated value and estimation bias of k Fs1 and k Fs2 They represent the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The linear feedback gain matrix and the nonlinear robust feedback gain matrix; d F and denote the low-frequency and high-frequency parts of the lumped uncertainty of rigid body dynamics, respectively. and They represent the low-frequency part of the lumped uncertainty of rigid body dynamics d F The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty based on rigid body dynamics d F Estimated value of The discontinuous projection function of γ F represents the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The update coefficient of the fast dynamic compensation term; d FM The low-frequency part of the lumped uncertainty representing the rigid body dynamics d F The maximum value of η F represents the third infinitesimal quantity; Indicates the back pressure chamber pressure p c The integrated function of .

[0071] The actual control flow output in real time by the multi-degree-of-freedom hydraulic manipulator is used as the virtual control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

[0072] The online adaptive update of parameters is as follows:

[0073]

[0074] ∈{i,o}

[0075]

[0076] in, and represent the derivatives of the desired chamber pressure for the rodless and rod-containing chambers, respectively; represents the generalized momentum regression matrix; u F1 Represents the first torque voltage input, Indicates the second torque voltage input u F2 The derivative of and are the derivatives of the regression matrices of the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively; u Qi and u Qo Respectively represent the voltage input of the rodless cavity and the rod cavity; is the auxiliary voltage filter variable ξ of the rodless cavity or the rod cavity · The derivative of λ · Indicates the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o Respectively represent the cutoff frequency of the first-order filter without rod cavity and with rod cavity; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; Auxiliary linear matrix filter variable ψ representing the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the rodless cavity or the rod cavity; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the rodless cavity or the rod cavity in the system; Φ · represents the linear regression matrix after the reorganization of the rodless cavity or the rod cavity; It represents the estimation error of the lumped parameters of the rodless cavity or the rod cavity; Represents the recursive least squares coefficient Γ of the rodless cavity or the rod cavity · The derivative of ι · Indicates the forgetting factor of the rodless cavity or the rod cavity; and ρ ·M They represent the upper bound and maximum value of the recursive least squares coefficients of the rodless cavity or the rod cavity, respectively.

[0077] The parameters of the adaptive robust controller are adaptively updated online, and the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator in the adaptive robust controller is updated using the obtained parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator. The estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller are updated respectively using the obtained parameter matrices of the rodless cavity and the rod cavity.

[0078] The virtual control flow Q of the rodless cavity id and the virtual control flow Q of the rod cavity odAfter static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained vi And the valve port control voltage u of the hydraulic valve with rod cavity vo , and then control the hydraulic valve of the multi-degree-of-freedom hydraulic robotic arm.

[0079] In the third step, the multi-degree-of-freedom hydraulic manipulator outputs the actual control flow, actual joint control torque and actual joint angle in real time and feeds back the state to the adaptive robust controller to realize the closed-loop control of the motion of the multi-degree-of-freedom hydraulic manipulator.

[0080] In a specific implementation, the proposed control method was applied to a hydraulic manipulator for testing. The flow rates in the two chambers of the hydraulic cylinder were independently regulated by a 3-position, 4-way proportional valve. The following three methods were compared.

[0081] C1: The controller designed by the present invention. The parameters are specified as follows:

[0082] C2: A controller similar to the controller C1 of the present invention, but lacking Online parameter estimation of

[0083] C3: The effective bulk modulus is considered as a lumped parameter for estimation and compensation, which is consistent with the mainstream control method. Specifically, is the parameter to be estimated, and α ·j ≡0, where ·∈i,o, j∈1,2,3, and j=1,2,3 represent the linear coefficient, quadratic coefficient, and cubic coefficient of the fitting polynomial of the effective bulk elastic modulus of the rodless cavity and the rod cavity, respectively. All other variables remain the same as C1. The above controllers are first compared in the joint space, and the reference trajectory is as follows Figure 2 As shown in (a), the experimental setting group 1 is a sine curve tracking experiment, and the required trajectory is set to q d (t) = 0.52sin(0.325πt) + 0.17rad, experimental setting group 2 is a point-to-point S curve tracking experiment, the S curve ranges from -0.25rad to 0.63rad, the maximum angular velocity Maximum angular acceleration In addition, a reference trajectory is set in Cartesian space. Experimental setting group 3 is a multi-degree-of-freedom trajectory tracking experiment. The preset endpoints of the hydraulic manipulator need to be in P A and P B During this process, inverse kinematics is used to calculate the reference trajectory in the joint space, which is then controlled by controllers C1 to C3. When comparing controllers, the performance indicators selected are as follows:

[0084]

[0085] e M·z =max{|·z|}

[0086]

[0087] Among them, e R·z represents the root mean square error, z∈{z1,z pi ,z po}, T represents the total length of the evaluation period; e M·z represents the peak error, z∈{z1,z pi ,z po};ρ e Represents the normalized performance index. The tracking results of experimental setting group 1 and experimental setting group 2 are as follows Figure 2 As shown in (b), where 1m rad = 10 -3 rad. It is noteworthy that, despite controller C3 being at the extreme end of performance, controllers C1 and C2 significantly outperform C3 in tracking performance, as evidenced by the large oscillations in their control errors. These results demonstrate that the nonlinear relationship between the effective bulk modulus and pressure cannot be considered a constant under low-pressure conditions, a key reason why some methods designed to reduce energy losses fail to maintain control performance. Furthermore, controller C1 exhibits superior performance compared to controller C2. The online learning enables the controller C1 to show greater adaptability when the operating conditions (oil temperature or entrained air content) change.

[0088] like Figure 3 (a) shows the reference pressure trajectory in the controller C1, where the required low back pressure chamber pressure P c =0.5MPa, the method of the present invention significantly reduces the pressure supply demand of the chamber, while ensuring that the net torque τ meets the predetermined requirements, thus laying the foundation for the subsequent reduction of throttling losses. Based on the reference pressure, Figure 3 (b) and Figure 3 The results of (c) show the pressure control effect of the method of the present invention. Table 1 provides a comparison of the performance indicators of pressure control. Both controller C1 and controller C2 show more accurate and stable pressure tracking performance. Specifically, due to Q ·ds1 Due to the direct influence of , ·∈{i,o}, controller C3 is more susceptible to significant pressure oscillations.

[0089] Table 1

[0090]

[0091]

[0092] Among them, e Rz1 、e Mz1 、 and They represent the root mean square error of the tracking error, the peak error of the tracking error, the root mean square error of the rodless cavity pressure tracking error, the root mean square error of the rod cavity pressure tracking error, the peak error of the rodless cavity pressure tracking error, and the peak error of the rod cavity pressure tracking error. Figure 4 (a) and Figure 4 As shown in (b), the controller C1 in the experimental setup group 1 is given to the rodless cavity and rod cavity The estimated results show that when there is no rod cavity, α i0 =1.85×10 -9 Pa -1 , α i1 =1.71×10 -8 Pa - 1, α i2 =2.98×10 -8 Pa -1 , α i3 =9.80×10 -9 Pa -1 , when there is a rod cavity, α o0 =3.77×10 -9 Pa -1 , α o1 =9.54×10 -9 Pa -1 , α o2 =4.24×10 -8 Pa -1 , α o3 =9.10×10 -8 Pa -1 , the parameters of the two chambers show a certain convergence effect, indicating that the model of the present invention accurately fits the real effective bulk elastic modulus model. Figure 4 Substitute the final converged value in into the original formula, The fitting results relative to the chamber pressure are as follows Figure 5 As shown in Figure 2, the proposed improved model is consistent with the results of the traditional tangent bulk modulus model, proving its accuracy. Figure 6 (a) Figure 6 (b) and Figure 6 (c) shows the multi-joint control results for experimental setup group 3. Controller C1 exhibits excellent tracking performance in all dimensions, especially along the Y axis. This indicates that the nonlinear effect of the effective bulk modulus is significant compared to other global nonlinearities in the hydraulic manipulator and cannot be ignored.

[0093] In summary, considering that the hydraulic cylinder needs to maintain a low back pressure chamber pressure to save energy, the method of the present invention. By constructing an improved effective bulk elastic modulus model, the dynamics of the effective bulk elastic modulus of the gas-liquid mixture under low pressure is accurately described. In addition, the internal parameter online adaptive method of the improved effective bulk elastic modulus model of the present invention shows good convergence, and the final fitting result is highly consistent with the standard model. Finally, a comparative experiment was carried out using a load-port independent hydraulic manipulator as a case study. This proves the low-pressure stable maintenance capability and high-precision motion tracking performance of the method of the present invention. It is worth noting that regardless of the energy-saving method adopted, the control method proposed in the present invention is very suitable for maintaining low pressure in the chamber. Future research will focus on matching the dynamic characteristics of the pump and valve port.

[0094] 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 in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A hydraulic manipulator motion control method based on low-pressure bulk elastic modulus compensation, characterized in that: include: The first step is to establish a dynamic linearization model of a multi-degree-of-freedom hydraulic manipulator including the effective bulk elastic modulus; In the second step, based on the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator, an adaptive robust controller for the multi-degree-of-freedom hydraulic manipulator is designed using the backstepping method. The desired joint angles of the multi-degree-of-freedom hydraulic manipulator are input into the adaptive robust controller for processing. At the same time, the parameters of the adaptive robust controller are adaptively updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The virtual control flow is statically mapped to obtain the valve port control voltage, which is then used to control the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator. In the third step, the multi-degree-of-freedom hydraulic manipulator outputs the actual control flow, actual joint control torque, and actual joint angle in real time and feeds the state feedback to the adaptive robust controller to achieve closed-loop motion control of the multi-degree-of-freedom hydraulic manipulator. In the first step, the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator is as follows: Where M( ), C( ) and G( ) represent the mass matrix, Coriolis term and gravity term respectively; q, and They represent the actual joint angle, actual joint angular velocity and actual joint angular acceleration of the multi-degree-of-freedom hydraulic manipulator; τ represents the actual joint control torque of the multi-degree-of-freedom hydraulic manipulator; f F represents the Stribeck friction torque of the friction model; Δ F represents the lumped modeling error; represents the function that transforms vector ·1 into a diagonal matrix; f v and f s Denote the Coulomb friction coefficient and the viscous friction coefficient, respectively, f c Represents the difference between the static friction coefficient and the viscous friction coefficient; S f Represents the symbol Sign function; e f represents the Stribeck overall coefficient of the friction model; represents the Stribeck velocity threshold of the friction model; J h ( ) represents the non-singular joint Jacobian matrix; A i and A o They represent the piston areas of the rodless and rod-end chambers of the cylinder of the multi-DOF hydraulic manipulator, respectively. i and p o Represent the chamber pressure of the rodless chamber and the rod chamber respectively, and Denote the derivatives of the chamber pressure of the rodless chamber and the rod chamber, V i and V o are the compressible volumes of the rodless and rod-containing cavities, β ei and β eo are the effective bulk elastic moduli of the rodless cavity and the rod cavity, Q i and Q o Represent the actual control flow of the rodless cavity and the rod cavity respectively, and They represent the flow modeling errors of the rodless cavity and the rod cavity, respectively, and k qi and k qo Respectively represent the flow gain coefficient of the valve port with and without rod cavity, h i and h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, u vi and u vo They represent the valve port control voltages of the hydraulic valves with and without rod chambers, respectively; S(·2) represents the selection function of vector ·2; It represents the effective bulk elastic modulus of the rodless cavity or the rod cavity, and Represents the effective bulk elastic modulus of the rodless cavity or the rod cavity, respectively The polynomial fitting part and infinitesimal residual term of Indicates that the ratio of the pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power of the multi-order term, θ βi and θ βo are the effective bulk elastic moduli of the rodless cavity and the rod cavity, respectively. The polynomial fitting part of and are the effective bulk elastic moduli of the rodless cavity and the rod cavity, respectively. The infinitesimal residual term of and Represents the effective bulk elastic modulus of the rodless cavity or the rod cavity, respectively The polynomial fitting part of The linear regression matrix and coefficient matrix of and are the effective bulk elastic moduli of the rodless cavity and the rod cavity, respectively. The polynomial fitting part of The coefficient matrix of p s and p r They represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator respectively; and Represent the lumped modeling error Δ F The nominal value and bounded deviation value of ; and denote the nominal value and bounded deviation value of the chamber flow rate of the rodless cavity, and They represent the nominal value and bounded deviation value of the chamber flow rate of the rod chamber respectively; φ F represents the control torque regression matrix; Θ F represents the parameter matrix of the control torque of the multi-degree-of-freedom hydraulic manipulator, θ1, θ2, θ3 and θ4 represent the first, second, third and fourth torque parameters in the parameter matrix of the control torque, respectively. and I represents the parameter matrices of the rodless cavity and the rod cavity, θ5 and θ6 represent the fifth and sixth torque parameters of the parameter matrices of the rodless cavity and the rod cavity, respectively; n Represents the n-dimensional identity matrix.

2. The hydraulic manipulator motion control method based on low-pressure bulk modulus compensation according to claim 1, characterized in that: In the second step, the adaptive robust controller of the multi-degree-of-freedom hydraulic manipulator is specifically as follows: Q id =Q ida1 +Q ids1 +Q ida2 +Q ids2 +Q ids3 Q od =Q oda1 +Q ods1 +Q oda2 +Q ods2 +Q ods3 z1=q-q d z3=τ-τ d t d =t da1 +t ds1 +t da2 +t ds2 z pi =p i -p id ,z po =p o -p od Among them, Q id , Q ida1 , Q ids1 , Q ids2 , Q ida2 and Q ids3 They represent the virtual control flow of the rodless cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity respectively; id and denote the desired chamber pressure and its derivative of the rodless chamber respectively; The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rodless cavity, and They represent the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity respectively; and They represent the virtual control flow Q of the rodless cavity respectively id The linear feedback gain matrix and nonlinear robust feedback gain matrix of z pi represents the pressure tracking error of the rodless cavity; z2 and Denote the quasi-sliding modulus and its derivative respectively; d Qi and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate of the rodless cavity, and They represent the low-frequency part of the lumped uncertainty of the chamber flow rate of the rodless cavity. The estimated value of and its derivative; Represents the low-frequency part of the lumped uncertainty of the chamber flow based on the rodless cavity Estimated value of The discontinuous projection function of Indicates the virtual control flow Q of the rodless cavity id The update coefficient of the fast dynamic compensation term; Represents the low-frequency part of the lumped uncertainty of the chamber flow rate of the rodless cavity The maximum value of Represents the first infinitesimal quantity; Q od , Q oda1 , Q ods1 , Q ods2 , Q oda2 and Q ods3 They represent the virtual control flow of the rod cavity and its feedforward compensation term, linear feedback term, nonlinear feedback term, fast dynamic compensation term and backstepping compensation term respectively; and They represent the estimated value and estimated deviation of the sixth torque parameter θ6 of the parameter matrix of the rod cavity respectively; od and denote the desired chamber pressure and its derivative of the rod chamber respectively; The linear regression matrix representing the polynomial fitting part of the effective bulk modulus of the rod cavity, and They represent the estimated value and estimation error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rod cavity respectively; and They represent the low-frequency and high-frequency parts of the lumped uncertainty of the chamber flow rate in the rod cavity, and They represent the low-frequency part of the lumped uncertainty of the chamber flow rate in the rod cavity. The estimated value of and its derivative; Represents the low-frequency part of the lumped uncertainty of the chamber flow rate based on the rod cavity Estimated value of The discontinuous projection function of Indicates the virtual control flow Q of the rod cavity od The update coefficient of the fast dynamic compensation term; z po Indicates the pressure tracking error of the rod cavity; Represents the low-frequency part of the lumped uncertainty of the chamber flow rate in the rod cavity The maximum value of and They represent the virtual control flow Q of the rod cavity respectively od The linear feedback gain matrix and the nonlinear robust feedback gain matrix; represents the second infinitesimal quantity; z1 and They represent the angle tracking error and its derivative of the multi-degree-of-freedom hydraulic manipulator, q d represents the desired joint angle of the multi-degree-of-freedom hydraulic manipulator, k1 represents the positive definite diagonal matrix of the sliding mode coefficient, q eq 、 and They represent the joint angle modulus value and its derivative and second-order derivative of the multi-degree-of-freedom hydraulic manipulator; z3 represents the torque tracking error of the multi-degree-of-freedom hydraulic manipulator; τ d , τ da1 , τ ds1 , τ da2 and τ ds2 They represent the joint desired control torque of the multi-DOF hydraulic manipulator and its feedforward compensation term, linear feedback term, fast dynamic compensation term and nonlinear robust feedback term respectively; and The parameter matrices Θ represent the control torque of the multi-degree-of-freedom hydraulic manipulator. F The estimated value and estimation bias of k Fs1 and k Fs2 They represent the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The linear feedback gain matrix and the nonlinear robust feedback gain matrix; d F and denote the low-frequency and high-frequency parts of the lumped uncertainty of rigid body dynamics, respectively. and They represent the low-frequency part of the lumped uncertainty of rigid body dynamics d F The estimated value of and its derivative; represents the low-frequency part of the lumped uncertainty based on rigid body dynamics d F Estimated value of The discontinuous projection function of γ F represents the desired control torque τ of the joints of the multi-DOF hydraulic manipulator d The update coefficient of the fast dynamic compensation term; d FM The low-frequency part of the lumped uncertainty representing the rigid body dynamics d F The maximum value of η F represents the third infinitesimal quantity; Indicates the back pressure chamber pressure p c The integrated function of The actual control flow output in real time by the multi-degree-of-freedom hydraulic manipulator is used as the virtual control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

3. The hydraulic manipulator motion control method based on low-pressure bulk modulus compensation according to claim 1, characterized in that: In the second step, the parameters are updated online adaptively as follows: ∈{i,o} in, and represent the derivatives of the desired chamber pressure for the rodless and rod-containing chambers, respectively; represents the generalized momentum regression matrix; u F1 Represents the first torque voltage input, Indicates the second torque voltage input u F2 The derivative of and denote the derivatives of the regression matrices of the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively; and Represent the voltage input of the rodless cavity and the rod cavity respectively; ξ · is the auxiliary voltage filter variable ξ of the rodless cavity or the rod cavity · The derivative of λ · Indicates the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o Respectively represent the cutoff frequency of the first-order filter without rod cavity and with rod cavity; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; Auxiliary linear matrix filter variable ψ representing the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the rodless cavity or the rod cavity; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the rodless cavity or the rod cavity in the system; Φ · represents the linear regression matrix after the reorganization of the rodless cavity or the rod cavity; It represents the estimation error of the lumped parameters of the rodless cavity or the rod cavity; Represents the recursive least squares coefficient Γ of the rodless cavity or the rod cavity · The derivative of ι · Indicates the forgetting factor of the rodless cavity or the rod cavity; and ρ ·M They represent the upper bound and maximum value of the recursive least squares coefficients of the rodless cavity or the rod cavity respectively; The parameters of the adaptive robust controller are adaptively updated online, and the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator in the adaptive robust controller is updated using the obtained parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator. The estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller are updated respectively using the obtained parameter matrices of the rodless cavity and the rod cavity.

4. The hydraulic manipulator motion control method based on low-pressure bulk modulus compensation according to claim 1, characterized in that: In the second step, the virtual control flow Q of the rodless cavity is id and the virtual control flow Q of the rod cavity od After static mapping, the valve port control voltage u of the hydraulic valve of the rodless cavity is obtained vi And the valve port control voltage u of the hydraulic valve with rod cavity vo , and then control the hydraulic valve of the multi-degree-of-freedom hydraulic robotic arm.

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