Hydraulic mechanical arm motion control method based on low-pressure volume elastic modulus compensation

Abstract

The invention discloses a hydraulic mechanical arm motion control method based on low-pressure volume elastic modulus compensation. The method comprises the steps that a dynamic linearization model of the multi-degree-of-freedom hydraulic mechanical arm containing the effective volume elastic modulus is established, a backstepping method is used for designing a self-adaptive robust controller, an expected joint angle is input into the self-adaptive robust controller, meanwhile, online self-adaptive parameter updating is carried out, and the optimal joint angle is obtained. The self-adaptive robust controller outputs virtual control flow of the multi-degree-of-freedom hydraulic mechanical arm after processing, and valve port control voltage is obtained after static mapping so as to control a hydraulic valve; and the multi-degree-of-freedom hydraulic mechanical arm outputs the actual control flow, the actual joint control torque and the actual joint angle to the self-adaptive robust controller in real time, and motion closed-loop control over the multi-degree-of-freedom hydraulic mechanical arm is achieved. According to the method, the high-precision motion tracking performance can be achieved under the condition that the hydraulic mechanical arm keeps stable low pressure.

Description

Technical Field

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

[0002] Hydraulic manipulators are in great demand in construction, underwater operations, and various other scenarios. Control accuracy is a key factor in determining the success rate of these tasks and is also the focus of current research. Model-based control methods, such as virtual decomposition control, robust integral control of error signs, and adaptive robust control, have achieved good results. In addition, the energy efficiency of hydraulic manipulators has attracted great attention in recent years due to environmental issues and economic benefits. There are three main types of energy losses: mechanical and volumetric losses in the pump, and throttling losses in the valve port. Typically, the pump of a hydraulic manipulator runs at a constant speed, so reducing throttling losses is the main strategy for optimizing energy efficiency. Specifically, this is achieved by minimizing the pressure loss when the fluid flows through the throttle valve to achieve energy saving. However, existing methods inherently require the back pressure chamber pressure of the hydraulic cylinder to be kept at a low level, which may make it difficult to balance control performance and energy efficiency. In the study of hydraulic system control, the effective bulk elastic modulus is usually regarded as a constant or lumped parameter, given that the system usually operates at high pressure. However, this approximation does not meet the low pressure conditions necessary for various energy-saving controls. Most methods for exhausting air from hydraulic systems are complicated and cannot completely remove all air. The compression characteristics of hydraulic oil and air change significantly after mixing, especially the effective bulk elastic modulus at different pressures may even differ by several times. This is why most energy-saving research often ignores control accuracy or only has simulation verification. Therefore, as a key parameter in control, further mechanism modeling and control compensation are particularly necessary. Summary of the invention

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

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

[0005] The hydraulic mechanical arm 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, according to 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 updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The valve port control voltage is obtained after static mapping of the virtual control flow, 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 motion control 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 respectively; 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 of transforming 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, 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 chamber and the rod chamber 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 pressures of the rodless chamber and the rod chamber, V i and V o denote the compressible volumes of the cavity without rod and the cavity with rod, β ei and β eo are the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively, Q i and Q o Respectively represent the actual control flow of the rodless cavity and the rod cavity, 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 without rod cavity and with rod cavity, h i and h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, respectively, u vi and u vo denote the valve port control voltage of the hydraulic valve with and without rod chamber respectively; S(·2) denotes the selection function of vector ·2, ·2 represents the vector to be processed; β e· represents the effective bulk elastic modulus of the cavity without or with a rod, θ β· and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part and infinitesimal residual term of It represents the multi-order term whose ratio of the air pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power, θ βi and θ βo Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The polynomial fitting part of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The infinitesimal residual term of and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part θ β· The linear regression matrix and coefficient matrix of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectivelye· The polynomial fitting part θ β· The coefficient matrix of s and p r They respectively represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator; and Respectively 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 chamber, respectively. 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, 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, θ5 and θ6 are the nominal values ​​of the nonlinear modeling errors of the rodless cavity or the rod cavity of the multi-degree-of-freedom hydraulic manipulator, respectively; 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 p respectively represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity; 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 fit part of the effective bulk modulus of the rodless cavity, and They represent the estimated value and estimated error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity respectively; 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 Respectively represent the quasi-sliding modulus and its derivative; 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 denote 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 total uncertainty of the chamber flow rate based on the rodless cavity d Qi Estimated value of The discontinuous projection function of 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 of the total uncertainty of the chamber flow rate of the rodless cavity is represented by d 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 expected pressure of the rod chamber and its derivative respectively; φ χo The linear regression matrix representing the polynomial fit part of the effective bulk modulus of the cavity with rod, and They represent the estimated value and estimated 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 with a rod cavity, respectively. and They represent the low-frequency part of the total uncertainty of the chamber flow rate in the rod cavity. Qo The estimated value of and its derivative; represents the low-frequency part of the total uncertainty of the chamber flow rate based on the cavity with a rod d Qo Estimated value of The discontinuous projection function of Qo Indicates the virtual control flow Q of the rod chamber 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 of the total uncertainty of the chamber flow rate in the rod chamber is represented by d 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; 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-DOF hydraulic manipulator, k1 represents the positive definite diagonal matrix of sliding mode coefficients, 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 of 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. 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 F Denotes 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 denote the derivatives of the desired chamber pressures for the rodless chamber and the rod chamber, 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 · Represents the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o They represent the cutoff frequencies of the first-order filters with and without rod cavities; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; The auxiliary linear matrix filter variable ψ represents the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the cavity without rod or cavity with rod; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the system with or without a rod cavity; Φ · represents the linear regression matrix after the reorganization of the cavity without rod or with rod; It represents the estimation error of the lumped parameters of the cavity without rod or with rod; 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 cavity without rod or with rod; 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. The parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm is used to update the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm in the adaptive robust controller. The parameter matrices of the rodless cavity and the rod cavity are used to update the estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller respectively.

[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 chamber is obtained. vi And the valve port control voltage u of the hydraulic valve with rod chamber vo , and then control the hydraulic valve of the multi-degree-of-freedom hydraulic robotic arm.

[0037] The present invention first takes into account that the hydraulic cylinder needs 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 volume elastic modulus model, the dynamics of the effective volume 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 volume elastic modulus model is designed based on X-swapping and least squares method. The method shows good convergence, and the final fitting result is highly consistent with the standard model. Finally, an expected pressure update algorithm and an adaptive robust controller are 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 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 a tracking error curve diagram of experimental setting group 1 and experimental setting group 2;

[0042] Figure 3is a comparison curve diagram 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 the specific implementation, wherein, Figure 3 (a) is the reference pressure trajectory curve of the rod cavity and the rodless cavity of the experimental setting group 1 and the 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 pressure tracking error curve diagram of the rod cavity of the experimental setting group 1 and the experimental setting group 2;

[0043] Figure 4 It is a diagram of the internal parameter estimation result 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 the estimation of the internal parameters 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 It is a fitting result diagram about pressure obtained by controller C1 in 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 the experimental setting 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 purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain 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 can be combined with each other as long as they do not conflict with each other.

[0047] like Figure 1 As shown, the hydraulic mechanical arm 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 a multi-degree-of-freedom hydraulic manipulator including an 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 respectively; 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 of transforming 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, 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 chamber and the rod chamber 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 pressures of the rodless chamber and the rod chamber, V i and V o denote the compressible volumes of the cavity without rod and the cavity with rod, β ei and β eo are the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively, Q i and Q o Respectively represent the actual control flow of the rodless cavity and the rod cavity, 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 without rod cavity and with rod cavity, h iand h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, respectively, u vi and u vo denote the valve port control voltage of the hydraulic valve with and without rod chamber respectively; S(·2) denotes the selection function of vector ·2, ·2 represents the vector to be processed; β e· represents the effective bulk elastic modulus of the cavity without or with a rod, θ β· and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part and infinitesimal residual term of It represents the multi-order term whose ratio of the air pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power, θ βi and θ βo Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The polynomial fitting part of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The infinitesimal residual term of and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part θ β· The linear regression matrix and coefficient matrix of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The polynomial fitting part θ β· The coefficient matrix of s and p r They respectively represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator; and Respectively 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 chamber, respectively. 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, 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, θ5 and θ6 are the nominal values ​​of the nonlinear modeling errors of the rodless cavity or the rod cavity of the multi-degree-of-freedom hydraulic manipulator, respectively; n Represents the n-dimensional identity matrix.

[0054] In the second step, according to 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 updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The valve port control voltage is obtained after static mapping of the virtual control flow, 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 p respectively represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity; 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 fit part of the effective bulk modulus of the rodless cavity, and They represent the estimated value and estimated error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity respectively; 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 Respectively represent the quasi-sliding modulus and its derivative; 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 denote 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 total uncertainty of the chamber flow rate based on the rodless cavity d Qi Estimated value of The discontinuous projection function of 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 of the total uncertainty of the chamber flow rate of the rodless cavity is represented by d 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 expected pressure of the rod chamber and its derivative respectively; φ χo The linear regression matrix representing the polynomial fit part of the effective bulk modulus of the cavity with rod, and They represent the estimated value and estimated 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 with a rod cavity, respectively. and They represent the low-frequency part of the total uncertainty of the chamber flow rate in the rod cavity. Qo The estimated value of and its derivative; represents the low-frequency part of the total uncertainty of the chamber flow rate based on the cavity with a rod d Qo Estimated value of The discontinuous projection function of Qo Indicates the virtual control flow Q of the rod chamber 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 of the total uncertainty of the chamber flow rate in the rod chamber is represented by d 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; 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-DOF hydraulic manipulator, k1 represents the positive definite diagonal matrix of sliding mode coefficients, 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 of 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. 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 F Denotes 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 denote the derivatives of the desired chamber pressures for the rodless chamber and the rod chamber, 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 · Represents the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o They represent the cutoff frequencies of the first-order filters with and without rod cavities; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; The auxiliary linear matrix filter variable ψ represents the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the cavity without rod or cavity with rod; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the system with or without a rod cavity; Φ · represents the linear regression matrix after the reorganization of the cavity without rod or with rod; It represents the estimation error of the lumped parameters of the cavity without rod or with rod; 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 cavity without rod or with rod; 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. The parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm is used to update the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm in the adaptive robust controller. The parameter matrices of the rodless cavity and the rod cavity are used to update the estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller respectively.

[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 chamber is obtained. vi And the valve port control voltage u of the hydraulic valve with rod chamber 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 motion control of the multi-degree-of-freedom hydraulic manipulator.

[0080] In the specific implementation of the present invention, the proposed control method is applied to a hydraulic mechanical arm for testing. The flow of the two chambers of the hydraulic cylinder is independently regulated by a 3-position 4-way proportional valve. The following three methods are compared.

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

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

[0083] C3: The effective bulk elastic modulus is regarded as a lumped parameter for estimation and compensation of the controller, 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, j=1,2,3 respectively represent the first-order coefficient, second-order coefficient and third-order coefficient of the fitting polynomial of the effective bulk elastic modulus of the rodless cavity and the rod cavity, and all other variables are consistent with 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, and 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 In this process, the reference trajectory in the joint space is calculated using inverse kinematics and 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 shown in Figure 2 As shown in (b), 1m rad = 10 -3 rad. It is worth mentioning that, although controller C3 is at the boundary value of extreme performance, the tracking performance of controllers C1 and C2 significantly exceeds that of controller C3, as indicated by the large oscillation of their control errors. These results indicate that the nonlinear relationship between the effective bulk elastic modulus and pressure cannot be regarded as a constant under low-pressure conditions, which is also the key reason why some methods aimed at reducing energy losses cannot maintain control performance. In addition, controller C1 shows superior performance compared to controller C2. The online learning enables the controller C1 to be more adaptable when the operating conditions (oil temperature or entrained air content) change.

[0088] like Figure 3 (a) is 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, thereby laying the foundation for the subsequent reduction of throttling losses. Based on the reference pressure, Figure 3 (b) and Figure 3 The pressure control effect of the method of the present invention is shown in (c). 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 non-rod cavity pressure tracking error, the root mean square error of the rod cavity pressure tracking error, the peak error of the non-rod cavity pressure tracking error, and the peak error of the rod cavity pressure tracking error. Figure 4 (a) and Figure 4 (b) shows the controller C1 in the experimental setup group 1 for the rodless cavity. and with rod cavity The estimated result is 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 shown in 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 of experimental setup group 3. Controller C1 shows excellent tracking performance in all dimensions, especially along the Y axis. This shows that the nonlinear effect of the effective bulk modulus is significant and cannot be ignored compared with other global nonlinearities in the hydraulic manipulator.

[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 volume elastic modulus model, the dynamics of the effective volume 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 volume 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 contents are only the technical ideas 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 solutions in accordance with the technical ideas 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, according to the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator, the adaptive robust controller of the multi-degree-of-freedom hydraulic manipulator is designed by using the backstepping method. Each desired joint angle of the multi-degree-of-freedom hydraulic manipulator is input into the adaptive robust controller for processing. At the same time, the parameters of the adaptive robust controller are updated online. After processing, the adaptive robust controller outputs the virtual control flow of the multi-degree-of-freedom hydraulic manipulator. The valve port control voltage is obtained after static mapping of the virtual control flow, and then the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator is controlled. 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 motion control of the multi-degree-of-freedom hydraulic manipulator.

2. The hydraulic mechanical arm motion control method based on low-pressure bulk elastic modulus compensation according to claim 1 is characterized in that: In the first step, the dynamic linearization model of the multi-degree-of-freedom hydraulic manipulator is as follows: ·∈{i,o} 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 respectively; 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, 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 chamber and the rod chamber 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 pressures of the rodless chamber and the rod chamber, V i and V o denote the compressible volumes of the cavity without rod and the cavity with rod, β ei and β eo are the effective bulk elastic modulus of the cavity without rod and the cavity with rod, respectively, Q i and Q o Respectively represent the actual control flow of the rodless cavity and the rod cavity, 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 without rod cavity and with rod cavity, h i and h o They represent the flow voltage mapping function of the rodless cavity and the rod cavity, respectively, u vi and u vo Respectively represent the valve port control voltage of the hydraulic valve with and without rod chamber; S(·2) represents the selection function of vector ·2; β e· represents the effective bulk elastic modulus of the cavity without or with a rod, θ β· and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part and infinitesimal residual term of It represents the multi-order term whose ratio of the air pressure in the rodless cavity or the rod cavity to the absolute pressure is higher than the fourth power, θ βi and θ βo Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The polynomial fitting part of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The infinitesimal residual term, φ χ· and represents the effective bulk elastic modulus β of the cavity without rod or with rod, respectively e· The polynomial fitting part θ β· The linear regression matrix and coefficient matrix of and Denote the effective bulk elastic modulus β of the cavity without rod and the cavity with rod, respectively e· The polynomial fitting part θ β· The coefficient matrix of s and p r They respectively represent the oil supply pressure and reference pressure of the hydraulic pump of the multi-degree-of-freedom hydraulic manipulator; and Respectively 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 chamber, respectively. and They represent the nominal value and bounded deviation value of the chamber flow rate of the rod chamber respectively; θ 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 cavity with a rod, θ5 and θ6 represent the fifth and sixth torque parameters of the parameter matrices of the rodless cavity and the cavity with a rod, respectively; n Represents the n-dimensional identity matrix.

3. The hydraulic mechanical arm motion control method based on low-pressure bulk elastic modulus compensation according to claim 2 is 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 p respectively represent the estimated value and estimated deviation of the fifth torque parameter θ5 of the parameter matrix of the rodless cavity; 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 fit part of the effective bulk modulus of the rodless cavity, and They represent the estimated value and estimated error of the coefficient matrix of the polynomial fitting part of the effective bulk elastic modulus of the rodless cavity respectively; 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 Respectively represent the quasi-sliding modulus and its derivative; 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 denote 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 total uncertainty of the chamber flow rate based on the rodless cavity d Qi Estimated value of The discontinuous projection function of 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 of the total uncertainty of the chamber flow rate of the rodless cavity is represented by d 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 expected pressure of the rod chamber and its derivative respectively; φ χo The linear regression matrix representing the polynomial fit part of the effective bulk modulus of the cavity with rod, and They represent the estimated value and estimated 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 with a rod cavity, respectively. and They represent the low-frequency part of the total uncertainty of the chamber flow rate in the rod cavity. Qo The estimated value of and its derivative; represents the low-frequency part of the total uncertainty of the chamber flow rate based on the cavity with a rod d Qo Estimated value of The discontinuous projection function of Qo Indicates the virtual control flow Q of the rod chamber 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 of the total uncertainty of the chamber flow rate in the rod chamber is represented by d 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; 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-DOF hydraulic manipulator, k1 represents the positive definite diagonal matrix of sliding mode coefficients, 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 of 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. 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 F Denotes 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 by the multi-degree-of-freedom hydraulic manipulator in real time is used as the virtual control flow of the rodless cavity and the rod cavity in the adaptive robust controller.

4. The hydraulic mechanical arm motion control method based on low-pressure bulk elastic modulus compensation according to claim 2 is characterized in that: In the second step, the parameters are updated online adaptively as follows: ∈{i,o} in, and denote the derivatives of the desired chamber pressures for the rodless chamber and the rod chamber, 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 · Represents the cutoff frequency of the first-order filter with or without a rod cavity, λ i and λ o They represent the cutoff frequencies of the first-order filters with and without rod cavities; u · Indicates the actual input voltage of the rodless cavity or the rod cavity; The auxiliary linear matrix filter variable ψ represents the rodless cavity or the rod cavity · The derivative of It represents the linear regression input quantity of the cavity without rod or cavity with rod; and Represent the linear regression input of torque, rod cavity and rodless cavity respectively; ∈ · Indicates the parameter estimation error of the system with or without a rod cavity; Φ · represents the linear regression matrix after the reorganization of the cavity without rod or with rod; It represents the estimation error of the lumped parameters of the cavity without rod or with rod; 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 cavity without rod or with rod; and ρ ·M They represent the upper bound and maximum value of the recursive least squares coefficients of the cavity without rod or cavity with rod respectively; The parameters of the adaptive robust controller are adaptively updated online. The parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm is used to update the estimated value of the parameter matrix of the control thrust of the multi-degree-of-freedom hydraulic manipulator arm in the adaptive robust controller. The parameter matrices of the rodless cavity and the rod cavity are used to update the estimated values ​​of the parameter matrices of the rodless cavity and the rod cavity in the adaptive robust controller respectively.

5. The hydraulic mechanical arm motion control method based on low-pressure bulk elastic modulus compensation according to claim 2 is 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 chamber is obtained. vi And the valve port control voltage u of the hydraulic valve with rod chamber vo , and then control the hydraulic valve of the multi-degree-of-freedom hydraulic robotic arm.

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