Hydraulic manipulator force estimation and motion control method based on extended state observer

Abstract

The application discloses a hydraulic mechanical arm force estimation and motion control method based on an extended state observer. The method comprises the following steps: establishing a pressure flow dynamics model of a multi-freedom hydraulic mechanical arm, and an arm dynamics model and a state space thereof; designing an extended state observer, and obtaining an observed estimation result of the arm through the observer; designing a nonlinear robust controller, and obtaining a virtual control thrust and flow of the arm through the controller, and then obtaining a valve control voltage to control the arm; and outputting actual control thrust and joint actual angle of the arm to the controller in real time to complete closed-loop control, so that force estimation and motion control of the hydraulic mechanical arm are realized. The method can solve the problems of unknown end contact force estimation and compensation in control of the hydraulic mechanical arm, and can realize precise motion control effect and accurate external force estimation effect in the case that there is no force sensor at the end of the hydraulic mechanical arm.

Description

Technical Field

[0001] This invention relates to a method for force estimation and motion control of a robotic arm, specifically a method for force estimation and motion control of a hydraulic robotic arm based on an extended state observer. Background Technology

[0002] Hydraulic robotic arms, due to their large output torque and high power density, play an indispensable role in some heavy-duty and harsh environments, such as emergency rescue and mining. With the continuous development of industrial automation, the requirements for the control precision of hydraulic robotic arms are becoming increasingly stringent, presenting new challenges. Traditional PID control methods are insufficient to meet current needs. First, in terms of dynamics, the inherent high-order complex dynamics of hydraulic systems (including cavity pressure, valve core, hydraulic oil leakage, etc.) result in a system dynamics order of at least 3. Furthermore, the nonlinear mapping relationship between joint torques and hydraulic cylinder forces in hydraulic robotic arms, coupled with the multi-joint coupling and multi-input multi-output characteristics introduced by multiple degrees of freedom, significantly increases the complexity of controller design. In addition, interactive operations involving contact with the environment are a common scenario for hydraulic robotic arms. Unknown environmental contact forces can degrade the stability and reliability of the interaction process. However, installing force / torque sensors on the end effector of the robotic arm is often challenging, posing additional technical challenges to the precise operation of the hydraulic robotic arm. Therefore, to achieve stable operation with effective interaction, contact forces must be estimated and compensated. However, existing research on hydraulic robotic arms rarely considers the estimation of environmental contact forces, although some findings can be utilized. Therefore, how to estimate the unknown end-effector contact forces faced by hydraulic robotic arms during control and how to compensate for them in the control process are urgent problems that need to be solved. Summary of the Invention

[0003] To address the problems existing in the background art, the present invention provides a hydraulic mechanical arm force estimation and motion control method based on an extended state observer.

[0004] The technical solution adopted in this invention is:

[0005] The hydraulic robotic arm force estimation and motion control method based on an extended state observer of the present invention includes:

[0006] The first step is to consider the high-order multi-input multi-output characteristics of the hydraulic manipulator, such as its multi-degree-of-freedom configuration and hydraulic transmission method, as well as various strong nonlinearities such as nonlinear friction within the hydraulic cylinder and nonlinear pressure-flow gain. This leads to the establishment of a hydraulic system pressure-flow dynamics model for the multi-degree-of-freedom hydraulic manipulator, and a manipulator dynamics model and its state space that includes the unknown end contact force.

[0007] The second step involves designing an extended state observer based on the hydraulic system pressure-flow dynamics model, the robotic arm dynamics model, and their state space, using the generalized momentum method. The use of generalized momentum avoids the use of acceleration, making the obtained data more reliable. The control state variables and control signals of the multi-free hydraulic robotic arm are input into the extended state observer, and the extended state observer outputs the modeling error of the multi-free hydraulic robotic arm and the observed external force as the observation estimation results.

[0008] The third step involves designing a nonlinear robust controller based on the observation and estimation results using the backstepping method. The actual joint angles, actual joint angular velocities, desired joint angles, and actual control thrust of the multi-free hydraulic manipulator are input into the nonlinear robust controller. The nonlinear robust controller outputs virtual control thrust and virtual control flow. The valve control voltage of the multi-free hydraulic manipulator is obtained based on the virtual control thrust and virtual control flow, thereby controlling the multi-free hydraulic manipulator.

[0009] The fourth step involves the multi-degree-of-freedom hydraulic manipulator outputting the actual control thrust and joint angle in real time to a nonlinear robust controller to complete closed-loop control, thereby realizing force estimation and motion control of the multi-degree-of-freedom hydraulic manipulator.

[0010] In the first step described above, the pressure-flow dynamics model of the hydraulic system of the multi-free hydraulic manipulator is as follows:

[0011]

[0012]

[0013] V i (x L ) = V hi +S i diag[x L ]

[0014] V o (x L ) = V ho +S o diag[x L ]

[0015] Q i =k qi Y i (P i U v )U v

[0016] Q o =k qo Y o (P o U v )U v

[0017]

[0018]

[0019] Among them, V i () and V o () represent the compressible cavity volumes of the rodless and rod-type chambers of the hydraulic actuators at each joint of a multi-free hydraulic robotic arm, respectively. L This indicates the extension of the push rod of each hydraulic actuator cylinder; β e Indicates the elastic modulus of the oil. P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively. S i and S o These represent the contact areas of the push rod in the rodless chamber and the rod chamber of each joint hydraulic actuator cylinder, respectively. J x () denotes the non-singular Jacobian matrix of each joint of a multi-free hydraulic manipulator. q and These represent the actual joint angles and actual joint angular velocities of each joint in a multi-free hydraulic robotic arm, respectively; Q i and Q o These represent the flow rates of the rodless and rod-side chambers of the hydraulic actuators for each joint, respectively; σ represents the oil leakage coefficient. V hi and V ho Let x represent the extension of the push rod of each hydraulic actuator cylinder at the initial moment. L The volumes of the rodless and rod-type cavities when the value is 0. Represents a diagonal matrix; k qi and k qo Y represents the first and second flow gain coefficients of the servo valve, respectively; i () and Y o () represent the nonlinear flow characteristic characterization functions of the rodless cavity and the rod cavity, respectively, U v This indicates the valve control voltage of a multi-free hydraulic robotic arm. P s and P r These represent the hydraulic system supply pressure and return pressure of the multi-free hydraulic robotic arm, respectively.

[0020] In the first step, the dynamic model and state space of the multi-degree-of-freedom hydraulic manipulator are as follows:

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Where M() represents the inertia matrix of the multi-free hydraulic manipulator. It is a symmetric positive definite matrix used to describe the inertial characteristics of a robotic arm system. The denoted represents the actual joint angular acceleration of each joint in a multi-free hydraulic manipulator; C() represents the Coriolis force and centrifugal force matrix, and G() represents the mass matrix. F c and F v These represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively; s() represents the sign function, using... This smooth function is used to represent the sign function to make it differentiable; F L This represents the actual control thrust of the hydraulic cylinders in a multi-free hydraulic robotic arm. τ ext The unknown contact force at the end of the multi-freedom hydraulic manipulator is represented by x1, x2, and x3, which represent the first, second, and third control state variables of the multi-freedom hydraulic manipulator, respectively, i.e., the actual joint angle q and the actual joint angular velocity of each joint. And the actual control thrust F of the hydraulic cylinder L , and Let represent the derivatives of the first, second, and third control state variables of the multi-free hydraulic manipulator, respectively; Q represents the control flow output of the multi-free hydraulic manipulator. and These represent the constant coefficients of the first and second sets, respectively.

[0029] In the second step, the extended state observer is specifically as follows:

[0030]

[0031]

[0032]

[0033]

[0034] β e =β en +Δβ e

[0035] F c =F cn +ΔF c

[0036] F v =F vn +ΔF v

[0037]

[0038]

[0039]

[0040]

[0041] R1(x1,x2)=-[F cn s(x2)+F vn x2]-GC T x2

[0042]

[0043] Δ1=-[ΔF c s(x2)+ΔF v x2]

[0044]

[0045] Where p and Let represent the generalized momentum and its derivative of a multi-free hydraulic manipulator, respectively. M represents the inertia matrix; q and Represent the actual joint angle and actual joint angular velocity of each joint, respectively; C represents the Coriolis force and centrifugal force matrix, and G represents the mass matrix; J x () denotes the non-singular Jacobian matrix of each joint; F L F represents the actual control thrust of the hydraulic cylinder in a multi-free hydraulic robotic arm. c and F v They represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively; s() represents the sign function; τ ext τ represents the unknown contact force at the end of a multi-free hydraulic manipulator. ctrl Represents the system control torque; β e β represents the elastic modulus of the oil. en Indicates the elastic modulus β of the oil e The nominal value, Δβ e Indicates the elastic modulus β of the oile and its nominal value β en The deviation between; F cn F represents the Coulomb coefficient of friction. c The nominal value, ΔF c F represents the Coulomb coefficient of friction. c The deviation between its nominal value and its actual value; F vn F represents the coefficient of viscous friction. v The nominal value; ΔF v F represents the coefficient of viscous friction. v and its nominal value F vn The deviations between them; x1, x2, x3 and x4 represent the first, second, third and fourth control state variables of the multi-free hydraulic manipulator, respectively, and the fourth control state variable x4 represents the generalized momentum p of the multi-free hydraulic manipulator; Δ1 and Δ2 represent the first and second unobtainable values ​​of the extended state observer, respectively; and These represent the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively. and These represent the derivatives of the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively. The fifth control state variable, x5, represents the unknown end-effector contact force τ of the multi-free hydraulic manipulator. ext The sum of the first unobtainable value Δ1 and the sixth control state variable x6 represents the second unobtainable value Δ2; R1() and R2() represent the first and second directly obtainable values ​​of the extended state observer, respectively; η1 and η2 represent the first and second adjustable parameters, respectively. To extend the bandwidth of the extended state observer (ESO); P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively. and σ represents the first and second lumped constant coefficients, respectively; σ represents the oil leakage coefficient.

[0046] The control state variables of the multi-free hydraulic manipulator input to the extended state observer include the first, second, third, and fourth control state variables, and the input control signals include the input pressure P of each joint hydraulic actuator cylinder. i and output pressure P o The modeling error of the multi-free hydraulic manipulator output by the extended state observer is the observed value of the fifth control state variable x5. That is, the unknown contact force τ at the end of a multi-free hydraulic robotic arm. ext Observations And the first observation value Δ1 that cannot be directly obtained The sum of these values, the output external force observation value is the observation value of the sixth control state variable x6. That is, the second observation value Δ2 that cannot be directly obtained.

[0047] In the third step, the nonlinear robust controller is specifically as follows:

[0048]

[0049]

[0050] F d =F da1 +F da2 +F ds1 +F ds2

[0051]

[0052]

[0053]

[0054]

[0055]

[0056]

[0057] Q d =Q da1 +Q da2 +Q ds1 +Q ds2

[0058]

[0059] Q ds1 =-k 3s1 e3,

[0060] Q ds2 =-k 3s2 e3

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070]

[0071]

[0072] Where e1, e2, and e3 represent the joint angle tracking error, sliding modulus-like value, and hydraulic thrust tracking error of the multi-free hydraulic manipulator, respectively. e1 represents the actual joint angle q and the desired joint angle q of the multi-freedom hydraulic manipulator. d Tracking error between Actual angular velocity of joints in a multi-free hydraulic robotic arm and joint expected angular velocity The tracking error between e2 and Let es represent the sliding modulus and its derivative, respectively, and let e3 represent the actual control thrust F of the multi-free hydraulic manipulator. L and virtual control thrust F d The tracking error between them; x1, x2, and x3 represent the first, second, and third control state variables of the multi-freedom hydraulic manipulator, respectively; x 1d and x 3d Let x represent the expected values ​​of the first and third control state variables, respectively, and let x be the expected value of the first control state variable. 1d The expected angle q of the joint d The expected value x of the third control state variable 3d Represents virtual control thrust F d , and These represent the observed values ​​of the fifth control state variable x5 and the sixth control state variable x6, respectively. and Let x5 and x6 represent the observation errors of the fifth control state variable and the sixth control state variable, respectively; k1 represents the first positive definite gain matrix. F d and Let F represent the virtual control thrust and its derivative, respectively. da1 and F da2 These represent the virtual control thrust F. d Feedforward model compensation term and fast dynamics compensation term, F ds1 and F ds2These represent the virtual control thrust F. d Linear stable feedback term and nonlinear robust feedback term; J x () denotes the non-singular Jacobian matrix of each joint; F vn and F cn F represents the coefficient of viscous friction. v Coulomb friction coefficient F c The nominal value; s() represents the sign function; G represents the mass matrix, M represents the inertia matrix, and C represents the Coriolis force and centrifugal force matrices; and Let q represent the joint expected sliding modulus in the sliding modulus e2, respectively. r The derivative and second derivative; k 2s1 and k 2s2 These represent the second and third positive definite gain matrices, respectively. d1、 and These represent the virtual control thrust F. d The static low-frequency component of the modeling error, its estimated value, and the first derivative of the estimated value, δd1(t) represents the virtual control thrust F at time t. d High-frequency components of modeling error, and γ1 and γ2 represent the first and second discontinuous projection functions, respectively; γ1 and γ2 represent the terms used to adjust the fast dynamic compensation term F. da2 The first and second diagonal positive definite gain matrices; Q d Q represents virtual control flow. da1 and Q da2 These represent the virtual control flow Q. d Feedforward model compensation term and fast dynamics compensation term, Q ds1 and Q ds2 These represent the virtual control flow Q. d The linear stable feedback term and the nonlinear robust feedback term, Q da and Q ds These represent the lumped feedforward compensation term and the lumped feedback term of the virtual control flow, respectively; and These represent the first and second lumped constant coefficients, respectively; σ represents the oil leakage coefficient; P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively; β e Indicates the elastic modulus of the oil; and These represent the virtual control thrust F. d The derivatives of the computable and incomputable parts of Y; Q k represents the compensation term for the backstepping method. 3s1 and k3s2 d2 and d3 represent the fourth and fifth positive definite gain matrices, respectively. and These represent the virtual control flow Q. d The static low-frequency component of the modeling error, its estimated value, and the first derivative of the estimated value, δd2(t), represent the virtual control flow rate Q at time t. d High-frequency components of modeling error, w1 and w2 represent the first and second preset constants used for balancing dimensions, respectively; and These represent the virtual control thrust F. d The static low-frequency component d1 and virtual control flow Q of the modeling error d The error value of the static low-frequency component d2 of the modeling error; ξ1 and ξ2 represent arbitrarily small first and second preset parameters, respectively;

[0073] The nonlinear robust controller continuously estimates and updates the unknown external forces / torques and modeling errors of the multi-degree-of-freedom hydraulic manipulator by using the observations of the extended state observer, and then compensates for them back into the controller.

[0074] Nonlinear friction within a hydraulic cylinder specifically includes Coulomb friction and viscous friction, while nonlinear pressure-flow gain specifically includes a nonlinear flow characteristic characterization function.

[0075] This invention first considers the inherent high-order complex dynamics of hydraulic systems (including cavity pressure, spool valve, hydraulic oil leakage, etc.) and the nonlinear mapping relationship between joint torques and hydraulic cylinder forces in a hydraulic manipulator. Adding the multi-joint coupling and multi-input multi-output characteristics introduced by multiple degrees of freedom, a pressure-flow dynamics model of the hydraulic system and a dynamic model of a multi-degree-of-freedom hydraulic manipulator including unknown end-effector contact forces are established and represented in state space. Then, to avoid data unreliability issues caused by the use of acceleration data, generalized momentum is used to optimize the model representation, and an extended state observer is designed based on this. Furthermore, a robust controller is designed within the framework of the backstepping method to control the multi-degree-of-freedom hydraulic manipulator and compensate for the estimated values ​​obtained from the observations, achieving accurate estimation of external forces and precise motion control even without sensors.

[0076] The beneficial effects of this invention are:

[0077] The method of this invention can solve the problem of estimating the unknown contact force at the end of a hydraulic robotic arm during the control process and compensating for it during control. It can achieve precise motion control and accurate external force estimation even when there is no sensor at the end of the hydraulic robotic arm. Attached Figure Description

[0078] Figure 1This is a schematic diagram of the hydraulic robotic arm used in this invention;

[0079] Figure 2 This is a block diagram of the hydraulic robotic arm force estimation and motion control system based on an extended state observer according to the present invention;

[0080] Figure 3 This is a performance curve diagram of the controller in this invention, wherein, Figure 3 (a) is the desired trajectory (point-to-point, P2P) graph. Figure 3 (b) is a comparison of the tracking errors of joint 1. Figure 3 (c) is a comparison of the tracking errors of joint 2;

[0081] Figure 4 This is a graph showing the estimated external forces of the two joints in this invention. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0083] like Figure 2 As shown, the hydraulic manipulator force estimation and motion control method based on the extended state observer of the present invention is as follows:

[0084] The first step is to consider the high-order multi-input multi-output characteristics of the hydraulic manipulator, such as its multi-degree-of-freedom configuration and hydraulic transmission method, as well as various strong nonlinearities such as nonlinear friction within the hydraulic cylinder and nonlinear pressure-flow gain. This leads to the establishment of a hydraulic system pressure-flow dynamics model for the multi-degree-of-freedom hydraulic manipulator, and a manipulator dynamics model and its state space that includes the unknown end contact force.

[0085] The pressure-flow dynamics model of the hydraulic system of a multi-free hydraulic manipulator is as follows:

[0086]

[0087]

[0088] V i (x L ) = V hi +S i diag[x L ]

[0089] V o (x L ) = V ho +So diag[x L ]

[0090] Q i =k qi Y i (P i U v )U v

[0091] Q o =k qo Y o (P o U v )U v

[0092]

[0093]

[0094] Among them, V i () and V o () represent the compressible cavity volumes of the rodless and rod-type chambers of the hydraulic actuators at each joint of a multi-free hydraulic robotic arm, respectively. L This indicates the extension of the push rod of each hydraulic actuator cylinder; β e Indicates the elastic modulus of the oil. P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively. S i and S o These represent the contact areas of the push rod in the rodless chamber and the rod chamber of each joint hydraulic actuator cylinder, respectively. J x () denotes the non-singular Jacobian matrix of each joint of a multi-free hydraulic manipulator. q and These represent the actual joint angles and actual joint angular velocities of each joint in a multi-free hydraulic robotic arm, respectively; Q i and Q o These represent the flow rates of the rodless and rod-side chambers of the hydraulic actuators for each joint, respectively; σ represents the oil leakage coefficient. V hi and V ho Let x represent the extension of the push rod of each hydraulic actuator cylinder at the initial moment. L The volumes of the rodless and rod-type cavities when the value is 0. diag[] represents a diagonal matrix; k qi and k qo Y represents the first and second flow gain coefficients of the servo valve, respectively; i () and Yo () represent the nonlinear flow characteristic characterization functions of the rodless cavity and the rod cavity, respectively, U v This indicates the valve control voltage of a multi-free hydraulic robotic arm. P s and P r These represent the hydraulic system supply pressure and return pressure of the multi-free hydraulic robotic arm, respectively.

[0095] The dynamic model and state space of the multi-degree-of-freedom hydraulic manipulator are as follows:

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] Where M() represents the inertia matrix of the multi-free hydraulic manipulator. It is a symmetric positive definite matrix used to describe the inertial characteristics of a robotic arm system. The denoted represents the actual joint angular acceleration of each joint in a multi-free hydraulic manipulator; C() represents the Coriolis force and centrifugal force matrix, and G() represents the mass matrix. F c and F v These represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively; s() represents the sign function, using... This smooth function is used to represent the sign function to make it differentiable; F L This represents the actual control thrust of the hydraulic cylinders in a multi-free hydraulic robotic arm. τ ext The unknown contact force at the end of the multi-freedom hydraulic manipulator is represented by x1, x2, and x3, which represent the first, second, and third control state variables of the multi-freedom hydraulic manipulator, respectively, i.e., the actual joint angle q and the actual joint angular velocity of each joint. And the actual control thrust F of the hydraulic cylinder L , and Let represent the derivatives of the first, second, and third control state variables of the multi-free hydraulic manipulator, respectively; Q represents the control flow output of the multi-free hydraulic manipulator. and These represent the constant coefficients of the first and second sets, respectively.

[0104] The second step involves designing an extended state observer based on the hydraulic system pressure-flow dynamics model, the robotic arm dynamics model, and their state space, using the generalized momentum method. The use of generalized momentum avoids the use of acceleration, making the obtained data more reliable. The control state variables and control signals of the multi-free hydraulic robotic arm are input into the extended state observer, and the extended state observer outputs the modeling error of the multi-free hydraulic robotic arm and the observed external force as the observation estimation results.

[0105] The extended state observer is as follows:

[0106]

[0107]

[0108]

[0109]

[0110] β e =β en +Δβ e

[0111] F c =F cn +ΔF c

[0112] F v =F vn +ΔF v

[0113]

[0114]

[0115]

[0116]

[0117] R1(x1,x2)=[F cn s(x2)+F vn x2]-GC T x2

[0118]

[0119] Δ1=-[ΔF c s(x2)+ΔF v x2]

[0120]

[0121] Where p and Let represent the generalized momentum and its derivative of a multi-free hydraulic manipulator, respectively. M represents the inertia matrix; q and Represent the actual joint angle and actual joint angular velocity of each joint, respectively; C represents the Coriolis force and centrifugal force matrix, and G represents the mass matrix; J x () denotes the non-singular Jacobian matrix of each joint; F L F represents the actual control thrust of the hydraulic cylinder in a multi-free hydraulic robotic arm. c and F v They represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively; s() represents the sign function; τ ext τ represents the unknown contact force at the end of a multi-free hydraulic manipulator. ctrl Represents the system control torque; β e β represents the elastic modulus of the oil. en Indicates the elastic modulus β of the oil e The nominal value, Δβ e Indicates the elastic modulus β of the oil e and its nominal value β en The deviation between; F cn F represents the Coulomb coefficient of friction. c The nominal value, ΔF c F represents the Coulomb coefficient of friction. c The deviation between its nominal value and its actual value; F vn F represents the coefficient of viscous friction. v The nominal value; ΔF v F represents the coefficient of viscous friction. v and its nominal value F vn The deviations between them; x1, x2, x3 and x4 represent the first, second, third and fourth control state variables of the multi-free hydraulic manipulator, respectively, and the fourth control state variable x4 represents the generalized momentum p of the multi-free hydraulic manipulator; Δ1 and Δ2 represent the first and second unobtainable values ​​of the extended state observer, respectively; and These represent the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively. and These represent the derivatives of the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively. The fifth control state variable, x5, represents the unknown end-effector contact force τ of the multi-free hydraulic manipulator. ext The sum of the first unobtainable value Δ1 and the sixth control state variable x6 represents the second unobtainable value Δ2; R1() and R2() represent the first and second directly obtainable values ​​of the extended state observer, respectively; η1 and η2 represent the first and second adjustable parameters, respectively. To extend the bandwidth of the extended state observer (ESO); P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively. and σ represents the first and second lumped constant coefficients, respectively; σ represents the oil leakage coefficient.

[0122] The control state variables of the multi-free hydraulic manipulator input to the extended state observer include the first, second, third, and fourth control state variables, and the input control signals include the input pressure P of each joint hydraulic actuator cylinder. i and output pressure P o The modeling error of the multi-free hydraulic manipulator output by the extended state observer is the observed value of the fifth control state variable x5. That is, the unknown contact force τ at the end of a multi-free hydraulic robotic arm. ext Observations And the first observation value Δ1 that cannot be directly obtained The sum of these values, the output external force observation value is the observation value of the sixth control state variable x6. That is, the second observation value Δ2 that cannot be directly obtained.

[0123] The third step involves designing a nonlinear robust controller based on the observation and estimation results using the backstepping method. The actual joint angles, actual joint angular velocities, desired joint angles, and actual control thrust of the multi-free hydraulic manipulator are input into the nonlinear robust controller. The nonlinear robust controller outputs virtual control thrust and virtual control flow. The valve control voltage of the multi-free hydraulic manipulator is obtained based on the virtual control thrust and virtual control flow, thereby controlling the multi-free hydraulic manipulator.

[0124] The nonlinear robust controller is as follows:

[0125]

[0126]

[0127] F d =F da1 +F da2 +F ds1 +F ds2

[0128]

[0129]

[0130]

[0131]

[0132]

[0133]

[0134] Q d =Q da1 +Q da2 +Q ds1 +Q ds2

[0135]

[0136] Q ds1 =-k 3s1 e3,

[0137] Q ds2 =-k 3s2 e3

[0138]

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148]

[0149] Where e1, e2, and e3 represent the joint angle tracking error, sliding modulus-like value, and hydraulic thrust tracking error of the multi-free hydraulic manipulator, respectively. e1 represents the actual joint angle q and the desired joint angle q of the multi-freedom hydraulic manipulator. d Tracking error between Actual angular velocity of joints in a multi-free hydraulic robotic arm and joint expected angular velocity The tracking error between e2 and Let es represent the sliding modulus and its derivative, respectively, and let e3 represent the actual control thrust F of the multi-free hydraulic manipulator. L and virtual control thrust F d The tracking error between them; x1, x2, and x3 represent the first, second, and third control state variables of the multi-freedom hydraulic manipulator, respectively; x 1d and x 3d Let x represent the expected values ​​of the first and third control state variables, respectively, and let x be the expected value of the first control state variable. 1d The expected angle q of the joint d The expected value x of the third control state variable 3d Represents virtual control thrust F d , and These represent the observed values ​​of the fifth control state variable x5 and the sixth control state variable x6, respectively. and Let x5 and x6 represent the observation errors of the fifth control state variable and the sixth control state variable, respectively; k1 represents the first positive definite gain matrix. F d and Let F represent the virtual control thrust and its derivative, respectively. da1 and F da2 These represent the virtual control thrust F. d Feedforward model compensation term and fast dynamics compensation term, F ds1 and F ds2 These represent the virtual control thrust F. d Linear stable feedback term and nonlinear robust feedback term; J x () denotes the non-singular Jacobian matrix of each joint; F vn and F cn F represents the coefficient of viscous friction. v Coulomb friction coefficient F c The nominal value; s() represents the sign function; G represents the mass matrix, M represents the inertia matrix, and C represents the Coriolis force and centrifugal force matrices; and Let q represent the joint expected sliding modulus in the sliding modulus e2, respectively. r The derivative and second derivative; k 2s1 and k 2s2 These represent the second and third positive definite gain matrices, respectively. d1、 and These represent the virtual control thrust F. d The static low-frequency component of the modeling error, its estimated value, and the first derivative of the estimated value, δd1(t) represents the virtual control thrust F at time t.d High-frequency components of modeling error, and γ1 and γ2 represent the first and second discontinuous projection functions, respectively; γ1 and γ2 represent the terms used to adjust the fast dynamic compensation term F. da2 The first and second diagonal positive definite gain matrices; Q d Q represents virtual control flow. da1 and Q da2 These represent the virtual control flow Q. d Feedforward model compensation term and fast dynamics compensation term, Q ds1 and Q ds2 These represent the virtual control flow Q. d The linear stable feedback term and the nonlinear robust feedback term, Q da and Q ds These represent the lumped feedforward compensation term and the lumped feedback term of the virtual control flow, respectively; and These represent the first and second lumped constant coefficients, respectively; σ represents the oil leakage coefficient; P i and P o These represent the input and output pressures of the hydraulic actuators for each joint, respectively; β e Indicates the elastic modulus of the oil; and These represent the virtual control thrust F. d The derivatives of the computable and incomputable parts of Y; Q k represents the compensation term for the backstepping method. 3s1 and k 3s2 d2 and d3 represent the fourth and fifth positive definite gain matrices, respectively. and These represent the virtual control flow Q. d The static low-frequency component of the modeling error, its estimated value, and the first derivative of the estimated value, δd2(t), represent the virtual control flow rate Q at time t. d High-frequency components of modeling error, w1 and w2 represent the first and second preset constants used for balancing dimensions, respectively; and These represent the virtual control thrust F. d The static low-frequency component d1 and virtual control flow Q of the modeling error d The error value of the static low-frequency component d2 of the modeling error; ξ1 and ξ2 represent arbitrarily small first and second preset parameters, respectively;

[0150] The nonlinear robust controller continuously estimates and updates the unknown external forces / torques and modeling errors of the multi-degree-of-freedom hydraulic manipulator by using the observations of the extended state observer, and then compensates for them back into the controller.

[0151] The fourth step involves the multi-degree-of-freedom hydraulic manipulator outputting the actual control thrust and joint angle in real time to a nonlinear robust controller to complete closed-loop control, thereby realizing force estimation and motion control of the multi-degree-of-freedom hydraulic manipulator.

[0152] Nonlinear friction within a hydraulic cylinder specifically includes Coulomb friction and viscous friction, while nonlinear pressure-flow gain specifically includes a nonlinear flow characteristic characterization function.

[0153] This invention addresses the high-performance control requirements of multi-degree-of-freedom hydraulic manipulators. It integrates the advantages of generalized momentum and extended state observers, designing a robust controller within a backstepping control framework to address the complex dynamics of the hydraulic manipulator. By combining generalized momentum and extended state observer theory, two low-order ESOs are proposed to estimate external forces / torques and modeling errors. This controller compensates for the estimated external forces and modeling errors, theoretically guaranteeing the stability of the entire system. Finally, simulations verify the effectiveness of the controller.

[0154] A simplified diagram of the hydraulic robotic arm in this embodiment of the invention is shown below. Figure 1 As shown, L1 and L2 represent the lengths of the upper arm and lower arm linkages, respectively, and x represents the actual value of the control state variable, x = [x1, x2, x3]. T .

[0155] like Figure 2 As shown, the main objectives of this invention are twofold: First, to obtain accurate estimates of force and torque by designing an extended state observer (ESO); second, to use the estimated force and torque to compensate for the feedforward model compensation, then synthesize the feedforward model compensation with the nonlinear robust feedback and linear stable feedback in the nonlinear robust controller, finally mapping it to the control voltage, and finally generating the control voltage to control the hydraulic robotic arm. Simultaneously, the tracking error calculated from the actual angle, angular velocity, and control thrust generated by the hydraulic robotic arm and the desired angle formed by the desired trajectory is further used as the input to the nonlinear robust controller, thus completing the closed-loop control of the entire control system.

[0156] Finally, simulation was performed using MATLAB Simulink. This simulation mainly considers two joints of the robotic arm (upper arm and forearm joints). Hereafter, joint 1 refers to the upper arm joint and joint 2 refers to the forearm joint.

[0157] The parameter configurations for the controller and observer are shown in Table 1:

[0158] Regarding the setting of initial values, The initial value is set to: The adaptive gain is γ1=diag([5,10]), γ2=diag(

[10] ). -6 10-6 ]).

[0159] Table 1 Controller and Observer Parameters

[0160]

[0161] The simulation uses a point-to-point (P2P) trajectory as the desired trajectory. Figure 3 (a) shows the P2P trajectory. The P2P trajectory consists of three phases: stationary, constant velocity, and constant acceleration. These phases encompass basic motion conditions and provide rich motion information, which can be effectively used to verify the performance of the controller. Furthermore, the P2P trajectory is three-order differentiable, satisfying the trajectory requirements of the control design phase. Figure 3 Table 2 illustrates the impact of tracking error on the two joints, where Figure 3 (b) corresponds to joint 1. Figure 3 (c) corresponds to joint 2. The curve shows that the trajectory with external torque compensation exhibits faster and better tracking performance. This improvement is more pronounced compared to joint 1 because joint 2 experiences a much larger torque. In the case of joint 1, the peak error of the compensation curve is 5.5 × 10⁻⁶. -3 The peak error of the uncompensated curve is 7.9 × 10⁻⁶. -3 For joint 2, the peak error of the compensation curve is 1.05 × 10⁻⁶. -2 The peak error of the uncompensated curve is 1.16 × 10⁻⁶. -2 Spend.

[0162] The comparison shows that the control accuracy of joint 1 improved by 30.3%, while that of joint 2 improved by 9.5%. Furthermore, the integral absolute error (IAE) of joint 1 was 93.7 (°·s) (with compensation) and 124.2 (°·s) (without compensation), representing a 24.56% improvement. For joint 2, the IAE values ​​were 82.8 (°·s) (with compensation) and 243.0 (°·s) (without compensation), an improvement of 65.93%, as detailed in Table 2. A decrease in error was observed in the curves exceeding 40 seconds, attributed to the fast dynamic compensation term that plays an integral role. In conclusion, external torque compensation significantly improved control efficiency.

[0163] We set the upper and lower limits of the P2P trajectory to -0.5 to 0.2 radians to closely approximate the angular range in actual operation. During the simulation, we applied a constant external torque (τ1 = 30 N / m, τ2 = 50 N / m) to each joint. We conducted a series of comparative simulations with this setting. By comparing the control performance with and without external torque compensation, while keeping other control gains constant, we verified the effectiveness of the proposed controller and observer.

[0164] Table 2

[0165]

[0166] This invention primarily focuses on the problem of external force compensation, therefore only the external force estimation results for ESO are presented here, such as... Figure 4 As shown, it can be observed that the low-order ESO designed in this study can accurately estimate the magnitude of the external force within approximately 23 seconds, even in the presence of modeling errors. This phenomenon also explains... Figure 3 The compensation error gradually decreases. As the external force compensation gradually approaches the actual value, the feedforward compensation in the controller becomes more accurate, thus achieving excellent control performance.

[0167] In summary, this invention develops a robust controller within a backstepping framework. This controller can compensate for the effects of unknown end-effector contact forces and modeling errors on a hydraulic manipulator, and can effectively estimate these unknown contact forces and modeling errors. Furthermore, by combining generalized momentum and extended state observer theory, two low-order ESOs are proposed to estimate external forces / torques and modeling errors. The estimation of unknown external forces / torques and modeling errors is performed in real time using the extended state observer. Then, a co-simulation method using MATLAB and Simulink is developed to test the effectiveness of the controller, primarily considering the effects on the upper and lower arm joints. The controller can effectively compensate for the additional torque caused by unknown end-effector forces, and the tracking accuracy is significantly improved. This demonstrates the potential of the proposed controller, which has high guiding significance for industrial production.

[0168] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for force estimation and motion control of a hydraulic robotic arm based on an extended state observer, characterized in that, include: The first step is to establish a pressure-flow dynamics model of the hydraulic system of the multi-free hydraulic manipulator, as well as a dynamics model of the manipulator and its state space. The second step involves designing an extended state observer based on the hydraulic system pressure-flow dynamics model, the manipulator dynamics model, and their state space using the generalized momentum method. The control state variables and control signals of the multi-free hydraulic manipulator are input into the extended state observer, and the extended state observer outputs the modeling error of the multi-free hydraulic manipulator and the observed external force as the observation estimation results. The third step is to design a nonlinear robust controller based on the observation and estimation results using the backstepping method. The actual joint angle, actual joint angular velocity, expected joint angle, and actual control thrust of the multi-free hydraulic manipulator are input into the nonlinear robust controller. The nonlinear robust controller outputs virtual control thrust and virtual control flow. The valve control voltage of the multi-free hydraulic manipulator is obtained based on the virtual control thrust and virtual control flow, and then the multi-free hydraulic manipulator is controlled. The fourth step involves the multi-degree-of-freedom hydraulic manipulator outputting the actual control thrust and joint angle in real time to the nonlinear robust controller to complete closed-loop control, thereby realizing force estimation and motion control of the multi-degree-of-freedom hydraulic manipulator. In the second step, the extended state observer is specifically as follows: in, and Let represent the generalized momentum and its derivative of a multi-free hydraulic manipulator, respectively; Represents the inertia matrix; and These represent the actual joint angle and actual joint angular velocity of each joint, respectively. Represents the matrix of Coriolis force and centrifugal force. Represents the mass matrix; Indicates the non-singular Jacobian matrix of each joint; This represents the actual control thrust of the hydraulic cylinder in a multi-free hydraulic robotic arm. and These represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively. Represents a symbolic function; This represents the unknown contact force at the end of a multi-free hydraulic manipulator; Indicates the elastic modulus of the oil. Indicates the elastic modulus of oil The nominal value, Indicates the elastic modulus of oil and its nominal value Deviation between; Represents the Coulomb coefficient of friction The nominal value, Represents the Coulomb coefficient of friction The deviation between its nominal value and its actual value; Indicates the coefficient of viscous friction The nominal value; Indicates the coefficient of viscous friction and its nominal value Deviation between; , , and These represent the first, second, third, and fourth control state variables of the multi-freedom hydraulic robotic arm, respectively. The fourth control state variable... Generalized momentum representing a multi-free hydraulic manipulator ; and These represent the first and second unobtainable values ​​of the extended state observer, respectively. , , and These represent the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively. , , and Let these represent the derivatives of the observed values ​​of the third, fourth, fifth, and sixth control state variables, respectively, and the fifth control state variable... Unknown contact force at the end of a multi-free hydraulic robotic arm The first value cannot be directly obtained The sum of the sixth control state variables This represents the second value that cannot be directly obtained. ; and These represent the first and second directly obtainable values ​​of the extended state observer, respectively. and These represent the first and second adjustable parameters, respectively. and These represent the input and output pressures of the hydraulic actuators for each joint, respectively. and These represent the total constant coefficients of the first and second sets, respectively; Indicates the oil leakage coefficient; The control state variables of the multi-free hydraulic manipulator input to the extended state observer include the first, second, third, and fourth control state variables, and the input control signals include the input pressure of the hydraulic actuators of each joint. and output pressure ; The modeling error of the multi-free hydraulic manipulator output by the extended state observer is the fifth control state variable. Observations The output external force observation value is the sixth control state variable. Observations .

2. The hydraulic manipulator force estimation and motion control method based on an extended state observer according to claim 1, characterized in that: In the first step described above, the pressure-flow dynamics model of the hydraulic system of the multi-free hydraulic manipulator is as follows: in, and These represent the compressible cavity volumes of the rodless and rod-type chambers of the hydraulic actuator cylinders at each joint of a multi-free hydraulic robotic arm, respectively. This indicates the extension of the push rod of each hydraulic actuator cylinder. Indicates the elastic modulus of the oil; and These represent the input and output pressures of the hydraulic actuators for each joint, respectively. and These represent the contact areas of the push rod in the rodless chamber and the rod chamber of each joint hydraulic actuator cylinder, respectively. Let the non-singular Jacobian matrices of each joint of a multi-free hydraulic manipulator be represented. and These represent the actual joint angles and actual joint angular velocities of each joint in a multi-free hydraulic robotic arm, respectively. and These represent the flow rates of the rodless and rod-type chambers of the hydraulic actuator cylinders at each joint, respectively. Indicates the oil leakage coefficient; and These represent the extension of the push rod of each hydraulic actuator cylinder at the initial moment. The volumes of the rodless and rod-shaped cavities below; Represents a diagonal matrix; and These represent the first and second flow gain coefficients of the servo valve, respectively. and Let represent the nonlinear flow characteristics of the rodless cavity and the rod cavity, respectively. This indicates the valve control voltage of a multi-free hydraulic robotic arm; and These represent the hydraulic system supply pressure and return pressure of the multi-free hydraulic robotic arm, respectively.

3. The hydraulic manipulator force estimation and motion control method based on an extended state observer according to claim 2, characterized in that: In the first step, the dynamic model and state space of the multi-degree-of-freedom hydraulic manipulator are as follows: in, The inertia matrix represents the inertia matrix of a multi-free hydraulic robotic arm. This represents the actual joint angular acceleration of each joint in a multi-free hydraulic robotic arm; Represents the matrix of Coriolis force and centrifugal force. Represents the mass matrix; and These represent the Coulomb coefficient of friction and the viscous coefficient of friction, respectively. Represents a symbolic function; This represents the actual control thrust of the hydraulic cylinder in a multi-free hydraulic robotic arm. This represents the unknown contact force at the end of a multi-free hydraulic manipulator; , and These represent the first, second, and third control state variables of the multi-freedom hydraulic robotic arm, respectively, which represent the actual joint angles of each joint. Actual joint angular velocity and the actual control thrust of the hydraulic cylinder , , and Let represent the derivatives of the first, second, and third control state variables of the multi-free hydraulic manipulator, respectively; This indicates the control flow output of a multi-free hydraulic robotic arm; and These represent the constant coefficients of the first and second sets, respectively.

4. The hydraulic manipulator force estimation and motion control method based on an extended state observer according to claim 1, characterized in that: In the third step, the nonlinear robust controller is specifically as follows: in, , and These represent the joint angle tracking error, sliding modulus-like quantity, and hydraulic thrust tracking error of a multi-free hydraulic robotic arm, respectively. This indicates the actual joint angles of a multi-free hydraulic robotic arm. and joint expected angle Tracking error between Actual angular velocity of joints in a multi-free hydraulic robotic arm and joint expected angular velocity Tracking error between and Let them represent the sliding modulus and its derivative, respectively. This represents the actual control thrust of a multi-free hydraulic robotic arm. and virtual control thrust Tracking error between; , and These represent the first, second, and third control state variables of the multi-free hydraulic robotic arm, respectively. and Let represent the expected values ​​of the first and third control state variables, respectively, and the expected value of the first control state variable. Represents the expected angle of the joint The expected value of the third control state variable Represents virtual control thrust ; and These represent the fifth control state variables. and the sixth control state variable Observations , and These represent the fifth control state variables. and the sixth control state variable The observation error; This represents the first positive definite gain matrix; and These represent the virtual control thrust and its derivative, respectively. and These represent virtual control thrust. The feedforward model compensation term and the fast dynamics compensation term, and These represent virtual control thrust. Linear stable feedback term and nonlinear robust feedback term; Indicates the non-singular Jacobian matrix of each joint; and They represent the coefficients of viscous friction, respectively. Coulomb friction coefficient The nominal value; Represents a symbolic function; Represents the mass matrix, Represents the inertia matrix. Represents the matrix of Coriolis force and centrifugal force; and They represent sliding moduli, respectively. Desired sliding modulus of joints The derivative and second derivative; and These represent the second and third positive definite gain matrices, respectively. , and These represent virtual control thrust. The static low-frequency component of the modeling error, its estimate, and the first derivative of the estimate. Represents the virtual control thrust at time t High-frequency components of modeling error; and These represent the first and second discontinuous projection functions, respectively. and These represent the first and second diagonal positive definite gain matrices, respectively. This indicates virtual control of traffic. and These represent virtual control flow. The feedforward model compensation term and the fast dynamics compensation term, and These represent virtual control flow. Linear stable feedback term and nonlinear robust feedback term; and These represent the total constant coefficients of the first and second sets, respectively; Indicates the oil leakage coefficient; and These represent the input and output pressures of the hydraulic actuators for each joint, respectively. Indicates the elastic modulus of the oil; and These represent virtual control thrust. The derivatives of the computable and incomputable parts; This represents the compensation term for the backstepping method; and These represent the fourth and fifth positive definite gain matrices, respectively. , and These represent virtual control flow. The static low-frequency component of the modeling error, its estimate, and the first derivative of the estimate. Indicates the virtual control flow at time t High-frequency components of modeling error; and These represent the first and second preset constants, respectively; and These represent virtual control thrust. The static low-frequency component of the modeling error and virtual control traffic The static low-frequency component of the modeling error The error value; and These represent the first and second preset parameters, respectively.

Images