Hydraulic mechanical arm virtual decomposition control system and control method configured with balance valve

Abstract

This invention relates to the field of multi-degree-of-freedom hydraulic robotic arm control technology, specifically to a virtual decomposition control system and method for a hydraulic robotic arm equipped with a balance valve. The hydraulic robotic arm includes a hydraulic cylinder and a balance valve disposed at the inlet and / or outlet of the hydraulic cylinder. The control system includes a virtual decomposition controller, which calculates the driving force of the hydraulic cylinder and generates a valve control signal for adjusting the opening pressure of the balance valve. This invention adjusts the opening pressure or flow rate of the balance valve in real time to achieve precise motion control.

Description

Technical Field

[0001] This invention relates to the field of multi-degree-of-freedom hydraulic robotic arm control technology, specifically to a virtual decomposition control system for a large hydraulic robotic arm equipped with a balance valve and a virtual decomposition control method for a large hydraulic robotic arm equipped with a balance valve. Background Technology

[0002] Large hydraulic robotic arms are mechanical systems characterized by strong nonlinearity and strong coupling, consisting of multiple links and joints. While their specialized luffing mechanisms expand the range of motion, their multi-closed-loop structure also presents challenges in determining the forces required for dynamic modeling. Motion is achieved through hydraulic drive, and the core control challenge lies in achieving high-precision flow distribution and stable pressure control, especially under dynamic loads and complex motion conditions.

[0003] Compared to electrically driven robotic arms, hydraulic robotic arms exhibit strong nonlinearity and are difficult to control, with significant pressure fluctuations directly impacting their performance. Because the balance valve provides back pressure and adjusts the pressure according to load fluctuations, the robotic arm exhibits higher stability under complex and variable working conditions, directly affecting the performance of high-inertia hydraulic robotic arms in controlling load lifting, holding, and lowering.

[0004] To ensure stability and accuracy in complex environments, hydraulic robotic arms require higher precision. Through high-precision position control, hydraulic robotic arms can achieve precise positioning and movement, thus demonstrating superior performance. Precise position control not only improves production efficiency but also reduces personnel injuries and error rates.

[0005] However, the hydraulic actuators and joint luffing mechanisms of hydraulic robotic arms form a multi-closed-loop joint structure, resulting in strong coupling between the linear actuator output force and the arm's gravity. This strong coupling can negatively impact the robotic arm's precise positioning and stable motion control. While there are existing authorized control methods for hydraulic robotic arms, such as patent publication number CN114536338A, titled "A Control Method for a Hydraulic Robotic Arm," this method does not provide a detailed analysis of the unique closed-loop structure of hydraulic robotic arms, thus failing to achieve high-precision control. Therefore, a parallel closed-loop solid-liquid decoupling control method is urgently needed.

[0006] Meanwhile, during operation, the complex working conditions and variable loads of hydraulic robotic arms can lead to problems such as sudden stalling, severe vibration, and unstable movement, affecting the safety and accuracy of the robotic arm. Currently, there are methods for decoupling solid-liquid coupling, such as patent publication number CN118123833A, entitled "A Virtual Decomposition Control Method for Flexible Hydraulic Robotic Arm Considering Nonlinear Deformation." This method decouples the closed-loop structure of the hydraulic robotic arm's lever and actuator. However, this method does not consider the problems of difficulty in force calculation and large pressure fluctuations caused by multiple closed-loop structures.

[0007] Traditional balancing valves typically have fixed set pressures, making them unsuitable for adapting to dynamic load changes. To address the challenges of strong coupling in the multi-closed-loop structure of hydraulic manipulators and the variable loads on the boom's motion, a large hydraulic manipulator with a balancing valve and its virtual decomposition control system is proposed. The aim is to design a virtual decomposition controller for the large, multi-closed-loop hydraulic manipulator, then perform dynamic modeling of the balancing valve's internal components, mathematical modeling of its flow and pressure, and integrate the balancing valve model into the virtual decomposition control model. This establishes a large hydraulic manipulator control system with a balancing loop, allowing for real-time adjustment of the balancing valve's opening pressure or flow rate, thus achieving more precise motion control. Summary of the Invention

[0008] In view of the technical problems mentioned above, the present invention aims to provide a control system and a control method for a hydraulic robotic arm.

[0009] According to the present invention, a control system for a hydraulic robotic arm is provided. The hydraulic robotic arm includes a hydraulic cylinder and a balance valve disposed at the inlet and / or outlet of the hydraulic cylinder. The control system includes a virtual decomposition controller, which is used to calculate the driving force of the hydraulic cylinder and generate a valve control signal for adjusting the opening pressure of the balance valve based on the driving force of the hydraulic cylinder.

[0010] According to the present invention, a control method for a hydraulic robotic arm is provided. The hydraulic robotic arm includes a hydraulic cylinder and a balance valve disposed at the inlet and / or outlet of the hydraulic cylinder. The control method for the hydraulic robotic arm includes:

[0011] The required driving force for the hydraulic cylinder is obtained, and the opening pressure of the balance valve is adjusted in real time to provide back pressure that reduces pressure fluctuations, so that the internal hydraulic pressure of the hydraulic cylinder is the same as the driving force.

[0012]

[0013] In the formula, F represents the driving force required by the hydraulic cylinder. a F represents the resultant force of the load. f P represents frictional force. k Indicates the minimum back pressure, ΔPs Characterizing pressure fluctuation properties, A s Indicates the area of ​​the cavity with or without rods.

[0014] In one specific embodiment, the method for obtaining the required driving force of the hydraulic cylinder is as follows:

[0015] The triangular closed-chain mechanism of the hydraulic robotic arm is divided into multiple first subsystems, and the resultant force vector F required for each first subsystem is calculated. r One of the first subsystems is the first hydraulic cylinder, and the driving force F1 of the first hydraulic cylinder is as follows:

[0016]

[0017] In the formula, =[1,0,0,0,0,0].

[0018] In one specific embodiment, the method for obtaining the required driving force of the hydraulic cylinder is as follows:

[0019] The multi-closed-loop structure of the hydraulic manipulator is decomposed into two series structures: a reduced amplitude model and a reduced actuator model. Then, it is further decomposed into multiple second subsystems. The Jacobian matrix J and the Hessian matrix H are solved to obtain the motion screw and force screw of each second subsystem.

[0020] The kinematics and dynamic equations of the reduced system are established under the framework of motion screws and force screws of each second subsystem, and its dynamic model in the generalized output coordinate system is obtained. Then, the inertial parameters and output torques of each second subsystem are integrated to reconstruct the joint dynamic model in the generalized output coordinate system. One of the second subsystems is the second hydraulic cylinder, and the driving force F2 of the second hydraulic cylinder is obtained.

[0021] In a specific embodiment, the multi-closed-loop structure of the hydraulic manipulator is decomposed into two cascaded structures: a reduced amplitude model and a reduced actuator model. Then, it is further decomposed into multiple second subsystems. The Jacobian matrix J and Hessian matrix H are solved to obtain the motion screw and force screw of each second subsystem, as detailed below:

[0022] Let {S} be the generalized coordinate system, and {T} be the object sub-coordinate system attached to the surface of the rigid body. The set of all transformation matrices is represented as:

[0023]

[0024] In the formula, SE(3) is a special Euclidean group for rigid body transformations in three-dimensional space. It is the position of the object's coordinate system {T} relative to the generalized coordinate system {S}. It is the orientation of the object's coordinate system relative to the generalized coordinate system, R. m×nLet R be an m x n matrix. a R represents a vector with 1 row and 1 column, that is, R 3×3 R represents a 3x3 matrix. 3 This represents a vector with 3 rows and 1 column.

[0025] The spinor of motion of a rigid body is represented by a unified matrix:

[0026]

[0027] In the formula, w is the angular velocity about the helical axis, and v is the linear velocity;

[0028] The force spinor is expressed as follows:

[0029]

[0030] In the formula, τ represents the three-dimensional torque, and f represents the three-dimensional force;

[0031] The velocity equations for the generalized coordinates of the i-th subsystem obtained by decomposing the hydraulic robotic arm can be shown below:

[0032]

[0033] In the formula, q is the joint space angle, and q is the relative operating space angle. It is joint space velocity, It is relative operating space speed; It is a variable and The Jacobian matrix between them;

[0034] Differentiating the above equation, we obtain the following equation:

[0035]

[0036] In the formula, For variables and The Hessian matrix between them describes the rate of change of the Jacobian matrix J. Represents a three-dimensional tensor;

[0037] For each subsystem i, for the rotary joint, the helical axis is represented as:

[0038]

[0039] In the formula, It is the position vector of a point on the subsystem;

[0040] For translational joints, the helical axis is represented as:

[0041]

[0042] In the formula, It is the unit vector in the direction of translation;

[0043] Each column of the object's Jacobian matrix corresponds to the helical axis of a joint in the object's coordinate system:

[0044]

[0045] The Hessian matrix H describes the rate of change of the Jacobian matrix J, and H can be obtained from J.

[0046] In a specific embodiment, the reduced system kinematics and reduced system dynamics equations are established under the framework of motion screws and force screws of each second subsystem, resulting in its dynamic model in the generalized output coordinate system. Then, the inertial parameters and output torques of each second subsystem are fused to reconstruct the joint dynamics model in the generalized output coordinate system. One of the second subsystems is the second hydraulic cylinder, and the driving force F2 of the second hydraulic cylinder is obtained as follows:

[0047] The reduced amplitude model is a series mechanism RR robotic arm ABCDEF. The velocity of the amplitude mechanism BCD in the C coordinate system is mapped to the reduced amplitude coordinate system as follows:

[0048]

[0049] In the formula, Let C be the velocity vector. , , and It is the helical motion of points D and B of the revolute joint;

[0050] The reduced amplitude mechanism is a structure with multiple rotational degrees of freedom in the xy plane, which can be simplified to the following form:

[0051]

[0052] The velocity state at point G of the serial mechanism RP robotic arm HG is represented as follows:

[0053]

[0054] In the formula, , , and For the helical shaft of the revolute joint G and the prism joint d;

[0055] The GH serial robotic arm is an RP robotic arm with 2-DOF translation only along the x and y axes, simplified to the following form:

[0056]

[0057] We obtain the following equation:

[0058] ;

[0059] Define the coordinate system and variables for each model, and give the variables of the reduced amplitude model. The reduced dynamic equations of the variable amplitude model are obtained:

[0060]

[0061] In the formula, q1 is a generalized variable. It is generalized angular velocity. It is generalized angular acceleration. It is a generalized force vector. The matrices represent the inertial parameters of the boom. It is a matrix of Coriolis terms and eccentric terms. A vector representing the gravitational term;

[0062] Reduced actuator model variables are The simplified dynamic equations of the actuator model are obtained as follows:

[0063]

[0064] To achieve variable unification, the subsystem variables velocity and acceleration are mapped to the generalized output coordinate system;

[0065] The reduced actuator model dynamic equations become:

[0066]

[0067] According to the principle of virtual work and d'Alembert's principle:

[0068]

[0069] In the formula, q represents the transpose of the Jacobian matrix, where q2 and q both represent generalized coordinate variables;

[0070] By fusing the inertial parameters and output torque of the subsystem, the joint dynamics equations in the generalized output coordinate system are obtained as follows:

[0071]

[0072] In the formula, F2 is the driving force of the second hydraulic cylinder.

[0073] In one specific embodiment, the method for adjusting the opening pressure of the balancing valve in real time includes the following steps:

[0074] Establish the dynamic equations of the balancing valve, including performing flow-pressure mathematical modeling of the balancing valve's internal structure and dynamic modeling of the auxiliary valve core and main valve core of the balancing valve;

[0075] A hydraulic system model with a balancing circuit is established using the dynamic equations of the balancing valve.

[0076] In one specific embodiment, during the load increase phase, the balancing valve acts as a check valve.

[0077] During the overload phase, the balancing valve performs a throttling function;

[0078] During the load holding phase, the balancing valve performs the load holding function.

[0079] In a specific embodiment, the dynamic equations of the balancing valve are established as follows:

[0080] The balancing valve consists of a main valve and an auxiliary valve. During the load increase phase, the auxiliary valve is responsible for controlling the pressure and flow of the main valve. Its action is achieved by adjusting the control pressure P2. The flow conservation equation for the auxiliary valve chamber is as follows:

[0081]

[0082] In the formula, Q2 represents the flow rate from the auxiliary valve cavity, y1 represents the displacement of the auxiliary valve core, V2 represents the volume of the auxiliary cavity, A2 represents the pressure-bearing area of ​​the left end face of the auxiliary valve core, and E is the elastic modulus of the oil.

[0083] Its flow continuity equation is as follows:

[0084]

[0085] In the formula, A1 represents the effective pressure-bearing area of ​​the main valve core. This indicates the main valve spool speed, q1 indicates flow leakage, and V1 indicates the main valve cavity volume. Indicates the pressure change gradient;

[0086] The dynamic equation of the auxiliary valve core:

[0087]

[0088] In the formula, p2 represents the auxiliary pressure, m2 represents the mass of the auxiliary valve core, A2 represents the equivalent pressure-bearing area at the left end of the auxiliary valve core, B2 represents the damping coefficient of the auxiliary valve core, K2 represents the stiffness of the limit spring, y represents the displacement of the auxiliary valve core, and y0 represents the initial length of the limit spring. Represents steady-state hydrodynamic forces;

[0089] The position of the main valve spool is mainly controlled by the pressure difference between the auxiliary pressure P2 and the feedback pressure P1. The dynamic equation of the main valve spool is as follows:

[0090]

[0091] In the formula, p2 represents the auxiliary pressure, p1 represents the feedback pressure, x represents the main valve core displacement, and A x B1 represents the effective pressure-bearing area at the right end of the main valve core, K1 represents the damping coefficient of the main valve core, x0 represents the stiffness of the pressure regulating spring, and F represents the initial length of the spring. w Indicates steady-state hydraulic force;

[0092] The displacement of the main valve spool and the flow rate in the auxiliary valve's upstream chamber control the flow rate in the upper chamber of the main valve. Simultaneously, the pressure P1 in the main valve chamber controls the displacement x of the main valve spool, forming a closed-loop control to achieve precise control of the system's outlet flow rate and load.

[0093]

[0094] In the formula, q2 represents the leakage flow rate, V1 represents the main valve chamber volume, x represents the main valve core displacement, p1 represents the feedback pressure, and A x This indicates the pressure-bearing area at the right end of the main valve core;

[0095] The flow rate Q0 entering the main valve chamber is controlled by the control pressure P1 through the upper chamber of the main valve, which controls the flow rate Q1 at the main valve orifice.

[0096]

[0097] In the formula, q1 represents flow leakage, p0 represents auxiliary pressure, x represents main valve core displacement, A0 represents the equivalent pressure-bearing area at the left end of the main valve core, and E represents the elastic modulus of the oil.

[0098] In a specific embodiment, the hydraulic system model with a balancing circuit is established using the dynamic equations of the balancing valve as follows:

[0099] Establish the flow equation:

[0100]

[0101] Where k is a positive constant, This is expressed as the pressure difference at the proportional servo valve orifice. This is expressed as the control voltage of the proportional servo valve;

[0102]

[0103]

[0104] In the formula, , These are import and export flows, respectively. , , , The valve orifice flow coefficient, For system pressure, For the oil tank pressure, For rodless cavity pressure, The pressure in the rod chamber is v, which is a sign function.

[0105]

[0106]

[0107] Pressure dynamic equation:

[0108]

[0109]

[0110] In the formula , is the area of ​​the rod-side and rodless chambers of the hydraulic cylinder, c is the displacement of the hydraulic rod, and E is the elastic modulus. This refers to the stroke of the hydraulic rod.

[0111] The output force of the hydraulic cylinder can be obtained as follows:

[0112]

[0113] In the formula, This is expressed as the output force of the hydraulic cylinder. Represented as:

[0114]

[0115] To limit the stroke position of the hydraulic rod, the following relationship holds:

[0116]

[0117] There exists monism, for a given It can map a unique valve control voltage u:

[0118]

[0119] In the formula, in the formula, , These are import and export flows, respectively. , , , The valve orifice flow coefficient, For system pressure, For the oil tank pressure, For rodless cavity pressure, Here, lo is the pressure in the rod chamber, x is the maximum stroke of the valve core, x is the displacement of the valve core, and v is a sign function.

[0120] The flow and pressure relationships of the balancing valve and the proportional servo valve are constructed and connected to the virtual decomposition controller model to obtain the flow and pressure of the hydraulic cylinder, which drives the hydraulic cylinder load movement to form a closed-loop system.

[0121] Compared with the prior art, the advantages of this application are as follows.

[0122] This invention addresses the problems of strong coupling and difficulty in force calculation in large hydraulic manipulators composed of multi-joint and multi-closed-loop structures. It adopts a virtual decomposition control method for multi-closed-loop hydraulic manipulators based on helical theory, which divides the multi-closed-loop structure into a reduced amplitude subsystem and a reduced actuator system. Jacobian and Hessian matrices are established between the subsystems, and dynamic equations with multi-closed-loop structures are established. This effectively reduces the strong coupling between the arm joints, simplifies the dynamic modeling process of multi-closed-loop structures, obtains more accurate hydraulic cylinder driving force, and improves positioning accuracy.

[0123] This invention addresses the problem that traditional balancing valves cannot adapt to dynamic load changes. By combining physical and algorithmic approaches, a hydraulic system with multiple balancing circuits is designed based on the different load characteristics of the robotic arm. Dynamic modeling of the balancing valve is performed, and a mathematical model of the internal flow and pressure of the balancing valve is established. By adjusting the return oil back pressure, speed fluctuations caused by load inertia are suppressed, making the robotic arm move more smoothly.

[0124] This invention proposes a large hydraulic manipulator equipped with a balance valve and its virtual decomposition control system. A system model of the large hydraulic manipulator including the nonlinear characteristics of the balance valve is established. Dynamic compensation of the load pressure-flow coupling characteristics is realized under the virtual decomposition control framework, which reduces the impact caused by the multi-closed-loop structure with special amplitude, and at the same time reduces the pressure fluctuation during the movement of the hydraulic manipulator, thereby improving the stability and accuracy of the manipulator system. Attached Figure Description

[0125] The present invention will now be described with reference to the accompanying drawings.

[0126] Figure 1 This is an overall control principle diagram of the control method for a multi-closed-loop hydraulic robotic arm with a balance valve configured in an embodiment of the present invention;

[0127] Figure 2 This is an exploded view of the multi-closed-loop hydraulic robotic arm in an embodiment of the present invention;

[0128] Figure 3 This is an exploded view of the multi-closed-loop structure in an embodiment of the present invention;

[0129] Figure 4This is a diagram showing the internal structure of the H5062N balance valve in an embodiment of the present invention;

[0130] Figure 5 This is a diagram of a hydraulic system with a balance valve configured in an embodiment of the present invention.

[0131] Attached reference numerals: 1. Main valve core; 2. First oil port; 3. Limit spring; 4. X oil port; 5. Valve body; 6. Second oil port; 7. Auxiliary valve core; 8. Gasket; 9. Pressure spring; 10. Pressure adjusting bolt;

[0132] 101. Triangular closed-loop mechanism; 102. First multi-closed-loop structure; 103. Second multi-closed-loop structure; 111. First joint; 112. Second joint; 113. Third joint; 121. First hydraulic cylinder; 122. Second hydraulic cylinder; 123. Third hydraulic cylinder; 131. First boom; 132. Second boom; 133. Third boom; 141. First balance valve; 142. Second balance valve; 143. Third balance valve.

[0133] In this application, all drawings are schematic and are used only to illustrate the principles of the invention, and are not drawn to scale. Detailed Implementation

[0134] To better understand the present invention, the following description, in conjunction with the accompanying drawings and embodiments, further clarifies the content of the invention; however, the scope of the invention is not limited to the embodiments described below. This embodiment pertains to the hydraulic robotic arm of a large hydraulic concrete placing boom.

[0135] See Figure 1 This embodiment proposes a control method for a large hydraulic robotic arm equipped with a balance valve, and the specific implementation steps are as follows.

[0136] According to a first aspect of the present invention, a multi-degree-of-freedom hydraulic robotic arm control system is provided, comprising a hydraulic power source, a proportional control valve group, an overflow safety valve, a multi-degree-of-freedom robotic arm, a hydraulic cylinder, a virtual decomposition controller, a pressure sensor group, an IMU sensor group, an angle encoder group, a balance valve module, an electrical control system, and upper and lower computers.

[0137] As a specific example, the hydraulic power source includes: a motor, an oil tank, and a pressure pump. The pressure pump is driven by the motor, with one end connected to the oil tank. The oil outlet of the pressure pump is connected to the proportional control valve group, the oil inlet of the relief valve is connected to the oil outlet of the hydraulic pump, and the oil outlet of the relief valve is connected to the oil tank.

[0138] As a specific example, the proportional control valve group consists of a three-position four-way proportional servo valve. The first port of the proportional control valve group is connected to the rod-side of the first actuator and the first port 2 of the first balance valve, respectively. The other port of the first port is connected to the pressure pump and the oil tank, respectively. The second port of the proportional control valve group is connected to the two ports of the second balance valve group, respectively. The other port of the second port of the proportional control valve group is connected to the two ports of the second balance valve group, respectively. The other port of the third port of the proportional control valve group is connected to the two ports of the third balance valve group, respectively. The other port of the third port of the proportional control valve group is connected to the pressure pump and the oil tank, respectively.

[0139] As a specific example, the balance valve assembly includes a single balance valve (first balance valve 141) and double symmetrical balance valves (second balance valve 142 and third balance valve 143), and the hydraulic cylinder has three sets, such as... Figure 2 and Figure 5 As shown, the first hydraulic cylinder 121, the second hydraulic cylinder 122, and the third hydraulic cylinder 123 are respectively installed on the first boom 131, the second boom 132, and the third boom 133 to drive and execute the operation. The tubular balance valve (first balance valve 141) is connected to one end of the rodless chamber of the first hydraulic cylinder 121. The rod chamber and the rodless chamber of the second hydraulic cylinder 122 are equipped with a double symmetrical tubular balance valve group (second balance valve 142), and the rod chamber and the rodless chamber of the third hydraulic cylinder 123 are equipped with a double symmetrical tubular balance valve group (third balance valve 143).

[0140] As a specific example, the first balancing valve 141, the second balancing valve 142, and the third balancing valve 143 have the same structure, each including a valve body 5, an auxiliary valve core 7, a main valve core 1, a valve sleeve, a push rod, an auxiliary valve core spring, a main valve core pressure regulating spring, a spring seat, a valve sleeve, an auxiliary valve core spring seat, a pressure regulating screw, multiple gaskets 8, a first oil port 2, a second oil port 6, an X oil port 4, a limit spring 3, and a pressure spring 9. The structure of balancing valves is well known to those skilled in the art and will not be described in detail here.

[0141] As a specific example, one end of the main valve core pressure regulating spring is connected to the pressure regulating screw, and the other end is connected to the left end of the main valve core. The spring seat is connected in series with the pressure regulating screw. The auxiliary valve core is located inside the main valve core. The piston end of the auxiliary valve core is connected to the push rod, and the right end of the main valve core is connected to the auxiliary valve core spring seat.

[0142] As a specific example, the pressure sensor group includes a first pressure sensor to a sixth pressure sensor. The first pressure sensor is connected to the rodless cavity side of the first actuator, the second pressure sensor is connected to the rod cavity side of the first actuator, the third pressure sensor is connected to the rodless cavity side of the second actuator, the fourth pressure sensor is connected to the rod cavity side of the second actuator, the fifth pressure sensor is connected to the rodless cavity side of the third actuator, the sixth pressure sensor is connected to the rod cavity side of the third actuator, the seventh pressure sensor is connected to the outlet of the hydraulic pump, and the eighth pressure sensor is connected to the oil tank.

[0143] As a specific example, the IMU sensor group includes a first IMU sensor to a second IMU sensor, with the first IMU sensor installed at the beginning of the forearm and the second IMU sensor installed at the end of the forearm.

[0144] As a specific example, the angle encoder group includes a first angle encoder to a third angle encoder. The first angle encoder is installed at the connection between the base and the first joint 111 of the upper arm, the second angle encoder is installed at the connection between the upper arm and the middle arm at the second joint 112, and the third angle encoder is installed at the connection between the middle arm and the forearm at the third joint 113.

[0145] As a specific example, the virtual decomposition controller receives signals from the host computer and various pressure sensors and displacement sensors, and sends valve core signals through the slave computer, so that each actuator moves as desired;

[0146] As a second aspect of the present invention, a large hydraulic robotic arm configured with a balance valve and its virtual decomposition control system are provided. In particular, the robotic arm system is virtually decomposed, and then a virtual decomposition controller is designed.

[0147] As a specific example, for step 1, see [link to relevant documentation]. Figure 2 To address the critical transition problem of strong coupling and multi-closed-loop structure in parallel structures of large hydraulic manipulators, the closed-loop structure of the multi-closed-loop large hydraulic manipulator is decomposed into multiple open-loop subsystems. A kinematic and dynamic recursive framework is established for the triangular closed-loop mechanism 101 to obtain the system's transfer matrix U. Through the Newton-Euler method, the kinematics is transmitted from the base to the end effector in the forward direction, and the dynamics are transmitted from the end effector load force to the base in the reverse direction. Finally, the magnitude of the resultant force vector F required for each subsystem is calculated.

[0148] The kinematic transfer matrix U is as follows, taking coordinate systems {A} and {B} as examples:

[0149]

[0150]

[0151] in, A RB Let A be the rotation matrix from subsystem A to subsystem B. A r AB ×) is an antisymmetric matrix operator, r x r y and r z These represent the x, y, and z components of the distance between the origin of subsystem A and the origin of subsystem B, respectively, along the x, y, and z axes of subsystem A.

[0152] Furthermore, the resultant force vectors of each subsystem described in step 1 are then subjected to reverse dynamic transmission, taking adjacent subsystems A and B as an example:

[0153]

[0154]

[0155]

[0156] in A F is the resultant force vector of subsystem A. B F* is the net force vector of subsystem B, R m×n Let R be an m x n matrix. p It is a p x 1 matrix, M A ∈R 6×6 It is the system's mass matrix, C A ( A w)∈R 6×6 G is the matrix of the Coriolis and eccentric terms of subsystem A. A ∈R 6 Let g be the gravity term of rigid body A.

[0157] Force / torque is transmitted between adjacent subsystems. As a subsystem, the hydraulic cylinder can ultimately convert the force into a resultant force F of the hydraulic cylinder. r .

[0158] Then, the driving force F1 of the hydraulic cylinder can be obtained:

[0159]

[0160] In the formula, F1 is the driving force of the first hydraulic cylinder. =[1,0,0,0,0,0],F r It is the combined force of the hydraulic cylinders.

[0161] As a specific example, in step 2, the multi-loop structure (the first multi-loop structure 102 and the second multi-loop structure 103 are the same; this embodiment only uses one of the multi-loop structures as an example) is decomposed into two series structures: a reduced amplitude model and a reduced actuator model. A generalized coordinate system and a sub-coordinate system are established, and the Jacobian matrix J and Hessian matrix H are solved using spinor theory, as follows:

[0162] Step 2.1: The attitude of a rigid body moving in space can be represented by the relative pose of a generalized coordinate system and a sub-coordinate system. {S} is the generalized coordinate system, and {T} is the object sub-coordinate system attached to the surface of the rigid body. The set of all transformation matrices is represented as:

[0163]

[0164] In the formula, It is a special Euclidean group for rigid body transformations in three-dimensional space. It is the position of the object's coordinate system {T} relative to the generalized coordinate system {S}. It is the orientation of the object's coordinate system relative to the generalized coordinate system.

[0165] The helical motion of a rigid body can be represented by a unified matrix:

[0166]

[0167] In the formula, w is called the angular velocity about the helical axis, and v is called the linear velocity.

[0168] Step 2.2, the velocity equation for the generalized coordinates of the i-th serial mechanism obtained by the virtual cutting of the robotic arm system can be shown below:

[0169]

[0170] In the formula, and It is a variable and These are the first derivatives relative to time; It is a variable and The Jacobian matrix between them.

[0171] Differentiating the above equation, we obtain the following equation:

[0172]

[0173] In the formula, Define as a variable and The Hessian matrix between them describes the rate of change of the Jacobian matrix J. Represents a three-dimensional tensor.

[0174] For each subsystem i, for the rotary joint, the helical axis is represented as...

[0175]

[0176] In the formula, It is the position vector of a point on the subsystem;

[0177] For translational joints, the helical axis is represented as:

[0178]

[0179] In the formula, It is the unit vector in the direction of translation.

[0180] Each column of the object's Jacobian matrix corresponds to the helical axis of a joint in the object's coordinate system:

[0181]

[0182] The Hessian matrix H describes the rate of change of the Jacobian matrix J, and H can be obtained from J.

[0183] As a specific example, in step 3, the kinematics and dynamic equations of the reduced system are established under the screw theory framework, and its dynamic model in the generalized output coordinate system is obtained. Then, the inertial parameters and output torque of the subsystem are fused to reconstruct the joint dynamic model in the generalized output coordinate system, as follows:

[0184] Step 3.1: Decompose the multi-closed-loop structure into a reduced amplitude model and a reduced actuator model. The reduced amplitude model is a series mechanism RR robotic arm ABCDEF, with detailed parameters shown in Table 1. Let i be the length of link i (i=1,2,3…); Let i be the mass of link i (i=1,2,3…); The length from the previous rotational joint point to the center of mass of link i; Let be the inertia matrix of link i (i=1,2,3…).

[0185] Table 1. Main geometric parameters of the multi-closed-loop structure;

[0186]

[0187] The velocity state of point C in the reduced amplitude coordinate system of the amplitude-changing mechanism BCD is represented as follows:

[0188]

[0189] In the formula, Let C be the velocity vector; and , , and It is the moving spiral of the rotating joint at points D and B.

[0190]

[0191]

[0192] This reduced amplitude mechanism is a structure with multiple rotational degrees of freedom in the xy plane, which can be simplified to the following form:

[0193]

[0194]

[0195] Step 3.2, further, the G-point velocity state of the serial mechanism RP robotic arm (HG) is represented as follows:

[0196]

[0197] In the formula, , , here and Let G be the helical shaft of the revolute joint G and the prism joint d.

[0198]

[0199]

[0200] Similarly, the GH serial robotic arm is an RP robotic arm with 2-DOF translation only along the x and y axes, which can be simplified to the following form:

[0201]

[0202]

[0203] Furthermore, we obtain the following equation:

[0204]

[0205] Step 3.3, further, determines the coordinate system and variables for each model, given the reduced amplitude model variables. The reduced dynamic equations of the variable amplitude model can be obtained:

[0206]

[0207] In the formula, It is a generalized force vector. The matrices represent the inertial parameters of the boom. It is a matrix representing the Coriolis and eccentric terms. The vector representing the gravitational term.

[0208] Reduced actuator model variables are The simplified dynamic equations of the actuator model can be obtained as follows:

[0209]

[0210] To achieve variable unification, the subsystem variables velocity and acceleration are mapped to the generalized output coordinate system.

[0211] The reduced actuator model dynamic equations become:

[0212]

[0213]

[0214] In the formula, q represents the transpose of the Jacobian matrix, where q2 and q both represent generalized coordinate variables;

[0215] Finally, after obtaining the dynamic equations of the reduced actuator model and the reduced amplitude model in the generalized output coordinate system, the inertial parameters and output torque of the subsystem are fused to obtain the joint dynamic equations in the generalized output coordinate system as follows:

[0216]

[0217] In the formula, F2 is the driving force of the second hydraulic cylinder.

[0218] From Appendix Figure 2 As shown, the first multi-closed-loop structure 102 and the second multi-closed-loop structure 103 have similar structures and can be virtually decomposed into a reduced amplitude model and a reduced actuator model. Similarly, based on the driving force F2 of the second hydraulic cylinder 1222, the driving force F3 of the third hydraulic cylinder 123 can be derived.

[0219] A control method for a large hydraulic robotic arm equipped with a balance valve is presented. The internal working principle of the balance valve is explained in detail. The designed balance valve is a motion control valve that integrates multiple functions. Different working conditions correspond to different working modes, mainly including load raising, overload, and load holding functions, as detailed below.

[0220] As a specific example, such as Figure 4As shown in step 3.1, during the load increase phase, the balance valve acts as a check valve. The second oil port 6 is connected to the check valve port A or B, and the first oil port 2 is connected to the rodless chamber of the hydraulic cylinder. When the check valve is in the left position, the high-pressure oil flows from the second oil port 6 to the first oil port 2. As long as the preload of the auxiliary valve core spring is overcome, the auxiliary valve port opens, and the high-pressure oil passes through the auxiliary valve chamber, enters the first oil port 2, and then enters the rodless chamber, pushing the hydraulic rod to move. The low-pressure oil in the rod chamber enters the oil tank through the check valve, forming a closed loop.

[0221] Step 3.2: During the overload stage, the second oil port 6 is connected to either port A or port B of the check valve, and the first oil port 2 is connected to the rodless chamber of the hydraulic cylinder; port X is the control oil port of the main valve core, which is equipped with damping and can act as a filter. When the check valve is in the right position, when the high-pressure oil flows from port 1 to the second oil port 6, under the combined action of the high-pressure oil at ports 1 and X, the main valve core and the auxiliary valve core move to the right simultaneously, overcoming the preload of the main valve core's pressure regulating spring. When the auxiliary valve core is limited by the pressure regulating screw, the auxiliary valve core stops moving, and the main valve core continues to move to the right. At this time, the throttling port formed by the check valve core and the main valve core opens, and the oil flows from the first oil port 2 into the second oil port 6 after the throttling effect, flowing into the oil tank. This is the throttling function of the balance valve.

[0222] Step 3.3, referring to the oil port connection in Step 3.2, control port X is pressureless. During the load holding phase, the check valve is in the neutral position, and the main valve core is in a leak-free closed state under the action of the return spring, cutting off the possibility of oil flowing from port 1 to port 2. The balance valve is in the locked state, forming a certain back pressure on port 1, which supports the hydraulic cylinder. This is the load holding function of the balance valve.

[0223] As a specific example, when the double-port symmetrical balance valve is in operation, it is similar to the design of the tubular balance valve. The two ports of the double-port symmetrical balance valve are connected to the check valve, and the two ports are connected to the rod chamber and rodless chamber of the hydraulic cylinder. The control port X4 is connected to the rodless chamber.

[0224] Furthermore, when the load condition is exceeded, high-pressure oil flows into the balance valve from the second oil port 6, overcomes the preload of the auxiliary spring, opens the main valve, and the oil flows into the rodless chamber through the second oil port 6. The oil flows into port 3, and under the combined action of the control X oil port 4, the return oil port 4 is opened and enters the oil tank.

[0225] Similarly, under positive load, high-pressure oil flows into the balance valve from port 4, overcomes the preload of the auxiliary spring, opens the main valve, and flows into the rod chamber through port 3. The oil flows into port 1, and under the combined action of controlling port X port 4, opens the return port 6 and enters the oil tank.

[0226] As a specific example, in step 4, flow-pressure mathematical modeling is performed on the details of the internal chambers, oil passages, and orifices of the balancing valve, and dynamic modeling is performed on the auxiliary valve core and the main valve core of the balancing valve, as detailed below.

[0227] Step 4.1: The auxiliary valve controls the pressure and flow rate of the main valve. Its operation is achieved by adjusting the auxiliary pressure P2 and the feedback pressure P1. The flow rate q2 conservation equation of the auxiliary valve chamber is based on the continuity principle, as follows:

[0228]

[0229] In the formula, Q2 represents the flow rate from the auxiliary valve cavity, y1 represents the displacement of the auxiliary valve core, V2 represents the volume of the auxiliary cavity, A2 represents the pressure-bearing area of ​​the left end face of the auxiliary valve core, and E is the elastic modulus of the oil.

[0230] The continuity equation for flow is:

[0231]

[0232] In the formula, A1 represents the effective pressure-bearing area of ​​the main valve core. This indicates the main valve spool speed, q1 indicates flow leakage, and V1 indicates the main valve cavity volume. Indicates the pressure change gradient;

[0233] The control of the auxiliary valve core is also affected by steady-state hydrodynamic forces, as shown below:

[0234]

[0235] In the formula, C d C v These represent the flow coefficient and the hydraulic coefficient, respectively, and D2 represents the auxiliary valve core diameter;

[0236] Furthermore, the movement of the auxiliary valve core is determined by the balance of multiple forces, including hydraulic pressure, inertial force, spring force, damping force, and hydraulic dynamic force, from which its dynamic equation can be obtained:

[0237]

[0238] In the formula, p2 represents the auxiliary valve chamber pressure, m2 represents the auxiliary valve core mass, A2 represents the equivalent pressure-bearing area at the left end of the auxiliary valve core, B2 represents the auxiliary valve core damping coefficient, K2 represents the limit spring stiffness, y represents the auxiliary valve core displacement, and y0 represents the initial length of the limit spring. Represents steady-state hydrodynamic forces;

[0239] Further, in step 4.2, the main valve control of the balance valve is mainly achieved by adjusting the position of the main valve core to control the back pressure and flow of the load in the hydraulic system. The action of the main valve is controlled by the auxiliary pressure, which drives the valve core to move through the pressure difference, thereby controlling the flow and load balance.

[0240] The position of the main valve spool is mainly controlled by the pressure difference between the auxiliary pressure P2 and the feedback pressure P1. The dynamic equation of the main valve spool is as follows:

[0241]

[0242] In the formula, p0 represents the auxiliary pressure, p1 represents the feedback pressure, x represents the main valve core displacement, and A x B1 represents the effective pressure-bearing area at the right end of the main valve core, K1 represents the damping coefficient of the main valve core, x0 represents the stiffness of the pressure regulating spring, and F represents the initial length of the spring. w Indicates steady-state hydraulic force;

[0243] The displacement of the main valve core and the flow rate in the front chamber of the auxiliary valve control the flow rate in the main valve chamber. At the same time, the pressure P1 in the main valve chamber controls the displacement x of the main valve core, forming a closed-loop control to achieve precise control of the system outlet flow rate and load.

[0244]

[0245] In the formula, q2 represents the leakage flow rate, V1 represents the main valve chamber volume, x represents the main valve core displacement, p1 represents the feedback pressure, and A x This indicates the pressure-bearing area at the right end of the main valve core;

[0246] Furthermore, the flow rate Q0 entering the main valve chamber is controlled by the control pressure P1 through the main valve chamber to control the flow rate Q1 at the main valve port;

[0247]

[0248] In the formula, q1 represents flow leakage, p0 represents auxiliary pressure, x represents main valve core displacement, A0 represents the equivalent pressure-bearing area at the left end of the main valve core, and E represents the elastic modulus of the oil.

[0249] As a specific example, the design of using a pipe-type balance valve at the oil return port described in step 5, based on the structure and working principle of the balance valve in step 3, designs a balance circuit that adapts to load fluctuations. When the load increases, it acts as a check valve; when the load is maintained, it acts as a lock-up valve; and when the load is exceeded, it acts as an overflow valve, mainly maintaining the load stability of the first boom 131.

[0250] Furthermore, the safety redundancy design of the double-linked symmetrical balance valve group described in step 6, based on the structure and working principle of the balance valve in step 3, designs a bidirectional balance circuit that adapts to load fluctuations, so that under all working conditions, the balance valve regulates the flow and pressure changes of the hydraulic cylinder, suppressing pressure shocks and oscillations.

[0251] As a specific example, based on the hydraulic balance circuit described in step 7, the dynamic equation of the balance valve is incorporated into the virtual decomposition control model to establish the hydraulic system model of the balance circuit. Referring to the actual hydraulic system and parameters, a system model of the multi-degree-of-freedom hydraulic manipulator is established, as follows.

[0252] Based on the fluid dynamics principle of Bernoulli's static flow equation, a linear relationship model was established between the flow rate at the orifice of a servo valve and the control voltage and the square root of the orifice pressure drop. This revealed the fundamental law that the square difference in flow velocity is proportional to the pressure difference, i.e., the flow equation is:

[0253]

[0254] Where k is a positive constant, This is expressed as a pressure difference. This is represented as the servo valve control voltage.

[0255] According to the definition of fluid bulk modulus, the dynamic equation for the compressibility of fluid within a cavity can be written as:

[0256]

[0257] Where P is the chamber pressure. Defined as the chamber volume, and g is the flow rate entering the chamber.

[0258]

[0259]

[0260] In the formula, , These are import and export flows, respectively. , , , The valve orifice flow coefficient, For system pressure, For the oil tank pressure, For rodless cavity pressure, For the rod chamber pressure, v is a sign function:

[0261]

[0262]

[0263] Furthermore, the dynamic equation for pressure can be written as:

[0264]

[0265]

[0266] In the formula , is the area of ​​the rod-side and rodless chambers of the hydraulic cylinder, c is the displacement of the hydraulic rod, and E is the elastic modulus. This refers to the stroke of the hydraulic rod.

[0267] Furthermore, the output force of the hydraulic cylinder can be obtained as follows:

[0268]

[0269] In the formula, This is expressed as the output force of the hydraulic cylinder. It can be represented as:

[0270]

[0271] To limit the stroke position of the hydraulic rod, the following relationship holds:

[0272]

[0273] Furthermore, There exists monism, for a given This can be mapped to a unique valve control voltage u, which is:

[0274]

[0275] In the formula, , These are import and export flows, respectively. , , , The valve orifice flow coefficient, For system pressure, For the oil tank pressure, For rodless cavity pressure, Let represent the pressure in the rod chamber, lo represent the maximum stroke of the valve core, x represent the displacement of the valve core, and v represent the sign function.

[0276] The flow and pressure relationships of the balancing valve and the proportional servo valve are constructed and connected to the virtual decomposition controller model. The virtual controller sends valve control signals to the proportional servo valve and the balancing valve, and the flow and pressure of the hydraulic cylinder are precisely adjusted to drive the hydraulic cylinder load movement, track the desired trajectory, and thus form a closed-loop system.

[0277] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0278] In this invention, unless otherwise explicitly specified and limited, the terms "installation," "connection," "linking," and "fixing," etc., should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0279] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0280] Finally, it should be noted that the above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A control method for a hydraulic robotic arm, characterized in that, The hydraulic robotic arm includes a hydraulic cylinder and a balance valve disposed at the inlet and / or outlet of the hydraulic cylinder. The control method for the hydraulic robotic arm includes: obtaining the required driving force for the hydraulic cylinder and adjusting the opening pressure of the balance valve in real time to provide back pressure that reduces pressure fluctuations, so that the internal hydraulic pressure of the hydraulic cylinder is the same as the driving force. The method for obtaining the driving force required by the hydraulic cylinder is as follows: The multi-closed-loop structure of the hydraulic manipulator is decomposed into two cascaded structures: a reduced amplitude model and a reduced actuator model. Then, it is further decomposed into multiple second subsystems. The Jacobian matrix J and Hessian matrix H are solved to obtain the motion screw and force screw of each second subsystem, as detailed below: Let {S} be the generalized coordinate system, and {T} be the object sub-coordinate system attached to the surface of the rigid body. The set of all transformation matrices is represented as: In the formula, SE(3) is the special Euclidean group of rigid body transformations in three-dimensional space. It is the position of the object's coordinate system {T} relative to the generalized coordinate system {S}. It is the orientation of the object's coordinate system relative to the generalized coordinate system, R. m×n Let R be an m x n matrix. a Represents a vector with row a and column a; The spinor of motion of a rigid body is represented by a unified matrix: In the formula, w is the angular velocity about the helical axis, and v is the linear velocity; The force spinor is expressed as follows: In the formula, τ represents the three-dimensional torque, and f represents the three-dimensional force; The velocity equations for the generalized coordinates of the i-th subsystem obtained by decomposing the hydraulic robotic arm can be shown below: In the formula, q is the joint space angle, and q is the relative operating space angle. It is joint space velocity, It is relative operating space speed; It is a variable and The Jacobian matrix between them; Differentiating the above equation, we obtain the following equation: In the formula, For variables and The Hessian matrix between them describes the rate of change of the Jacobian matrix J. Represents a three-dimensional tensor; For each subsystem i, for the rotary joint, the helical axis is represented as: In the formula, It is the position vector of a point on the subsystem; For translational joints, the helical axis is represented as: In the formula, It is the unit vector in the direction of translation; Each column of the object's Jacobian matrix corresponds to the helical axis of a joint in the object's coordinate system: The Hessian matrix H describes the rate of change of the Jacobian matrix J, and H can be obtained from J. The kinematics and dynamic equations of the reduced system are established under the framework of motion screws and force screws of each second subsystem, and its dynamic model in the generalized output coordinate system is obtained. Then, the inertial parameters and output torques of each second subsystem are integrated to reconstruct the joint dynamic model in the generalized output coordinate system. One of the second subsystems is the second hydraulic cylinder, and the driving force F2 of the second hydraulic cylinder is obtained.

2. The control method for the hydraulic robotic arm according to claim 1, characterized in that, The method for obtaining the driving force required by the hydraulic cylinder is as follows: The triangular closed-chain mechanism of the hydraulic robotic arm is divided into multiple first subsystems, and the resultant force vector F required for each first subsystem is calculated. r One of the first subsystems is the first hydraulic cylinder, and the driving force F1 of the first hydraulic cylinder is as follows: In the formula, =[1,0,0,0,0,0].

3. The control method for the hydraulic robotic arm according to claim 1, characterized in that, The reduced system kinematics and dynamic equations are established within the framework of motion screws and force screws of each second subsystem, yielding its dynamic model in the generalized output coordinate system. Then, the inertial parameters and output torques of each second subsystem are fused to reconstruct the joint dynamic model in the generalized output coordinate system. One of the second subsystems is the second hydraulic cylinder, and the driving force F2 of the second hydraulic cylinder is obtained, as follows: The reduced amplitude model is a series mechanism RR robotic arm ABCDEF. The velocity of the amplitude mechanism BCD in the C coordinate system is mapped to the reduced amplitude coordinate system as follows: In the formula, Let C be the velocity vector. , , and It is the helical motion of points D and B of the revolute joint; The reduced amplitude mechanism is a structure with multiple rotational degrees of freedom in the xy plane, which can be simplified to the following form: The velocity state at point G of the serial mechanism RP robotic arm HG is represented as follows: In the formula, , , and For the helical shaft of the revolute joint G and the prism joint d; The GH serial robotic arm is an RP robotic arm with 2-DOF translation only along the x and y axes, simplified to the following form: We obtain the following equation: ； Define the coordinate system and variables for each model, and give the variables of the reduced amplitude model. The reduced dynamic equations of the variable amplitude model are obtained as follows: In the formula, q1 is a generalized variable. It is generalized angular velocity. It is generalized angular acceleration. It is a generalized force vector. The matrices represent the inertial parameters of the boom. It is a matrix of Coriolis terms and eccentric terms. A vector representing the gravitational term; Reduced actuator model variables are The simplified dynamic equations of the actuator model are obtained as follows: The reduced actuator model dynamic equations become: In the formula, q represents the transpose of the Jacobian matrix, where q2 and q both represent generalized coordinate variables; By fusing the inertial parameters and output torque of the subsystem, the joint dynamics equations in the generalized output coordinate system are obtained as follows: In the formula, F2 is the driving force of the second hydraulic cylinder.

4. The control method for a hydraulic robotic arm according to any one of claims 1 to 3, characterized in that, The method for adjusting the opening pressure of the balance valve in real time includes the following steps: Establish the dynamic equations of the balancing valve, including performing flow-pressure mathematical modeling of the balancing valve's internal structure and dynamic modeling of the auxiliary valve core and main valve core of the balancing valve; A hydraulic system model with a balancing circuit is established using the dynamic equations of the balancing valve.

5. The control method for the hydraulic robotic arm according to claim 4, characterized in that, During the load increase phase, the balancing valve acts as a check valve; During the overload phase, the balancing valve performs a throttling function; During the load holding phase, the balancing valve performs the load holding function.

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