An independent control system for valve ports of a multi-degree-of-freedom hydraulic manipulator and its dual virtual decomposition control method

Abstract

The present invention discloses an independent control system for valve ports of a multi-degree-of-freedom hydraulic manipulator and a dual virtual decomposition control method therefor. First, an independent control system for valve ports of a multi-degree-of-freedom hydraulic manipulator is established, solving the problems of mechanical coupling at the inlet and outlet of a traditional electro-hydraulic system and low energy efficiency. Then, a virtual decomposition control method for the manipulator based on screw theory is proposed. By using the exponential product formula and adjoint matrix to iteratively calculate the velocity screw and force screw of the connecting rod, the geometric characteristics of the manipulator are fully utilized, avoiding the dynamic coupling of the closed-chain structure and greatly simplifying the modeling process. Finally, a virtual decomposition control method for the independent control system of valve ports is invented. By dividing the high-order nonlinear hydraulic dynamic system into multiple simple subsystems, the problem of mutual interference between the speed and pressure of the hydraulic system is solved, greatly improving the stability and control accuracy of the multi-degree-of-freedom hydraulic manipulator.

Description

Technical Field

[0001] The present invention relates to the technical field of hydraulic manipulator control, and particularly relates to a multi-degree-of-freedom hydraulic manipulator valve port independent control system and a dual virtual decomposition control method therefor. Background Art

[0002] Hydraulic manipulators have the characteristics of high energy density, compact structure, good environmental adaptability, etc., and are widely used in the fields of construction machinery, aerospace, marine equipment, nuclear industry, etc. Hydraulic manipulators generally drive the manipulator through an electro-hydraulic control system. In a traditional electro-hydraulic control system, one directional valve controls one actuator, and there is mechanical coupling between the inlet and outlet valve ports, resulting in large throttling losses and low energy efficiency. At the same time, the control of the system relies on a large number of mechanical-hydraulic feedback loops, and the degree of intelligence is low. Therefore, a valve port independent control system is introduced to reduce energy loss by breaking the structural coupling of the inlet and outlet throttle ports, and electronic feedback is introduced to realize the transformation from "hardware determines function" to "software determines function".

[0003] However, although the valve port independent electro-hydraulic control system breaks the coupling of the inlet and outlet valve ports in structure, there is still physical coupling between speed / pressure in the hydraulic system, which will cause interference between the two, thereby affecting the control accuracy. In addition, sudden changes in actual working conditions, loads or commands will cause relatively serious oscillations, seriously affecting the stability and handling comfort of the system. Currently authorized solutions, such as patent publication number CN116447191A, titled an active damping compensation anti-vibration method for a dual-actuator valve port independent control system, but this method realizes the anti-vibration effect by increasing the damping, does not eliminate the coupling of speed / pressure, and increases the system energy consumption.

[0004] At the same time, the hydraulic actuator and the rigid link of the manipulator form a closed-loop structure, resulting in strong coupling between them in kinematics and dynamics. Especially for multi-degree-of-freedom hydraulic manipulators, the computational complexity of the control algorithm of the overall dynamic model is approximately proportional to the fourth power of the number of degrees of freedom of the manipulator, further making the high-precision motion control of the hydraulic manipulator challenging. Currently, the widely used method for solving the dynamic coupling of the closed-loop structure is: virtual decomposition control (Li Lin'an, et al. High-precision motion control method for hybrid hydraulic manipulators. Journal of Xi'an Jiaotong University, 2023). Although the dynamic model established by this method has the form of decoupling of each joint dynamics, which simplifies the difficulty of controller design, this method is modeled based on homogeneous transformation matrices, and local coordinate systems need to be established for each joint, and the postures of each coordinate system are different according to different joint types, and the modeling process is complex and cumbersome, and the geometric meaning is not obvious. Therefore, the present invention proposes a virtual decomposition control method for multi-degree-of-freedom hydraulic manipulators based on screw theory. Summary of the Invention

[0005] The present invention provides a valve-port independent control system for a multi-degree-of-freedom hydraulic manipulator and its dual virtual decomposition control method. A virtual decomposition control method for a multi-closed-loop structure based on screw theory is proposed, which avoids the dynamic coupling problem of the hydraulic manipulator and has simple calculations. Then, through the virtual decomposition control of the valve-port independent control system, the interference problem of pressure / velocity is solved, aiming to achieve high-precision motion control of a multi-degree-of-freedom hydraulic manipulator based on the valve-port independent control system. The technical solution to achieve the object of the present invention is as follows:

[0006] According to the first aspect of the present invention, there is provided a valve-port independent control system for a multi-degree-of-freedom hydraulic manipulator, which includes a hydraulic power source, a relief valve, a valve-port independent control valve group, an actuator, a dual virtual decomposition controller, a pressure sensor, a displacement sensor, and a handle. One end of the valve-port independent control valve group is connected to the rodless chamber or rod chamber of the actuator, and the other end is connected to the hydraulic pump or the oil tank.

[0007] Further, the hydraulic power source includes: a motor, a hydraulic pump, and an oil tank. The hydraulic pump is driven by the motor, the hydraulic pump is connected to the oil tank, the oil outlet of the hydraulic pump is connected to the valve-port independent 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.

[0008] Further, the valve-port independent control valve group is composed of a six-way three-position three-way proportional valve. The first connection of the valve-port independent control valve group is connected to the rodless chamber side of the first actuator, the second connection of the valve-port independent control valve group is connected to the rod chamber side of the first actuator, the third connection of the valve-port independent control valve group is connected to the rodless chamber side of the second actuator, the fourth connection of the valve-port independent control valve group is connected to the rod chamber side of the second actuator, the fifth connection of the valve-port independent control valve group is connected to the rodless chamber side of the third actuator, and the sixth connection of the valve-port independent control valve group is connected to the rod chamber side of the third actuator.

[0009] Further, the pressure sensor includes a first pressure sensor to an eighth pressure sensor. The first pressure sensor is connected to the rodless chamber side of the first actuator, the second pressure sensor is connected to the rod chamber side of the first actuator, the third pressure sensor is connected to the rodless chamber side of the second actuator, the fourth pressure sensor is connected to the rod chamber side of the second actuator, the fifth pressure sensor is connected to the rodless chamber side of the third actuator, the sixth pressure sensor is connected to the rod chamber 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.

[0010] Further, the displacement sensor includes a first displacement sensor to a third displacement sensor. The first displacement sensor is connected to the first actuator, the second displacement sensor is connected to the second actuator, and the third displacement sensor is connected to the third actuator.

[0011] Further, the dual virtual decomposition controller receives the signals from the handle, pressure sensors, and displacement sensors, and issues a spool displacement signal to make the actuator move as expected.

[0012] According to the second aspect of the present invention, a dual virtual decomposition control method for an independent valve port control system of a multi-degree-of-freedom hydraulic manipulator is provided. In particular, the manipulator uses screw theory for virtual decomposition control, including the following steps:

[0013] Step 1: Decompose the multi-joint closed-chain structure of the hydraulic manipulator into multiple closed-chain subsystems. Further, decompose the closed-chain subsystems into two open-chain subsystems.

[0014] Step 2: Establish a corresponding link coordinate system in each closed-chain subsystem, and establish the coordinates of each joint screw axis in the link coordinate system based on screw theory.

[0015] Step 3: Solve the transformation matrix between coordinate systems through the exponential product formula, and then solve the velocity adjoint matrix and force adjoint matrix.

[0016] Step 4: Perform forward iterative kinematics along the hydraulic manipulator to determine the reference motion screw of each link, and perform reverse iterative dynamics along the hydraulic manipulator to determine the reference force screw of each link.

[0017] Step 5: Decompose the independent valve port hydraulic system into a rodless subsystem and a rod subsystem. Further, decompose each subsystem into a cavity subsystem and a valve subsystem.

[0018] Step 6: Solve the reference force of the hydraulic actuator, perform a first-order differentiable chamber pressure planning, and ensure that the pressure in the low-pressure chamber is maintained at a low level.

[0019] Step 7: According to the chamber pressure planned in Step 6, design the virtual decomposition controllers for the inlet and outlet valves respectively to make the output of the system track the desired position command.

[0020] Further, in Step 1, the 3-joint hydraulic manipulator is decomposed into 3 closed-chain subsystems, and each closed-chain subsystem is decomposed into 2 open-chain subsystems, namely a rotational subsystem and a translational subsystem. i represents the i-th closed-chain subsystem, and j represents the open-chain subsystem. When j is odd, it represents the rotational subsystem, and when j is even, it represents the translational subsystem, transforming the problem of solving the dynamics of a complex hydraulic manipulator into the problem of solving the dynamics of simple subsystems.

[0021] Further, in Step 2, a corresponding link coordinate system is established in each closed-chain subsystem, and the coordinates of each joint screw axis in the link coordinate system are established based on screw theory, specifically as follows:

[0022] Step 2.1, establish a link coordinate system (right-handed system) at the head and end of each closed-loop subsystem. The X-axis of the coordinate system is parallel to the link. Considering two adjacent links of the robotic arm connected by a revolute joint or a prismatic joint, the link-fixed coordinate systems are {B i-1} and {B i};

[0023] Step 2.2, based on screw theory, establish the coordinates of each joint screw axis in the link coordinate system. represents the coordinates of the joint axis relative to the coordinate system {B i}, ω i ∈ R 3 is the unit angular velocity of the joint axis relative to the coordinate system {B i}, v i ∈ R 3 is the unit linear velocity relative to the coordinate system {B i}:

[0024]

[0025] In the formula, L represents the length of the end link.

[0026] Further, in Step 3, solve the transformation matrix between coordinate systems through the exponential product formula, and then solve the velocity adjoint matrix and the force adjoint matrix, specifically as follows:

[0027] Step 3.1, solve the transformation matrix between coordinate systems. Define the initial position when two adjacent links are horizontal. represents the transformation matrix of {B i} relative to {B i-1} when the joint is in the initial position. The exponential product formula establishes the mapping relationship from the screw axis coordinates to the matrix:

[0028]

[0029] In the formula, the operators “∧” (vee) and “∨” (wedge) can realize the and mutual conversion and are inverse operators to each other:

[0030]

[0031] Therefore, in the link motion, the transformation matrix of {B i} relative to {B i-1} is:

[0032]

[0033] Step 3.2, solve the velocity adjoint matrix and the force adjoint matrix. According to the {B i} relative to {Bi-1 If it is the transformation matrix of {}, then the velocity adjoint matrix Ad between the two linkages V and the force adjoint matrix Ad F are as follows:

[0034]

[0035] In the formula, Ad(T) is the operator for finding the adjoint matrix of the transformation matrix, that is:

[0036]

[0037] Furthermore, in step 4, iterate the kinematics of each linkage along the positive direction of the hydraulic manipulator to determine the reference motion screw of each linkage, and iterate the dynamics of each linkage along the reverse direction of the hydraulic manipulator to obtain the reference force screw of each linkage, specifically as follows:

[0038] Step 4.1, determine the reference motion screw of each linkage along the positive direction of the manipulator. The reference motion screw defines the angular velocity and linear velocity required by the rigid body in the body coordinate system {B i}:

[0039]

[0040] The relationship between the reference velocity screws between two adjacent linkages is established through the velocity adjoint matrix:

[0041]

[0042] In the formula, is the joint reference velocity, θ id is the joint desired velocity, θ i is the joint actual velocity, and λ is the position feedback gain;

[0043] Step 4.2, determine the reference force screw of each linkage along the reverse direction of the manipulator. The reference force screw defines the reference torque and force received by the rigid body in the body coordinate system {B i}:

[0044]

[0045] According to the Newton-Euler dynamics equation, the reference net force screw of the linkage {B i} is:

[0046]

[0047] In the formula, represents the spatial inertia matrix expressed in {B i}, is the gravity vector, K is the velocity screw feedback gain, is the actual velocity screw, and Ad(V) is the adjoint matrix of the velocity screw:

[0048]

[0049] The relationship between the reference force screws of two adjacent links is established through the force adjoint matrix:

[0050]

[0051] Furthermore, in step 6, considering that the two links are connected by a hydraulic cylinder, the reference force of the hydraulic actuator is solved according to step 4:

[0052]

[0053] Plan the reference pressure p of the high-pressure chamber according to the hydraulic actuator ar and the reference pressure p of the low-pressure chamber br , and ensure that the low-pressure chamber pressure is maintained at a low level. Generally, take Δp c = 0.2 MPa without cavitation:

[0054]

[0055] In the formula, A a is the effective area of the rodless chamber, A b is the effective area of the rod chamber, η dc (f pr ) is a continuous and smooth switching function, c η is a very small constant, generally taken as 5:

[0056]

[0057] Furthermore, in step 7, according to the chamber pressures planned in step 6, the virtual decomposition controllers of the inlet and outlet valves are designed respectively, as follows:

[0058] Step 7.1, considering the rodless subsystem, the chamber subsystem controller is designed as:

[0059]

[0060] In the formula, u v1d is the item related to the control voltage of the inlet valve, Q 1r is the reference flow rate of the high-pressure chamber, β f is the bulk modulus of the oil, x is the actual displacement of the hydraulic cylinder, x r is the reference displacement, p a is the actual pressure of the rodless chamber, k p is the pressure feedback gain, k v is the velocity feedback gain;

[0061] According to the relevant items of the control voltage, the inlet valve subsystem controller is designed as:

[0062]

[0063] In the formula, u 1 is the control voltage of the inlet valve, p s is the system pressure, p r is the oil return pressure, c p1 and c n1 are the flow coefficients of the inlet valve respectively. The pressure-related function v(·) and the selection function S(u) are:

[0064]

[0065]

[0066] Step 7.2, considering the rod subsystem, the chamber subsystem controller is designed as:

[0067]

[0068] In the formula, u v2d is the relevant item of the outlet valve control voltage, Q 2r is the reference flow rate of the low-pressure chamber, x max is the maximum stroke of the hydraulic actuator, p b is the actual pressure of the rod chamber;

[0069] According to the relevant item of the control voltage, the outlet valve subsystem controller is designed as:

[0070]

[0071] In the formula, u 2 is the control voltage of the outlet valve, c p2 and c n2 are the flow coefficients of the inlet valve respectively;

[0072] The virtual decomposition controller of the hydraulic system designed through Step 7 enables the output of the system to track the desired position command.

[0073] Compared with the prior art, the beneficial effects of the present invention are: (1) A multi-degree-of-freedom hydraulic manipulator valve port independent control system and its dual virtual decomposition control method proposed by the present invention avoid the problem that it is difficult to solve the overall dynamics of the multi-closed-chain structure through the dual virtual decomposition control of the hydraulic manipulator and the valve port independent control system, solve the problem of speed / pressure coupling in the hydraulic system, and achieve high-precision motion control of the multi-degree-of-freedom hydraulic manipulator based on the valve port independent control system;

[0074] (2) The present invention proposes a virtual decomposition control method for a multi-degree-of-freedom hydraulic manipulator based on screw theory. Compared with the virtual decomposition control method based on homogeneous transformation matrices, the establishment of local coordinate systems is simplified, making full use of the geometric characteristics of the manipulator. More importantly, in dynamic modeling, only relevant dimensional parameters are required, and the dynamic model can be iteratively obtained using the product of exponentials formula and the adjoint matrix. The modeling process is greatly simplified and programmed, the calculation efficiency is improved, and the portability is strong;

[0075] (3) The present invention proposes a virtual decomposition control method for a valve-port independent control system. By dividing a high-order nonlinear hydraulic dynamic system into multiple simple subsystems, compared with the overall dynamic modeling method, the amount of calculation involved in this method is only proportional to the number of subsystems, the efficiency is greatly improved, and the complexity of control is reduced. At the same time, the problem of mutual interference between pressure / velocity in the hydraulic system is solved through virtual decomposition control, realizing stable and precise control of the hydraulic system. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and those of ordinary skill in the art can obtain other drawings based on these drawings without creative efforts.

[0077] Figure 1 is a schematic diagram of the principle of the valve-port independent control system of the multi-degree-of-freedom hydraulic manipulator in the embodiment of the present invention;

[0078] Figure 2 is a schematic flow chart of the double virtual decomposition control method of the valve-port independent control system of the multi-degree-of-freedom hydraulic manipulator in the embodiment of the present invention;

[0079] Figure 3 is a schematic structural diagram of the hydraulic manipulator of the three-degree-of-freedom valve-port independent electro-hydraulic control system in the embodiment of the present invention;

[0080] Figure 4 is a schematic diagram of the virtual decomposition of the mechanical part of the hydraulic manipulator in the embodiment of the present invention;

[0081] Figure 5 is a schematic diagram of the virtual decomposition of the valve-port independent hydraulic system of the hydraulic manipulator in the embodiment of the present invention;

[0082] Figure 6 is a graph showing the tracking performance and tracking error of joint 1 over time using the double virtual decomposition control method in the embodiment of the present invention;

[0083] Figure 7It is a graph showing the tracking performance of joint 2 and the variation of tracking error over time using the dual virtual decomposition control method in the embodiments of the present invention;

[0084] Figure 8 It is a graph showing the tracking performance of joint 3 and the variation of tracking error over time using the dual virtual decomposition control method in the embodiments of the present invention; Detailed implementation manners

[0085] For the purpose, features and advantages of the embodiments of the present invention to be more obvious and understandable, the following will describe in detail the specific implementation manners of the present invention with reference to the accompanying drawings. The specific implementation manners described herein are only used to illustrate and explain the present invention and are not used to limit the present invention. In addition, in order to make the drawings clear and easy to understand, some components are simplified and schematically shown. For those of ordinary skill in the art, the specific meanings of the reference numerals can be understood according to specific situations.

[0086] The present invention relates to a valve port independent control system for a multi-degree-of-freedom hydraulic manipulator and its dual virtual decomposition control method. This embodiment uses a hydraulic manipulator with a three-degree-of-freedom valve port independent electro-hydraulic system, and takes the first closed-chain analysis object. Similarly, other closed-chains can be solved. Its main structure diagram is referred to Figure 3 as described below:

[0087] According to the first aspect of the present invention, there is provided a valve port independent control system for a multi-degree-of-freedom hydraulic manipulator, referring to Figure 1 , which includes a hydraulic power source 1, a relief valve 2, a valve port independent control valve group 3, an actuator, a dual virtual decomposition controller 5, a pressure sensor, a displacement sensor, and a handle 8. One end of the valve port independent control valve group 3 is connected to the rod chamber or non-rod chamber of the actuator, and the other end is connected to the hydraulic pump 1-1 or the oil tank 1-2.

[0088] As a specific example, the hydraulic power source 1 includes: a hydraulic pump 1-1, a motor 1-2, and an oil tank 1-3. The hydraulic pump 1-1 is driven by the motor 1-2, the hydraulic pump 1-1 is connected to the oil tank 1-3, the oil outlet of the hydraulic pump 1-1 is connected to the valve port independent control valve group 3, the oil inlet of the relief valve 2 is connected to the oil outlet of the hydraulic pump 1-1, and the oil outlet of the relief valve 2 is connected to the oil tank 1-3.

[0089] As a specific example, the valve port independent control valve group 3 is composed of six three-position three-way proportional valves. The first connection 3-1 of the valve port independent control valve group is connected to the rodless cavity side of the first actuator 4-1. The second connection 3-2 of the valve port independent control valve group is connected to the rod side cavity of the first actuator 4-1. The third connection 3-3 of the valve port independent control valve group is connected to the rodless cavity side of the second actuator 4-2. The fourth connection 3-4 of the valve port independent control valve group is connected to the rod side cavity of the second actuator 4-2. The fifth connection 3-5 of the valve port independent control valve group is connected to the rodless cavity side of the third actuator 4-3. The sixth connection 3-6 of the valve port independent control valve group is connected to the rod side cavity of the third actuator 4-3.

[0090] As a specific example, the pressure sensors include the first pressure sensor to the eighth pressure sensor. The first pressure sensor 6-1 is connected to the rodless cavity side of the first actuator 4-1. The second pressure sensor 6-2 is connected to the rod side cavity of the first actuator 4-1. The third pressure sensor 6-3 is connected to the rodless cavity side of the second actuator 4-2. The fourth pressure sensor 6-4 is connected to the rod side cavity of the second actuator 4-2. The fifth pressure sensor 6-5 is connected to the rodless cavity side of the third actuator 4-3. The sixth pressure sensor 6-6 is connected to the rod side cavity of the third actuator 4-3. The seventh pressure sensor 6-7 is connected to the outlet of the hydraulic pump 1-1. The eighth pressure sensor 6-8 is connected to the fuel tank 1-3.

[0091] As a specific example, the displacement sensors include the first displacement sensor to the third displacement sensor. The first displacement sensor 7-1 is connected to the first actuator 4-1. The second displacement sensor 7-2 is connected to the second actuator 4-2. The third displacement sensor 7-3 is connected to the third actuator 4-3.

[0092] As a specific example, the dual virtual decomposition controller 5 receives the signals of the handle 8, each pressure sensor, and displacement sensor, and issues a spool displacement signal, so that the actuator moves as expected.

[0093] According to the second aspect of the present invention, a dual virtual decomposition control method for a valve port independent control system of a multi-degree-of-freedom hydraulic manipulator is provided. In particular, the manipulator uses screw theory for virtual decomposition control, including the following steps:

[0094] As a specific example, in step 1, the 3 closed-chain structures of the three-degree-of-freedom hydraulic manipulator are decomposed into 3 closed-chain subsystems. Further, the closed-chain subsystems are decomposed into two open-chain subsystems, namely a rotational subsystem and a translational subsystem. i represents the i-th closed-chain subsystem, and j represents the open-chain subsystem. When j is odd, it represents the rotational subsystem, and when j is even, it represents the translational subsystem. The problem of solving the dynamics of a complex hydraulic manipulator is transformed into the problem of solving the dynamics of simple subsystems. Refer to Figure 3 .

[0095] As a specific example, in step 2, a corresponding link coordinate system is established for each closed - chain subsystem, and the coordinates of each joint screw axis in the link coordinate system are established based on screw theory, as follows:

[0096] Step 2.1, establish a link coordinate system (right - hand system) at the head and end of each open - chain subsystem. The X - axis of the coordinate system is parallel to the link. Referring to Figure 4 , establish coordinate systems {S i1}, {B i1}, {S i2} and {B i2}, which represent the motion of each link;

[0097] Step 2.2, establish the coordinates of each joint screw axis in the link coordinate system based on screw theory, represents the coordinates of the joint axis relative to the coordinate system {B ij}, represents the coordinates of the joint axis relative to the coordinate system {S ij}:

[0098]

[0099] In the formula, referring to Figure 4 , represents the coordinates of the rotational joint axis 1 of the i - th closed chain in the coordinate system {B i1}, represents the coordinates of the rotational joint axis 2 of the i - th closed chain in the coordinate system {S i2}, represents the coordinates of the translational joint axis 3 of the i - th closed chain in the coordinate system {B i2}.

[0100] As a specific example, in step 3, solve the transformation matrix between coordinate systems through the exponential - product formula, and then solve the velocity adjoint matrix and force adjoint matrix, as follows:

[0101] Step 3.1, solve the transformation matrix between coordinate systems. Define the initial position when the horizontal or rotational angle between two adjacent links is 0, represents the transformation matrix of {B i1} relative to {S i1} when the joint is in the initial position, represents the transformation matrix of {S i2} relative to {S i1} when the joint is in the initial position, represents the transformation matrix of {B i2} relative to {S i2} when the joint is in the initial position;

[0102] The exponential product formula establishes the mapping relationship from the screw axis coordinates to the matrix:

[0103]

[0104] In the formula, the operators “∧” (vee) and “∨” (wedge) can achieve and to convert with each other and are inverse operators:

[0105]

[0106] Therefore, the transformation matrix between two adjacent coordinate systems in the link motion is:

[0107]

[0108] In the formula, represents the transformation matrix of {B i1} relative to {S i1}, represents the transformation matrix of {S i2} relative to {S i1}, represents the transformation matrix of {B i2} relative to {S i2};

[0109] Step 3.2, solve the velocity adjoint matrix and the force adjoint matrix. According to the transformation matrix in Step 3.1, the velocity adjoint matrix Ad V and the force adjoint matrix Ad F between the two links are:

[0110]

[0111] In the formula, Ad(T) is the operator for finding the adjoint matrix of the transformation matrix, that is:

[0112]

[0113] Similarly, the velocity adjoint matrix and the force adjoint matrix between the remaining coordinate systems can be obtained.

[0114] As a specific example, in Step 4, the forward iterative kinematics of the hydraulic robotic arm is carried out to determine the reference motion screw of each link, and the reverse iterative dynamics of the hydraulic robotic arm is carried out to determine the reference force screw of each link, as follows:

[0115] Step 4.1, determine the reference motion screw of each link along the forward direction of the robotic arm. The reference motion screw defines the angular velocity and linear velocity required by the rigid body in the body coordinate system {B i}:

[0116]

[0117] The reference velocity screw of each link can be solved by forward iteration through the velocity adjoint matrix:

[0118]

[0119] where, is the joint reference velocity, θ id is the joint desired velocity, θ i is the joint actual velocity, and λ is the position feedback gain;

[0120] Step 4.2, determine the reference force screw of each link along the manipulator in reverse. The reference force screw is defined as the reference torque and force acting on the rigid body in the body coordinate system {B i}:

[0121]

[0122] According to the Newton-Euler dynamics equation, the reference net force screw of link {B i} is:

[0123]

[0124] where, represents the spatial inertia matrix expressed in {B i}, is the gravity vector, K is the velocity screw feedback gain, is the actual velocity screw, and Ad(V) is the adjoint matrix of the velocity screw:

[0125]

[0126] The reference force screw of each link can be solved by reverse iteration through the force adjoint matrix:

[0127]

[0128] As a specific example, in step 5, the orifice independent hydraulic system is decomposed into a rodless subsystem and a rod subsystem. Further, each subsystem is decomposed into a chamber subsystem and a valve subsystem, referring to Figure 5 .

[0129] As a specific example, in step 6, solve the reference force of the hydraulic actuator, perform a first-order differentiable chamber pressure planning, and ensure that the pressure in the low-pressure chamber is maintained at a low level. First, solve the reference force of the hydraulic actuator according to step 4:

[0130]

[0131] According to the hydraulic actuator planning, the reference pressure p of the high-pressure chamberar For the reference pressure p of the low-pressure chamber br , and to ensure that the low-pressure chamber pressure is maintained at a low level, generally take Δp c = 0.2 MPa, and no cavitation occurs:

[0132]

[0133] In the formula, A a is the effective area of the rodless chamber, A b is the effective area of the rod chamber, η dc (f pr ) is a continuous and smooth switching function, c η is a very small constant, generally take 5:

[0134]

[0135] As a specific example, in step 7, according to the chamber pressure planned in step 6, the virtual decomposition controllers of the inlet and outlet valves are designed respectively to make the output of the system track the desired position command, specifically as follows:

[0136] Step 7.1, considering the rodless subsystem, the chamber subsystem controller is designed as:

[0137]

[0138] In the formula, u v1d is the item related to the control voltage of the inlet valve, Q 1r is the reference flow rate of the high-pressure chamber, β f is the elastic modulus of the oil, x is the actual displacement of the hydraulic cylinder, x r is the reference displacement, p a is the actual pressure of the rodless chamber, k p is the pressure feedback gain, k v is the velocity feedback gain;

[0139] According to the item related to the control voltage, the inlet valve subsystem controller is designed as:

[0140]

[0141] In the formula, u 1 is the control voltage of the inlet valve, p s is the system pressure, p r is the return oil pressure, c p1 、c n1 are the flow coefficients of the inlet valve respectively, the pressure-related function v(·) is and the selection function S(u) is:

[0142]

[0143]

[0144] Step 7.2, considering the rod system, the chamber subsystem controller is designed as follows:

[0145]

[0146] where u v2d is the item related to the control voltage of the outlet valve, Q 2r is the reference flow rate of the low-pressure chamber, x max is the maximum stroke of the hydraulic actuator, and p b is the actual pressure of the rod chamber;

[0147] According to the item related to the control voltage, the outlet valve subsystem controller is designed as follows:

[0148]

[0149] where u 2 is the control voltage of the outlet valve, and c p2 , c n2 are the flow coefficients of the inlet valve respectively;

[0150] The virtual decomposition controller of the hydraulic system designed through Step 7 enables the output of the system to track the desired position command.

[0151] Effect of the control method: Figure 6 , Figure 7 and Figure 8 are the curves of the tracking performance of the three joints of the hydraulic manipulator and the variation of the tracking error with time using the double virtual decomposition control method. It can be seen from the three figures that the tracking error of the method proposed in the present invention reaches a relatively high tracking accuracy, thus verifying the effectiveness of the method.

[0152] The above content is only an illustration and explanation of the independent control system of the valve ports of the multi-degree-of-freedom hydraulic manipulator and its double virtual decomposition control method. In addition, the above embodiments are only examples. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic manipulator, using an independent valve control system, characterized in that: It includes a hydraulic power source, a relief valve, a valve port independent control valve group, an actuator, a dual virtual decomposition controller, a pressure sensor, a displacement sensor, and a handle. One end of the valve port independent control valve group is connected to the rod chamber or rodless chamber of the actuator, and the other end is connected to the hydraulic pump or the oil tank. The hydraulic power source includes: a motor, a hydraulic pump, and an oil tank. The hydraulic pump is driven by the motor, the hydraulic pump is connected to the oil tank, the hydraulic pump oil outlet is connected to the valve port independent control valve group, the relief valve oil inlet is connected to the hydraulic pump oil outlet, and the relief valve oil outlet is connected to the oil tank. It includes the following steps: Step 1, decomposing the multi-joint closed chain structure of the hydraulic mechanical arm into multiple closed chain subsystems, and further decomposing the closed chain subsystem into two open chain subsystems; Step 2, establish the corresponding connecting rod coordinate system in each closed chain subsystem, and establish the coordinates of each joint screw axis in the connecting rod coordinate system based on the screw theory; Step 3, solving the transformation matrix between the coordinate systems by using the exponential product formula, and then solving the velocity adjoint matrix and the force adjoint matrix; Step 4, iterate the kinematics along the hydraulic mechanical arm forward to determine the reference motion screw of each connecting rod, and iterate the dynamics along the hydraulic mechanical arm reverse to determine the reference force screw of each connecting rod; Step 5, decomposing the valve port independent hydraulic system into a rodless subsystem and a rod subsystem, and further decomposing each subsystem into a cavity subsystem and a valve subsystem; Step 6, solving the reference force of the hydraulic actuator, performing first-order differentiable chamber pressure planning, and ensuring that the low-pressure chamber pressure is maintained at a low level; Step 7, according to the chamber pressure planned in step 6, design the virtual decomposition controllers of the inlet and outlet valves respectively, so that the output of the system tracks the desired position instruction.

2. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In the valve port independent control system, the valve port independent control valve group is composed of a six-way three-position proportional valve, the first link of the valve port independent control valve group is connected to the rodless cavity side of the first actuator, the second link of the valve port independent control valve group is connected to the rod cavity side of the first actuator, the third link of the valve port independent control valve group is connected to the rodless cavity side of the second actuator, the fourth link of the valve port independent control valve group is connected to the rod cavity side of the second actuator, the fifth link of the valve port independent control valve group is connected to the rodless cavity side of the third actuator, and the sixth link of the valve port independent control valve group is connected to the rod cavity side of the third actuator; The pressure sensors include first to eighth pressure sensors, 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; The displacement sensor includes a first displacement sensor to a third displacement sensor, the first displacement sensor is connected to the first actuator, the second displacement sensor is connected to the second actuator, and the third displacement sensor is connected to the third actuator; The dual virtual decomposition controller receives signals from the handle and each pressure sensor and displacement sensor, and sends a valve core displacement signal to make the actuator move as expected.

3. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 1, the multi-joint closed chain structure is decomposed into multiple closed chain subsystems, and further, the closed chain subsystem is decomposed into two open chain subsystems, namely a rotation subsystem and a movement subsystem.

4. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 2, the corresponding link coordinate system is established in each closed chain subsystem, and the coordinates of the screw axis of each joint in the link coordinate system are established based on the screw theory, as follows: Step 2.1: Establish a link coordinate system (right-hand system) at the beginning and end of each closed chain subsystem. The X-axis of the coordinate system is parallel to the link. Consider two adjacent links of the robot arm connected by a revolute joint or a translation joint. The link fixed coordinate systems are {B i-1 } and {B i }; Step 2.2, based on the screw theory, establish the coordinates of each joint screw axis in the connecting rod coordinate system. Represents the relative coordinate system of the joint axis {B i } coordinates, ω i ∈R 3 is the relative coordinate system of the joint axis {B i } unit angular velocity, v i ∈R 3 Relative coordinate system {B i Unit linear velocity of}: Where L is the length of the end link.

5. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 3, the transformation matrix between the coordinate systems is solved by the exponential product formula, and then the velocity adjoint matrix and the force adjoint matrix are solved, as follows: Step 3.1, solve the transformation matrix between the coordinate systems, define the initial position when two adjacent links are horizontal, Indicates that the joint is in the initial position {B i }Relative to {B i-1 }, the exponential product formula establishes the mapping relationship from the spiral axis coordinates to the matrix: Therefore, in the connecting rod motion {B i }Relative to {B i-1 The transformation matrix of} is: Step 3.2, solve the velocity adjoint matrix and force adjoint matrix, according to step 3.1 {B i }Relative to {B i-1 }, then the velocity adjoint matrix Ad between the two connecting rods is V and the force adjoint matrix Ad F for:

6. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 4, the kinematics of each link is iterated forward along the hydraulic manipulator to determine the reference motion rotation of each link, and the dynamics of each link is iterated backward along the hydraulic manipulator to obtain the reference force rotation of each link, as follows: Step 4.1, determine the reference motion spin of each link along the forward direction of the robot arm, and the relationship between the reference velocity spins of two adjacent links is established through the velocity adjoint matrix: In the formula, is the joint reference velocity, θ id is the desired joint velocity, θ i is the actual joint velocity, λ is the position feedback gain; Step 4.2, determine the reference force rotation of each link along the reverse direction of the robot arm. According to the Newton-Euler dynamics equation, the link {B i The reference net force screw of} is: In the formula, Indicates that {B i }, is the gravity vector, K is the velocity spinor feedback gain, is the actual velocity spinor; The relationship between the reference force screws of two adjacent links is established by the force adjoint matrix:

7. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 6, consider that the two connecting rods are connected by a hydraulic cylinder and solve the reference force of the hydraulic actuator: Planning the reference pressure p of the high pressure chamber according to the hydraulic actuator ar is the reference pressure of the low pressure chamber p br , and ensure that the pressure in the low-pressure chamber is maintained at a low level, generally taking Δp c =0.2MPa: In the formula, A a A is the effective area of ​​the rodless cavity, b is the effective area of ​​the rod cavity, η dc (f pr ) is a continuous and smooth switching function, c η is a small constant:

8. A dual virtual decomposition control method for a multi-degree-of-freedom hydraulic mechanical arm according to claim 1, characterized in that: In step 7, the virtual decomposition controllers of the inlet and outlet valves are designed respectively, as follows: Step 7.1, considering the rodless subsystem, the chamber subsystem controller is designed as: In the formula, u v1d is the inlet valve control voltage related term, Q 1r is the reference flow rate of the high pressure chamber, β f is the elastic modulus of the oil, x is the actual displacement of the hydraulic cylinder, x r is the reference displacement, p a is the actual pressure of the rodless cavity, k p is the pressure feedback gain, k v is the speed feedback gain; According to the control voltage related items, the inlet valve subsystem controller is designed as: Where u1 is the control voltage of the inlet valve, p s is the system pressure, p r is the oil return pressure, c p1 、c n1 are the flow coefficient of the inlet valve, v(·) is the pressure-related function and S(u) is the selection function; Step 7.2, considering the rod subsystem, the chamber subsystem controller is designed as: In the formula, u v2d is the outlet valve control voltage related term, Q 2r is the reference flow rate of the low pressure chamber, x max is the maximum stroke of the hydraulic actuator, p b is the actual pressure of the rod cavity; According to the control voltage related items, the outlet valve subsystem controller is designed as: Where, u2 is the control voltage of the outlet valve, c p2 、c n2 are the flow coefficients of the inlet valve respectively; Through the virtual decomposition controller of the hydraulic system designed in step 7, the output of the system tracks the desired position command.

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