Modeling method and system for solving rope flexible deformation vibration problem of rope-driven mechanical arm

Abstract

The invention provides a modeling method and system for solving the problem of rope flexible deformation vibration of a rope-driven mechanical arm. The method comprises the steps that the mapping relation between a rope and a joint angle is established; rope deformation elastic potential energy is established according to the rope take-up and pay-off variable quantity driven by a motor-driven winch and the current joint rope mapping length; kinetic energy and potential energy of joint rotation and arm lever movement of a motor-driven rope transmission mechanical arm are defined, and a Lagrange function is constructed; according to the second type of Lagrange equation, a rope-driven mechanical arm system kinetic equation of the mapping relation between the rope variation control input and the mechanical arm joint angle is deduced; optimizing the model, proving the stability, and verifying the effectiveness and reliability of the algorithm. The technical problems of mechanical arm reliability servo defects, low set expected track tracking precision and high-frequency vibration caused by nonlinear characteristics such as flexible vibration, friction, rope deformation and hysteresis existing in a circuit, rope flexibility and a mechanical arm system are solved.

Description

Technical Field

[0001] The invention relates to the field of robot motion and control technology, and in particular to a modeling method and system test for a rope-driven mechanical arm to solve rope deformation and flexible vibration problems. Background Art

[0002] At present, one of the key challenges in building a high-torque robot is to design a joint module that meets the requirements. The joint module determines a series of important characteristics of the robot, such as the range of motion, positioning accuracy, operation stability, joint compliance and load capacity. In order to achieve the design requirements of robot integration, modularization and convenient replacement, people often adopt the modular rotary joint design concept, integrate drive, transmission, sensing, control and other technologies in the joint space, and create a highly integrated electromechanical component. The traditional robot structure is mainly composed of modular rotary joints and metal or carbon fiber composite tube arms. The joints integrate torque sensors, encoders, harmonic reducers, servo motors, motor control boards and other components. The high degree of integration leads to crowded joint space, increases the volume and mass of the joints, and makes the design more complicated. This type of rigid robotic arm composed of traditional joint modules is difficult to meet the requirements of long distance, light weight, large adjustable stiffness and large extension ratio.

[0003] The central nervous system adjusts the mechanical properties of the limbs according to the task requirements by activating the antagonist muscles around the joints at the same time - including maintaining posture and limb movement. The biological skeletal muscle system is different from the traditional robotic system. The natural human movements are more fluent, dexterous and stable than any existing robot movements. The bionic skeletal muscle system can be tried to break through the limitations of traditional rotational joints. 1) The rope replaces the biological tendon with elasticity, so it can only pull but not push; 2) The joint movement freedom is driven by multiple pairs of agonist muscles and antagonists. NASA describes a new type of robotic arm - tendon-driven lightweight robotic arm (TALISMAN), which combines tendon-driven joints and a new type of hinge joint that allows a full 360-degree rotation between the connecting links and can combine auxiliary and passive tension reinforcement. A suspension rod structure is set at the joint to obtain a longer moment arm between the tendon tension and the joint rotation axis, thereby obtaining a mechanical advantage in generating torque and driving the joint. However, the hinge joint relies on four rotating shafts for movement, and the actual controllability of the rotating shafts is not ideal. The working condition analysis is complex. In order to meet the application requirements of high precision and high reliability, it is necessary to improve the joint structure. Combined with NASA's design ideas, the torque and range of motion of the skeletal muscle system are improved, and the joint structure design is innovated to build a high-precision motion joint module with simple model and excellent controllability. The joint module integrates the arm and joint integrated design. Based on the skeletal muscle system, antagonistically arranged ropes are used as driving tendons. Similar to muscles, ropes can only provide contraction tension, and elastic tendons give the joints good compliance. The motor drives the winch to control the active contraction of the agonist muscle, and the antagonist muscle on the other side also contracts under the control of the winch, thereby controlling the smooth movement of the joint, and at the same time having a wide range of stiffness adjustment capabilities. The front end of the muscle is generally differentiated into multiple heads, which are connected to different bone positions, and at the end, the multiple heads converge together and connect to the position near the driven joint. This front-end multi-head connection mechanism gives the joint a stronger movement ability. Similarly, we can also use multi-branch tendon drive, each branch is connected to different positions of the arm or different arms, and different branch drive strategies are designed according to the driving task requirements. However, the attachment point of the end at the joint makes the moment arm between the muscle and the joint axis very small, and the advantage of tendon drive cannot be fully utilized. A suspension rod structure is set at the joint to increase the length of the moment arm between the tendon tension and the joint axis, improve the torque output performance of the skeletal muscle system, and achieve a large torque output of the joint. Due to the mechanical limitations of bones, muscles and joint articulation factors, the range of motion of the skeletal muscle system is very limited, and the hinge joint cleverly reduces the mechanical limitations at the joint and can achieve a full 360° rotation. In view of this, a new joint structure is designed, which only needs 2 internal shafts to achieve a full 360° rotation, and the model is simple, with good control accuracy, and is easier to apply in practice.Based on the above design strategy, we completed the design of a planar single degree of freedom with a full 360° rotation range, a moment arm amplification boom, a modular arm, a motor and a winch drive module, see. Figure 1 The tendon-driven joint module structure shown.

[0004] Nonlinear characteristics of rope-driven mechanisms, such as flexible vibration, dead zone-hysteresis, friction deformation, etc., are very common in circuits, gears, and robotic arm systems. As we all know, robotic arms are a typical type of nonlinear system, and they play a very important role in industrial manufacturing, deep-sea exploration, aerospace, and other fields. However, how to achieve fast and accurate tracking control of rope-driven robotic arm systems with flexible deformation of ropes is a difficult problem that needs to be solved urgently, and it is also a hot topic for current scholars.

[0005] The existing invention patent application document "A rope-driven space manipulator modeling test method and system" with publication number CN117245670A, the method includes: assuming the flexible link parameters in a global range, in the kinematic model of the rope-driven space manipulator system, calculating the coordinate transformation equation in the topological manipulator state space through coordinate transformation, vector operation and matrix processing to establish the kinematic equation, in the rope drive system, integrating the motor, reducer, winch and other devices to drive the rope tension change, mapped to the movement of the joint shafts of the manipulator, and controlling the target at the end of the manipulator; according to the kinematic model, using the second-class Lagrange equation, deriving the dynamic equation of the carrier position uncontrolled, attitude controlled floating base flexible joint, and flexible arm space robot system. However, the aforementioned prior art cannot make full use of the mapping change relationship of the rope, resulting in a high system error of the scheme; at the same time, the prior art is difficult to take into account the solution of the nonlinear coupling problem and the reduction of the vibration caused by the flexible rope, the rope self-adjustment modeling method and the system operation performance of the model adopted need to be improved, and the rope length change established by the existing modeling method has the problem of weak representativeness.

[0006] In summary, the existing technology has technical problems such as nonlinear characteristics such as flexible vibration, friction, rope deformation and hysteresis in circuits, rope flexibility and robotic arm systems, which lead to reliability servo defects of the robotic arm, low accuracy in tracking a predetermined desired trajectory and high-frequency vibration. Summary of the invention

[0007] The technical problem to be solved by the present invention is: how to solve the technical problem that the nonlinear characteristics such as flexible vibration, friction, rope deformation and hysteresis in the circuit, rope flexibility and robot arm system in the prior art lead to reliability servo defects of the robot arm, low accuracy in tracking a predetermined expected trajectory and high-frequency vibration.

[0008] The present invention adopts the following technical solutions to solve the above technical problems: A modeling method for a rope-driven manipulator to solve the problem of flexible deformation and vibration of ropes includes:

[0009] S1. Establish the mapping relationship from rope to joint angle according to the joint module motion form, joint module state, arm, sling and joint rotation angle; construct a kinematic model to describe the change in the robot system motion process, and obtain the coordinate transformation equation in the topological robot state space through coordinate transformation operations, vector operations and matrix calculations;

[0010] S2. Obtain and establish an elastic potential energy model of rope deformation based on the change in rope retraction and release driven by the motor-driven winch and the mapped length of the current joint rope; define the kinetic energy and potential energy of the motor-driven rope-driven mechanical arm joint rotation and arm movement to construct the second kind of Lagrangian equations;

[0011] S3. Based on the second kind of Lagrangian equation, the dynamic equation of the rope-driven manipulator system of the mapping relationship between the rope variation control input and the manipulator joint angle is derived;

[0012] S4. Optimize the dynamic model and elastic potential energy model, use Lyapunov stability principle to prove the stability of the dynamic model and elastic potential energy model, and use the preset physical prototype to perform verification operations.

[0013] The present invention designs the control input item of the motor-driven rope variation for the rope-driven manipulator system with flexible deformation, and verifies the reliability and stability of the model creation based on the physical prototype. The feasibility analysis of the new tendon-driven manipulator mechanism is carried out, and the multi-rope antagonistic drive is introduced to complete the kinematic modeling. In view of the deformation and flexible vibration caused by the rope force, the present invention proposes a dynamic model of the motor rope variation item based on the Lagrangian function of the conservation of elastic potential energy and kinetic energy.

[0014] In a more specific technical solution, S1 includes:

[0015] S11. Use the following logic to express the distance between the end of the spreader and the joint axis:

[0016]

[0017] Where, d i (i=1,2,3…n) is the distance from the rotation axis of each joint module to the center of the sling; h i (i=1,2,3…n) is the distance from the end of the sling to the center of the sling; S ij (i=1,2,3…n;j=1,2,3,4) is the distance from the end of the sling to the center of the shaft;

[0018] S12. Use the following logic to express the rope length from the contact end of the sling rope to the contact point of the winch rope:

[0019]

[0020] Where, L i (i=1,2,3…n,n+1) is the length of each manipulator rod in the rope-driven manipulator system, l ij (i=1,2,3…n;j=1,2,3,4) is the rope length of each part of the rope-driven manipulator system; q=[q1 q2…q n ] T : is the relative rotation angle column vector of each arm of the rope-driven space manipulator; q i (i=1,2,3…n) is the arm L i+1 Compared to L i Angle of rotation;

[0021] It is the angle between the line from the end of the sling to the rotating shaft and the central axis of the sling; r is the radius of the capstan.

[0022] S13. Using the following logic, take the derivative within time t to obtain the differential relationship between the change in rope length and the rotation angle q of the joint shaft:

[0023] dl ij =J ij dq i (3)

[0024] In the formula,

[0025] In a more specific technical solution, S2 includes:

[0026] S21. Equivalently treat the linkage rope as a geometric constraint spring with a larger stiffness. Use the following logic to express the change in the retractable rope of the drum-driven mechanical arm when the motor rotor rotates θ:

[0027] Δl θ =K r θ;

[0028] S22. Use the following logic to express the rotation angle q of the joint shaft, corresponding to the length change from the sling to the motor drum:

[0029] Δl=l-l0

[0030] S23. Define K as the stiffness coefficient matrix of each rope, and use the following logic to establish the elastic potential energy model of the flexible rope:

[0031] S24. Using coefficient logic, establish the second kind of Lagrangian equation:

[0032] L=EU (5).

[0033] The present invention aims at the reliability servo problem of the new tendon-driven manipulator mechanism caused by uncertain interferences such as multi-rope antagonistic drive, rope elastic deformation and rope flexible vibration. By using the second kind of Lagrangian theorem, conservation of kinetic energy and elastic potential energy of rope change, the dynamic model of the tendon-driven manipulator system is established, which provides a basis for the design of a high-performance servo controller.

[0034] In a more specific technical solution, in S21, the variation of the retractable rope is equivalent to a geometric constraint, and:

[0035] Δl θ = l θ -l0

[0036] In the formula, l θ is a variable related to θ.

[0037] In more specific technical solutions, S3 includes:

[0038] S31. Using the second language method and the system momentum conservation relationship, according to the following logic, the dynamic equation of the space manipulator driven by the motor with flexible rope is derived:

[0039]

[0040] Where q = [q1 q2 q3] T is the column vector of the actual joint angles of each robot arm, M(q)∈R n×n , are the positive definite symmetric inertia matrix of the connecting rod end of the robot arm and the column vector containing the Coriolis force and the centrifugal force, Δl θ is the control input item of each rope variation matrix, J kq ∈R 4n×n is the mapping matrix from the stiffness coefficient of each rope to the rotational joint;

[0041] S32. According to the dynamic equation of the space manipulator, the dynamic equation of the rope-driven space manipulator system is derived:

[0042]

[0043] In the formula, Δl θ is the deformation of the motor rope.

[0044] In a more specific technical solution, in S4, the state space of the rope-driven manipulator is expressed using the following logic:

[0045]

[0046] In a more specific technical solution, in S4, the stability proof operation includes: open-loop control based on an inverse dynamics model and error-based feedback control.

[0047] In a more specific technical solution, in S4, the generalized force of each joint is obtained by using the motion of the inverse dynamics joint model in the dynamic model and the driver, and the feedback control of the joint error is performed through the mapping relationship of the motor rope. The actual control output of the rope-driven manipulator system is defined by the following logic:

[0048] q=[q1 q2…q n ] T , the corresponding ideal state control output is q d ;

[0049] Use the following logic to express the desired angle: q d =[q 1d q 2d …q nd ] T ;

[0050] Using the following logic, define the system tracking error:

[0051]

[0052] According to the feedback control item of the system tracking error and the rope-driven manipulator model of the controlled object, the stability can be determined by the Lyapunov function.

[0053] In a more specific technical solution, in S4, the input form of the controller is set using the following logic:

[0054]

[0055] In the formula, e, are the joint angle tracking error, joint angular velocity tracking error and joint angular acceleration tracking error shown in formula (10), respectively. d , K p It is a homogeneous quadratic differential function. Under specific parameters, the error e converges to zero exponentially quickly, and the system reaches dynamic stability.

[0056] For the rope-driven manipulator system, not only the rope deformation and flexible vibration uncertain interference factors must be considered, but the proposed new mechanism must also consider problems such as system nonlinearity, friction and parameter perturbation. To ensure that the rope-driven manipulator system with antagonism can achieve precise control, the present invention designs PID control for the rope length change input control item to make the tracking error converge to zero asymptotically, and verifies the reliability and stability of the method through simulation and physical prototypes.

[0057] The present invention utilizes an angular encoder to collect the rotation angle of the joint shaft, compares it with the established expected trajectory signal to form a closed-loop circuit for error feedback, and designs a PID control scheme for the rope retraction and release amount, so that the tendon-driven robotic arm prototype can track the established expected trajectory with high precision, and largely eliminate the high-frequency vibration problem caused by rope flexibility and rope deformation.

[0058] In a more specific technical solution, the modeling system of the rope-driven manipulator to solve the problem of flexible deformation and vibration of the rope includes:

[0059] The kinematic model building module is used to establish the mapping relationship from rope to joint angle according to the joint module motion form, joint module state, arm, sling and joint rotation axis angle; build a kinematic model to describe the change in the robot system motion process, and obtain the coordinate transformation equation in the topological robot state space through coordinate transformation operations, vector operations and matrix calculations;

[0060] The Lagrangian equation building module is used to obtain and establish an elastic potential energy model of rope deformation according to the change in the rope retraction and release driven by the motor-driven winch and the mapped length of the current joint rope; define the kinetic energy and potential energy of the motor-driven rope transmission mechanical arm joint rotation and arm movement to build the second kind of Lagrangian equation. The Lagrangian equation building module is connected with the kinematic model building module;

[0061] A dynamic equation building module is used to derive the dynamic equation of the rope-driven manipulator system of the mapping relationship between the rope variation control input and the manipulator joint angle according to the second kind of Lagrangian equation. The dynamic equation building module is connected with the Lagrangian equation building module.

[0062] The model verification module is used to optimize the dynamic model and the elastic potential energy model, and to prove the stability of the dynamic model and the elastic potential energy model by using the Lyapunov stability principle, and to perform verification operations using preset physical prototypes. The model verification module is connected to the dynamic equation construction module and the kinematic model construction module.

[0063] Compared with the prior art, the present invention has the following advantages:

[0064] The present invention designs the control input item of the motor-driven rope variation for the rope-driven manipulator system with flexible deformation, and verifies the reliability and stability of the model creation based on the physical prototype. The feasibility analysis of the new tendon-driven manipulator mechanism is carried out, and the multi-rope antagonistic drive is introduced to complete the kinematic modeling. In view of the deformation and flexible vibration caused by the rope force, the present invention proposes a dynamic model of the motor rope variation item based on the Lagrangian function of the conservation of elastic potential energy and kinetic energy.

[0065] The present invention aims at the reliability servo problem of the new tendon-driven manipulator mechanism caused by uncertain interferences such as multi-rope antagonistic drive, rope elastic deformation and rope flexible vibration. By using the second kind of Lagrangian theorem, conservation of kinetic energy and elastic potential energy of rope change, the dynamic model of the tendon-driven manipulator system is established, which provides a basis for the design of a high-performance servo controller.

[0066] For the rope-driven manipulator system, not only the rope deformation and flexible vibration uncertain interference factors must be considered, but the proposed new mechanism must also consider problems such as system nonlinearity, friction and parameter perturbation. To ensure that the rope-driven manipulator system with antagonism can achieve precise control, the present invention designs PID control for the rope length change input control item to make the tracking error converge to zero asymptotically, and verifies the reliability and stability of the method through simulation and physical prototypes.

[0067] The present invention utilizes an angular encoder to collect the rotation angle of the joint shaft, compares it with the established expected trajectory signal to form a closed-loop circuit for error feedback, and designs a PID control scheme for the rope retraction and release amount, so that the tendon-driven robotic arm prototype can track the established expected trajectory with high precision, and largely eliminate the high-frequency vibration problem caused by rope flexibility and rope deformation.

[0068] Compared with the existing patent with publication number CN117245670A, the present invention can make good use of the mapping change relationship of the rope to greatly reduce the system error and improve the accuracy, solve the nonlinear coupling problem and greatly reduce the vibration caused by the flexible rope. The relatively good rope self-adjustment modeling method and model reduce the system's computing performance, can have a good practical application scope in the prototype, and accurately establish a representative modeling method for rope length change, providing technical support and means for the research and application of rope mechanism systems.

[0069] The present invention solves the technical problems in the prior art that nonlinear characteristics such as flexible vibration, friction, rope deformation and hysteresis in circuits, rope flexibility and robot arm systems lead to reliability servo defects of the robot arm, low tracking accuracy of a predetermined desired trajectory and high-frequency vibration. BRIEF DESCRIPTION OF THE DRAWINGS

[0070] Figure 1 A schematic diagram of the tendon-driven joint module configuration of the background technology of the present invention;

[0071] Figure 2 This is a schematic diagram of the basic steps of a modeling method for solving the problem of flexible deformation vibration of ropes in a rope-driven manipulator according to Example 1 of the present invention;

[0072] Figure 3 Schematic diagram of the configuration of the rope-driven manipulator system according to Embodiment 1 of the present invention;

[0073] Figure 4This is a schematic diagram of the transmission structure of a novel rope-driven space manipulator according to Example 1 of the present invention;

[0074] Figure 5 This is a PID control principle diagram of embodiment 2 of the present invention;

[0075] Figure 6 This is a first joint angle tracking curve diagram of Example 2 of the present invention;

[0076] Figure 7 A second joint angle tracking curve diagram of Example 2 of the present invention;

[0077] Figure 8 is a tracking error curve diagram of Example 2 of the present invention;

[0078] Fig. 9 This is a physical prototype diagram of Embodiment 2 of the present invention;

[0079] Fig.10 This is a schematic diagram of joint angle tracking according to Embodiment 2 of the present invention;

[0080] Fig.11 Schematic diagram of joint angle tracking error of embodiment 2 of the present invention;

[0081] Fig.12 Schematic diagram of the rope forces of the rope-driven manipulator of Example 2 of the present invention;

[0082] Fig.13 This is a schematic diagram of joint angle tracking according to Embodiment 2 of the present invention;

[0083] Fig.14 Schematic diagram of joint angle tracking error of embodiment 2 of the present invention;

[0084] Fig.15 Schematic diagram of the rope forces of the rope-driven manipulator according to Example 2 of the present invention. DETAILED DESCRIPTION

[0085] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0086] Example 1

[0087] like Figure 2 and Figure 3 As shown, the modeling method for solving the problem of flexible deformation and vibration of ropes provided by the rope-driven manipulator of the present invention includes the following basic steps:

[0088] S1. According to the movement form and state of the joint module, a mapping relationship from the rope to the joint angle is established according to the arm, the sling and the joint shaft angle;

[0089] like Figure 3 As shown, in this embodiment, for the new rope-driven space manipulator system, the motor drives the winch at both ends of the joint module to transmit the drive device on the rope, which is assembled into an arm L i —Spreader i —Arm L i-1 The joint module configuration of the rope-driven space manipulator system, O is the initial point of the manipulator rod, L i1 and L i2 , L i3 and L i4 The two motors on the same arm are driven in coordination, and a constant force spring is used to keep the rope in a tensioned state and realize the rope collection device. The rope drives the arm and the sling shaft to rotate to realize the capture of the end effector of the space manipulator. The structure is shown in Figure 3 . Considering that the rope-driven space manipulator system performs planar motion, it is necessary to establish a simplified structural model and conduct dynamic analysis to complete the research on high-precision control. The kinematic model is used to describe the change in the motion process of the robot system. The coordinate transformation equation in the state space of the topological robot is calculated through coordinate transformation, vector operation and matrix calculation. In the rope drive system, the integrated motor, worm gear, planetary reducer, winch and other devices drive the rope change and tension, which are then mapped to the motion of the rotating shaft of each joint of the manipulator to achieve the capture of the target at the end of the manipulator.

[0090] L i (i=1,2,3…n,n+1): length of each manipulator rod in the rope-driven manipulator system;

[0091] m i (i=1,2,3…n,n+1): is the mass of each manipulator rod in the rope-driven manipulator system;

[0092] I i (i=1,2,3…n,n+1): is the moment of inertia of each manipulator rod in the rope-driven manipulator system;

[0093] m si (i=1,2,3…n): is the mass of the sling in each joint module of the rope-driven manipulator system;

[0094] I si (i=1,2,3…n): is the moment of inertia of the hanger and gear in each joint module;

[0095] d i(i=1,2,3…n): the distance from the rotation axis of each joint module to the center of the sling;

[0096] h i (i=1,2,3…n): the distance from the end of the sling to the center of the sling;

[0097] l ij (i=1,2,3…n;j=1,2,3,4): is the rope length of each part of the rope-driven manipulator system;

[0098] f ij (i=1,2,3…n;j=1,2,3,4): is the rope tension of each part in the rope-driven manipulator system;

[0099] S ij (i=1,2,3…n;j=1,2,3,4): is the distance from the end of the sling to the center of the shaft;

[0100] It is the angle between the line from the end of the spreader to the rotating shaft and the center axis of the spreader;

[0101] q i (i=1,2,3…n): arm L i+1 Compared to L i Angle of rotation;

[0102] q=[q1 q2…q n ] T : is the relative rotation angle column vector of each arm of the rope-driven space manipulator;

[0103] r: winch radius.

[0104] In this embodiment, the kinematic model is used to describe the change in the motion process of the rope-driven space manipulator system, and the coordinate transformation equation in the state space of the topological robot is calculated through coordinate transformation, vector operation and matrix calculation. In the rope drive system, the integrated motor, worm gear, planetary reducer, winch and other devices drive the rope change and tension, which are then mapped to the movement of the joint shafts of the manipulator to achieve the capture of the target at the end of the manipulator. Among them, the distance between the end of the sling and the joint shaft is:

[0105]

[0106] In this embodiment, the rope length from the contact end of the spreader rope to the contact point of the winch rope is expressed as follows:

[0107]

[0108] In this embodiment, the differential relationship between the change in rope length and the angle q can be obtained by taking the derivative of equation (1.2) with respect to time t as follows:

[0109] dl ij =J ij dq i (14)

[0110] in,

[0111] S2. Due to the deformation of the rope flexibility, the elastic potential energy of the rope deformation is established according to the change in the rope retraction and release driven by the motor-driven winch and the mapped length of the current joint rope; the kinetic energy and potential energy of the motor-driven rope-driven mechanical arm joint rotation and arm movement are defined, and the Lagrangian function is constructed;

[0112] In this embodiment, the rope-driven space manipulator system is mainly composed of a transmission mode of motor drum-rope-arm. The linkage rope used is a flexible rope, which is equivalent to a geometric constraint spring with large stiffness. The change of the retracting and releasing rope of the drum-driven manipulator when the motor rotor rotates θ is Δl θ =K r θ, which is equivalent to a geometric constraint, let Δl θ = l θ -l0, where l θ The only variable related to θ is that the length change from the sling to the motor drum corresponding to the rotation q of the joint shaft is Δl=l-l0. Define K as the stiffness coefficient matrix of each rope, then the elastic potential energy in the flexible rope is:

[0113]

[0114] In this embodiment, when moving in a space without gravity potential energy, the kinetic energy E of the system is the sum of the kinetic energy of each arm and the sling, and the potential energy of the system is the sum of the elastic potential energy of each rope. The second type of language function can be expressed as follows:

[0115] L=EU (16)

[0116] S3. Based on the second kind of Lagrangian equation, the dynamic equation of the rope-driven manipulator system is derived, which is the mapping relationship between the control input of the rope variation and the joint angle of the manipulator.

[0117] In this embodiment, it is assumed that the tendons drive the various parts of the space manipulator to move on a plane, the weight of the rope is ignored, and the manipulator system is a linkage rope-driven multi-body system without external force. Then, the second kind of language method and the system momentum conservation relationship are used to derive the dynamic equation of the space manipulator driven by the motor with flexible rope as follows:

[0118]

[0119] Where q = [q1 q2 q3] Tis the column vector of the actual joint angles of each robot arm, M(q)∈R n×n , are the positive definite symmetric inertia matrix of the connecting rod end of the robot arm and the column vector containing the Coriolis force and the centrifugal force, Δl θ is the control input item of each rope variation matrix, J kq ∈R 4n×n is the mapping matrix from the stiffness coefficient of each cable to the rotational joint.

[0120] In this embodiment, the dynamic equation of the rope-driven space manipulator system can be derived from equations (17) and (18) as follows:

[0121]

[0122] Among them, Δl θ is the deformation of the motor rope.

[0123] S4. Consider the influence of flexible vibration of rope drive, optimize the system model, prove the stability by Lyapunov stability principle, and verify the effectiveness and reliability of this method on the physical prototype.

[0124] In this embodiment, a flexible rope-driven multi-input multi-output highly nonlinear manipulator system is considered. From equation (19), it can be seen that the state space expression of the rope-driven manipulator can be expressed as follows:

[0125]

[0126] In the control method design and stability proof process of this embodiment, the methods used to deal with the problem of manipulator control include but are not limited to: open-loop control based on inverse dynamics model and feedback control based on error. Since the open-loop control system cannot control the generated error, this study uses the dynamic model and the driver to use the motion of the inverse dynamics joint model to calculate the generalized force of each joint, and realizes the feedback control of the joint error through the mapping relationship of the motor rope. The actual control output of the rope-driven manipulator system is defined as: q = [q1 q2…q n ] T , the corresponding ideal state control output is q d , that is, the expected angle is expressed as: q d =[q 1d q 2d …q nd ] T , define the tracking error of the system as:

[0127]

[0128] In this embodiment, according to the feedback control item of the error combined with the controlled object rope-driven manipulator model, stability determination can be achieved through the Lyapunov function. The core of the PID control method is to set the controller to transform the dynamic model of the rope-driven manipulator system (controller + controlled object) into a closed-loop system that is inevitably stable, such as formula (20), that is, the form of the controller input can be expressed as follows:

[0129]

[0130] Among them, e, are the joint angle tracking error, joint angular velocity tracking error and joint angular acceleration tracking error shown in formula (21), respectively. d , K p It is a homogeneous quadratic differential function. Under specific parameters, the error e converges to zero exponentially quickly, and the system reaches dynamic stability.

[0131] Example 2

[0132] like Figure 5 As shown, in this embodiment, in order to verify the reliability of the method designed by the present invention and the high control performance of the control design, a rope-driven robotic arm dual-joint module is used to verify the new architecture system, and the design method is verified based on the PID control scheme. The sampling frequency is L=0.001s and the sampling period is 50s.

[0133] Table 1 Characteristic parameters of each component of the double-joint rope-driven manipulator

[0134]

[0135] In this embodiment, in order to verify the effectiveness of the control scheme, the control scheme proposed in the present invention is simulated, and the control parameters based on the PID controller are designed as follows: p =diag(50,50),K d =diag(10,10),K i =diag(0.05,0.05), where the expected trajectory of the joint angles of each joint axis is as follows:

[0136]

[0137] In this embodiment, the new rope-driven manipulator system is designed as shown in equation (22), and its simulation results are as follows: Figures 5 to 7 As shown, Figure 5 It is the simulation curve diagram of the joint angle 1 of the robot system. Figure 6 It is the simulation curve diagram of the joint angle 2 of the robot system. Figure 7 It is the simulation curve diagram of the joint angle error tracking of the robotic arm system.

[0138] like Figure 8 As shown in the figure, in this embodiment, the test process is based on the output error between the angle encoder and the expected trajectory, the PID control design under the rope length change is designed as shown in formula (22), a dynamic trajectory of a single joint motion angle of ±30° is established, and the position signal of the four-motor drive is imported, where the expected trajectory of the single joint is designed as follows:

[0139]

[0140] In this embodiment, the trajectory planning cycle is defined as 0.02s, the entire planning time is 100s, the first 5s is the rope pre-tightening time, and the PID parameters are adjusted to test the tracking of the robot prototype. The average error is 0.0107°, and the maximum error is 3.22° at the beginning of the joint rotation. The tracking of the test experiment is shown in Figures 9 to 11 .

[0141] In this embodiment, the high-frequency oscillation problem existing in the above-mentioned rope-driven manipulator prototype test is solved by adjusting the parameters and adding the desired trajectory design after filtering. The test results are as follows: Figure 12 to Figure 14 shown.

[0142] In this embodiment, when the initial sampling point has a large error, the rope tensioning setting is first performed for 5 seconds. The average error of the joint angle trajectory tracking is 0.1737°, and the maximum error is 3.8697 during the tensioning stage of the initial movement stage of the joint rotation. The scheme and modeling method studied in the present invention have high reliability and effectiveness for the high-precision control of the rope-driven robotic arm system.

[0143] In summary, the present invention designs the control input item of the motor-driven rope variation for the rope-driven manipulator system with flexible deformation, and verifies the reliability and stability of the model creation based on the physical prototype. The feasibility analysis of the new tendon-driven manipulator mechanism is carried out, and the multi-rope antagonistic drive is introduced to complete the kinematic modeling. In view of the deformation and flexible vibration caused by the rope force, the present invention proposes a dynamic model of the motor rope variation item based on the Lagrangian function of the conservation of elastic potential energy and kinetic energy.

[0144] The present invention aims at the reliability servo problem of the new tendon-driven manipulator mechanism caused by uncertain interferences such as multi-rope antagonistic drive, rope elastic deformation and rope flexible vibration. By using the second kind of Lagrangian theorem, conservation of kinetic energy and elastic potential energy of rope change, the dynamic model of the tendon-driven manipulator system is established, which provides a basis for the design of a high-performance servo controller.

[0145] For the rope-driven manipulator system, not only the rope deformation and flexible vibration uncertain interference factors must be considered, but the proposed new mechanism must also consider problems such as system nonlinearity, friction and parameter perturbation. To ensure that the rope-driven manipulator system with antagonism can achieve precise control, the present invention designs PID control for the rope length change input control item to make the tracking error converge to zero asymptotically, and verifies the reliability and stability of the method through simulation and physical prototypes.

[0146] The present invention utilizes an angular encoder to collect the rotation angle of the joint shaft, compares it with the established expected trajectory signal to form a closed-loop circuit for error feedback, and designs a PID control scheme for the rope retraction and release amount, so that the tendon-driven robotic arm prototype can track the established expected trajectory with high precision, and largely eliminate the high-frequency vibration problem caused by rope flexibility and rope deformation.

[0147] The present invention solves the technical problems in the prior art that nonlinear characteristics such as flexible vibration, friction, rope deformation and hysteresis in circuits, rope flexibility and robot arm systems lead to reliability servo defects of the robot arm, low tracking accuracy of a predetermined desired trajectory and high-frequency vibration.

[0148] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A modeling method for solving the problem of flexible deformation and vibration of ropes in a rope-driven manipulator, characterized in that: The method comprises: S1. Establish the mapping relationship from rope to joint angle according to the joint module motion form, joint module state, arm, sling and joint rotation angle; construct a kinematic model to describe the change in the robot system motion process, and obtain the coordinate transformation equation in the topological robot state space through coordinate transformation operations, vector operations and matrix calculations; S2. Obtain and establish an elastic potential energy model of rope deformation based on the change in rope retraction and release driven by the motor-driven winch and the mapped length of the current joint rope; define the kinetic energy and potential energy of the motor-driven rope-driven mechanical arm joint rotation and arm movement to construct the second kind of Lagrangian equations; S3. According to the second kind of Lagrangian equation, the dynamic equation of the rope-driven manipulator system of the mapping relationship between the rope variation control input and the manipulator joint angle is derived; S4. Optimize the dynamic model and the elastic potential energy model, perform stability proof operation on the dynamic model and the elastic potential energy model using Lyapunov stability principle, and perform verification operation using a preset physical prototype.

2. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: The S1 includes: S11. Use the following logic to express the distance between the end of the spreader and the joint axis: Where, d i (i=1,2,3…n) is the distance from the rotation axis of each joint module to the center of the sling; h i (i=1,2,3…n) is the distance from the end of the sling to the center of the sling; S ij (i=1,2,3…n;j=1,2,3,4) is the distance from the end of the sling to the center of the shaft; S12. Use the following logic to express the rope length from the contact end of the sling rope to the contact point of the winch rope: Where, L i (i=1,2,3…n,n+1) is the length of each manipulator rod in the rope-driven manipulator system, l ij (i=1,2,3…n;j=1,2,3,4) is the rope length of each part of the rope-driven manipulator system; q=[q1 q2…q n ] T : is the relative rotation angle column vector of each arm of the rope-driven space manipulator; q i (i=1,2,3…n) is the arm L i+1 Compared to L i Angle of rotation; It is the angle between the line from the end of the sling to the rotating shaft and the central axis of the sling; r is the radius of the capstan. S13. Using the following logic, take the derivative within time t to obtain the differential relationship between the change in rope length and the rotation angle q of the joint shaft: dl ij =J ij dq i (25) In the formula, 3. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: The S2 includes: S21. Equivalently treat the linkage rope as a geometric constraint spring with a larger stiffness. Use the following logic to express the change in the retractable rope of the drum-driven mechanical arm when the motor rotor rotates θ: Δl θ =K r θ; S22. Use the following logic to express the rotation angle q of the joint shaft, corresponding to the length change from the sling to the motor drum: Δl=l-l0 S23. Define K as the stiffness coefficient matrix of each rope, and use the following logic to establish the elastic potential energy model of the flexible rope: S24. Using coefficient logic, establish the second type of Lagrangian equation: L = EU (27).

4. The modeling method for solving the problem of flexible deformation and vibration of ropes for a rope-driven manipulator according to claim 3 is characterized in that: In S21, the variation of the retractable rope is equivalent to a geometric constraint, and it is set as follows: Δl θ =l θ -l0 In the formula, l θ is a variable related to θ.

5. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: The S3 includes: S31. Using the second language method and the system momentum conservation relationship, according to the following logic, the dynamic equation of the space manipulator driven by the motor with flexible rope is derived: Where q = [q1 q2 q3] T is the column vector of the actual joint angles of each robot arm, M(q)∈R n×n , are the positive definite symmetric inertia matrix of the connecting rod end of the robot arm and the column vector containing the Coriolis force and the centrifugal force, Δl θ is the control input item of each rope variation matrix, J kq ∈R 4n×n is the mapping matrix from the stiffness coefficient of each rope to the rotational joint; S32. According to the dynamic equation of the space manipulator, the dynamic equation of the rope-driven space manipulator system is derived: In the formula, Δl θ is the deformation of the motor rope.

6. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: In S4, the state space of the rope-driven manipulator is expressed using the following logic:

7. The modeling method for solving the problem of flexible deformation and vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: In S4, the stability proof operation includes: open-loop control based on an inverse dynamics model and feedback control based on errors.

8. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: In S4, the generalized force of each joint is obtained by using the motion of the inverse dynamics joint model in the dynamic model and the driver, and the feedback control of the joint error is performed through the mapping relationship of the motor rope. The actual control output of the rope-driven manipulator system is defined by the following logic: q=[q1 q2 … q n ] T , the corresponding ideal state control output is q d ; Use the following logic to express the desired angle: q d =[q 1d q 2d … q nd ] T ; Using the following logic, define the system tracking error: According to the feedback control item of the system tracking error and in combination with the rope-driven manipulator model of the controlled object, stability determination can be performed through the Lyapunov function.

9. The modeling method for solving the problem of flexible deformation vibration of ropes for a rope-driven manipulator according to claim 1 is characterized in that: In S4, the input form of the controller is set using the following logic: In the formula, e, are the joint angle tracking error, joint angular velocity tracking error and joint angular acceleration tracking error shown in formula (21), respectively. d , K p It is a homogeneous quadratic differential function. Under specific parameters, the error e converges to zero exponentially quickly, and the system reaches dynamic stability.

10. A modeling system for a rope-driven manipulator to solve the problem of flexible deformation and vibration of ropes, characterized in that: The system comprises: The kinematic model building module is used to establish the mapping relationship from rope to joint angle according to the joint module motion form, joint module state, arm, sling and joint rotation axis angle; build a kinematic model to describe the change in the robot system motion process, and obtain the coordinate transformation equation in the topological robot state space through coordinate transformation operations, vector operations and matrix calculations; A Lagrangian equation construction module is used to obtain and establish an elastic potential energy model of rope deformation according to the change in rope retraction and release driven by the motor-driven winch and the mapped length of the current joint rope; define the kinetic energy and potential energy of the motor-driven rope transmission mechanical arm joint rotation and arm movement to construct the second kind of Lagrangian equation, and the Lagrangian equation construction module is connected to the kinematic model construction module; A dynamic equation building module is used to derive the dynamic equation of the rope-driven manipulator system of the mapping relationship between the rope variation control input and the manipulator joint angle according to the second type Lagrangian equation, and the dynamic equation building module is connected to the Lagrangian equation building module; A model verification module is used to optimize the dynamic model and the elastic potential energy model, perform stability proof operations on the dynamic model and the elastic potential energy model using the Lyapunov stability principle, and perform verification operations using a preset physical prototype. The model verification module is connected to the dynamic equation construction module and the kinematic model construction module.

Images