Low-dimensional equivalent dynamic modeling method for rope cluster driven mechanical arm and high-agility controller

Abstract

The invention provides a low-dimensional equivalent dynamic modeling method for a rope cluster driven mechanical arm, a high-agility controller and the rope cluster driven mechanical arm, and relates to the technical field of rope cluster driven mechanical arms. The low-dimensional equivalent dynamic modeling method for the rope cluster driven mechanical arm comprises the steps that planar motion of a wrist joint and planar motion of an elbow joint are equivalently simplified into pure rolling motion; on the basis of the moment of momentum theorem, dynamic modeling is conducted on the wrist joint or the elbow joint in combination with the driving moment of the driving rope and the gravity moment; and performing dynamic modeling on the whole arm of the rope cluster driven mechanical arm based on at least one of an improved iterative Newton-Euler method and a second-class Lagrange equation. The equivalent rope modeling method which considers the elastic characteristic of the driving rope and ignores the inertia characteristic of the driving rope is established, so that the driving rope does not need to be divided into rope units under the condition that the calculation precision is met, the modeling process and the equation complexity are simplified while the dynamic characteristic of the driving rope is reserved, and the modeling efficiency is improved. And controller design is facilitated.

Description

Technical Field

[0001] The present application relates to the technical field of rope cluster driven robotic arms, and in particular to a low-dimensional equivalent dynamics modeling method for rope cluster driven robotic arms, a high-agility controller, and a rope cluster driven robotic arm. Background Art

[0002] The rope cluster drive (abbreviated as rope drive, rope cluster means multiple ropes) agile robotic arms control joint movement through ropes. The drive motor can be placed at the base end, which significantly reduces the mass and inertia of the robotic arm system. The movement ability and control accuracy of the rope cluster drive robotic arms can be greatly improved, making human-computer interaction safer. It has broad application prospects in aerospace, medical rehabilitation, environmental testing and other fields, and has high research value.

[0003] Controller design is the core link in the development of the rope cluster driven agile manipulator. In the control design process, it is necessary to design based on the rope cluster driven manipulator model. Due to the existence of pure rolling joints, the modeling difficulty of the rope cluster driven agile manipulator is greater than that of the traditional rope cluster driven manipulator rotation joints. In addition, most of the existing rope cluster driven manipulator modeling is based on kinematic modeling, ignoring the inertia brought by the rigid body motion of the corresponding system in the rope cluster driven manipulator. The controller designed based on kinematics does not fully consider the dynamic characteristics of the system. The designed controller is only suitable for the working conditions of the rope cluster driven manipulator with slow motion, and has poor performance under high-speed motion conditions.

[0004] In addition, existing commercial multibody dynamics software can establish a differential algebraic equation model corresponding to the rope cluster driven manipulator based on the first kind of Lagrangian equations, but there are many unknown variables in the model, the number of generalized coordinates is large and not intuitive enough, and it is generally not suitable for controller design. Moreover, when considering the elasticity of the rope in the model, it is necessary to divide the rope into finite element meshes and take into account the generalized coordinates of the rope nodes, which makes the model establishment process complicated and further increases the complexity of the equations, making the controller design more difficult. Summary of the invention

[0005] Based on this, the present application provides a low-dimensional equivalent dynamic modeling method for a rope cluster-driven robotic arm, a high-agility controller and a rope cluster-driven robotic arm, so as to establish a simplified, low-dimensional and intuitive dynamic modeling method to facilitate the design of the controller.

[0006] The present application provides a low-dimensional equivalent dynamics modeling method for a rope cluster driven manipulator, comprising: The planar motion of the wrist joint and the elbow joint of the rope cluster driven manipulator is simplified to pure rolling motion, and both the wrist joint and the elbow joint include basic joint components and planar pure rolling joint components; Based on the momentum moment theorem, the first dynamic modeling of the wrist or elbow joint in pure rolling motion is carried out by combining the driving torque of the driving rope and the gravity torque; Performing second dynamic modeling of the whole arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and an improved second kind of Lagrangian equation; The results of the first dynamics modeling and the second dynamics modeling are used to control the movement of the rope cluster driven manipulator.

[0007] Optionally, based on the momentum moment theorem and in combination with the driving torque of the driving rope and the gravity torque, the first dynamic modeling of the wrist joint or elbow joint in pure rolling motion includes: The contact point between the base joint component and the planar pure rolling joint component is set as the base point; Set the momentum theorem equation for the base point; The driving torque, gravity torque and inertia torque of the driving rope are set corresponding to the position of the base point, and the momentum theorem equation is transformed based on the driving torque, gravity torque and inertia torque to obtain the dynamic equation of the wrist joint or the dynamic equation of the elbow joint.

[0008] Optionally, based on the momentum moment theorem and in combination with the driving torque of the driving rope and the gravity torque, the first dynamic modeling of the wrist joint or elbow joint in pure rolling motion further includes: When the rotation angle of the wrist joint is set to be less than 5° and the driving rope at the wrist joint or elbow joint is kept taut, the dynamic equation of the wrist joint or elbow joint is linearized into a micro-vibration equation.

[0009] Optionally, the dynamic equation of the wrist joint is:

[0010] in, is the moment of inertia of the plane pure rolling joint component in the wrist joint around its own center of mass, is the tension difference between the two ropes of the driving rope in the wrist joint, m is the mass of the planar pure rolling joint component in the wrist joint, h is the center distance between the basic joint component in the wrist joint and the plane pure rolling joint component in the wrist joint, e is the distance between the center of mass of the plane pure rolling joint component in the wrist joint and the center of the circle of the plane pure rolling joint component in the wrist joint; θ is the rotation angle of the plane pure rolling joint component in the wrist joint relative to the wrist joint component; w is the distance between the two connection points of the driving cable in the wrist joint and the planar pure rolling joint component in the wrist joint; g is the acceleration due to gravity.

[0011] Optionally, the dynamic equation of the elbow joint is:

[0012] in, is the moment of inertia of the plane pure rolling joint component in the elbow joint around its own center of mass, is the tension difference between the two ropes of the drive rope in the elbow joint, m is the mass of the planar pure rolling joint component in the elbow joint, h is the center distance between the basic joint component in the elbow joint and the plane pure rolling joint component in the elbow joint, e is the distance between the center of mass of the plane pure rolling joint component in the elbow joint and the center of the circle of the plane pure rolling joint component in the elbow joint; θ is the rotation angle of the plane pure rolling joint component in the elbow joint relative to the elbow joint component; w=2R , R is the radius of the circle of the planar pure rolling joint component in the elbow joint; g is the acceleration due to gravity.

[0013] Optionally, performing a second dynamic modeling of the entire arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and a second kind of Lagrangian equations comprises: determining a coordinate system of a plurality of links included in the rope cluster driven robot arm; and The coordinate system is used to model the dynamics of the rope cluster driven manipulator based on the improved iterative Newton-Euler method and / or the improved second kind Lagrangian equation.

[0014] Optionally, performing a second dynamic modeling of the entire arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and a second kind of Lagrangian equations further comprises: Compare the results of the dynamic equations for dynamic modeling of the rope cluster driven manipulator based on the improved iterative Newton-Euler method with the results of the dynamic equations for dynamic modeling of the rope cluster driven manipulator based on the improved second kind Lagrangian equations to verify the correctness of the results; or The improved iterative Newton-Euler method and / or the improved second-kind Lagrangian equations are applied to at least one of the wrist joint and the elbow joint to verify whether the obtained dynamic equation of the wrist joint or the elbow joint is consistent with the dynamic equation obtained based on the angular momentum theorem.

[0015] Optionally, determining a coordinate system of a plurality of links protected in a rope cluster driven manipulator comprises: The coordinate system origins and coordinate system directions of the multiple connecting rods are determined according to the modified DH method, thereby determining the coordinate system of the multiple connecting rods.

[0016] Optionally, dynamic modeling of the rope cluster driven manipulator based on the improved iterative Newton-Euler method includes: Iterate outwardly through the coordinate systems of multiple connecting rods to obtain the velocities, accelerations, angular velocities, and angular accelerations of the multiple connecting rods, and then obtain the inertia forces and inertia moments of the multiple connecting rods; Iterate the coordinate systems of multiple links inwards, and establish the torque balance equation applicable to the plane pure rolling joints in the rope cluster driven manipulator to obtain the joint torques at multiple joints in the rope cluster driven manipulator. Calculating the driving torques at multiple joints, and arranging the driving torques at the multiple joints to obtain a driving torque vector of the rope cluster driven manipulator; According to the joint torques and driving torques at multiple joints, the dynamic equations of the rope cluster driven manipulator based on the improved iterative Newton-Euler method are formed.

[0017] Optionally, the dynamic equation of the rope cluster driven manipulator based on the improved iterative Newton-Euler method is:

[0018] in, is the inertia matrix of the rope cluster driven manipulator, is the vector formed by multiple joint angles in the rope cluster driven robot arm, is the sum of the centrifugal inertia moment, Coriolis inertia moment, gravity moment, and external force moment of the rope cluster driven manipulator, is the driving torque vector of the rope cluster driven manipulator.

[0019] Optionally, dynamic modeling of the rope cluster driven manipulator based on the improved second kind Lagrangian equation includes: According to the modified DH method, the homogeneous transformation matrix between the coordinate systems of two adjacent links in the rope cluster driven manipulator and the homogeneous transformation matrix between the coordinate systems of multiple links and the ground coordinate system are calculated, and the homogeneous transformation matrix corresponding to the physical link is extracted and selected and reordered; According to the reordered homogeneous transformation matrix, the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator are calculated; According to the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator, the dynamic equation of the rope cluster driven manipulator based on the improved second kind Lagrangian equation is formed.

[0020] Optionally, the dynamic equation of the rope cluster driven manipulator based on the improved second kind Lagrangian equation is:

[0021] in, is the generalized inertia force of the rope cluster driving the manipulator, is the inertia matrix of the rope cluster driven manipulator, is the velocity coupling matrix of the rope cluster driven manipulator, is the generalized gravity of the rope cluster driven manipulator, It is the generalized driving force of the rope cluster driven manipulator.

[0022] The present application provides a highly agile controller, comprising: Processor; and The memory stores a computer program, and when the computer program is executed by the processor, the processor executes the above method.

[0023] The present application provides a rope cluster driven mechanical arm, comprising: A robot body; and The controller is used to control the movement of the rope cluster driven mechanical arm.

[0024] The present application provides a low-dimensional equivalent dynamics modeling method for a rope cluster driven manipulator, a high-agility controller, and a rope cluster driven manipulator. The dynamics model established by dynamics modeling of the whole arm, wrist joint, and elbow joint of the rope cluster driven manipulator fully considers the inertia characteristics caused by the rigid body motion of the rope cluster driven manipulator. The controller designed by the dynamics model of the present application is suitable for both slow and high-speed working conditions, thereby enhancing the effect of the controller design and helping to improve the motion performance of the rope cluster driven manipulator.

[0025] A simplified model of the driving rope is established, taking into account the elastic characteristics of the driving rope and ignoring the inertial characteristics of the simplified driving rope. Therefore, there is no need to divide the driving rope into rope units while meeting the calculation accuracy. The dynamic characteristics of the driving rope are retained while simplifying the modeling process and the complexity of the equations, which is convenient for controller design.

[0026] Moreover, the number of equations for the dynamic modeling of the rope cluster driven manipulator of the present application is relatively small, the equations are concise and intuitive, the numerical solution is simple, and the controller design is easy. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without exceeding the scope of protection required by the present application.

[0028] Figure 1 It is a schematic diagram of the structure of the rope cluster driven robotic arm; Figure 2 It is a flowchart of this application; Figure 3 It is a schematic diagram of the structure of the wrist joint in this application; Figure 4 It is a schematic diagram of the structure of the elbow joint in this application; Figure 5 It is a flowchart of step S120 in this application; Figure 6 It is a flowchart of step S130 in this application; Figure 7 It is a schematic diagram of the structure of the three-degree-of-freedom rope cluster driven manipulator and its modified DH coordinate system; Figure 8 It is a schematic diagram of the algorithm flow for dynamic modeling of the whole arm of the rope cluster driven manipulator based on the improved iterative Newton-Euler method in the present application; Fig. 9 It is a force analysis diagram of the connecting rod containing a plane pure rolling joint in this application; Fig.10 It is a flowchart of step S133 in this application; Fig.11 is a graph of the undamped free vibration dynamic response of the wrist joint in this application; Fig.12 is a sinusoidal drive dynamic response curve diagram of the wrist joint in this application; Fig.13 is an angle response curve diagram of the undamped free vibration of the elbow joint in the present application; Fig.14 is the angle response curve diagram of the slow and small angle sinusoidal drive of the elbow joint in this application; Fig.15 is an angle response curve diagram of a fast small-angle sinusoidal drive of an elbow joint in the present application; Fig.16 is a free vibration response curve diagram of the whole arm of the rope cluster driven mechanical arm in the present application; Fig.17 is a sinusoidal drive response curve diagram of the whole arm of the rope cluster driven mechanical arm in this application; Fig.18 It is a schematic diagram of the structure of the controller in this application.

[0029] Explanation of the reference numerals: 1. connecting rod; 2. joint; 21. shoulder joint; 22. elbow joint; 23. wrist joint; 201. basic joint component; 202. plane pure rolling joint component; 3. end tool; 4. driving rope; 200. controller; 210. processing unit; 220. storage unit; 2201. random access storage unit; 2202. cache storage unit; 2203. read-only storage unit; 2204. program / utility; 2205. program module; 230. bus; 240. display unit; 250. input / output (I / O) interface; 260. network adapter; 300. external device. DETAILED DESCRIPTION

[0030] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in many forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this application will be comprehensive and complete and will fully convey the concepts of the example embodiments to those skilled in the art. In the figures, the same figures show the same or similar parts, and thus their repeated description will be omitted.

[0031] The described features, structures or characteristics may be combined in one or more embodiments in any suitable manner. In the following description, many specific details are provided to provide a full understanding of the embodiments of the present disclosure. However, those skilled in the art will appreciate that the technical solutions of the present disclosure may be practiced without one or more of these specific details, or other modes, components, materials, devices or operations may be adopted. In these cases, known structures, methods, devices, implementations, materials or operations will not be shown or described in detail.

[0032] The flowcharts shown in the accompanying drawings are only exemplary and do not necessarily include all the contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps can be decomposed, and some operations / steps can be combined or partially combined, so the actual execution order may change according to actual conditions.

[0033] The terms "first", "second", etc. in the specification and claims of this application and the above-mentioned drawings are used to distinguish different objects, rather than to describe a specific order. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device that includes a series of steps or units is not limited to the listed steps or units, but optionally includes steps or units that are not listed, or optionally includes other steps or units inherent to these processes, methods, products or devices.

[0034] The specific embodiments of the present application are described in detail below in conjunction with the accompanying drawings.

[0035] refer to Figure 1 The rope cluster driven manipulator usually includes a connecting rod 1, a joint 2, an end tool 3 and a driving rope 4. The joint 2 is connected between two adjacent connecting rods 1, and the end tool 3 is located at the end of the connecting rod 1, which is a free end. The joint 2 includes a shoulder joint 21, an elbow joint 22 and a wrist joint 23. Figure 1 As shown, the shoulder joint 21 has three degrees of freedom, the elbow joint 22 has one degree of freedom, and the wrist joint 23 has three degrees of freedom. This application mainly deals with the planar single-degree-of-freedom pure rolling joint in the joint 2, and does not consider the spatial two-degree-of-freedom pure rolling motion of the wrist joint 23. The elbow joint 22 and the wrist joint 23 are both driven by the driving rope 4, and the shoulder joint 21 is directly driven by the motor.

[0036] For ease of understanding, the system in the present application includes a system corresponding to the elbow joint 22, a system corresponding to the wrist joint 23, or a system corresponding to the rope cluster driven robotic arm.

[0037] refer to Figure 1-Figure 4 The present application provides a low-dimensional equivalent dynamics modeling method for a rope cluster driven robotic arm, including steps S101-S104.

[0038] In step S101 , the planar motion of the wrist joint 23 and the elbow joint 22 of the rope cluster driven manipulator is equivalently simplified to pure rolling motion, and both the wrist joint 23 and the elbow joint 22 include a basic joint component 201 and a planar pure rolling joint component 202 .

[0039] In step S102 , a first dynamic model is performed on the wrist joint 23 or the elbow joint 22 in pure rolling motion based on the momentum moment theorem and in combination with the driving torque of the driving rope 4 and the gravity torque.

[0040] In step S103, a second dynamic modeling is performed on the whole arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and an improved second kind of Lagrangian equation; In step S104, the movement of the rope cluster driven manipulator is controlled by using the results of the first dynamic modeling and the second dynamic modeling, that is, the movement of the rope cluster driven manipulator is controlled by using the results of dynamic modeling of the wrist joint or elbow joint of pure rolling motion based on the momentum moment theorem and dynamic modeling of the whole arm of the rope cluster driven manipulator based on the improved iterative Newton-Euler method or the improved second kind Lagrange equation.

[0041] The dynamic model established by dynamic modeling of the whole arm, wrist joint 23 and elbow joint 22 of the rope cluster driven manipulator fully considers the inertial characteristics caused by the rigid body motion of the rope cluster driven manipulator. The controller designed by the dynamic model of the present application is suitable for both slow and high speed working conditions, thereby enhancing the effect of the controller design and helping to improve the motion performance of the rope cluster driven manipulator.

[0042] By dynamically modeling the wrist joint 23 or elbow joint 22 based on the momentum moment theorem and in combination with the driving torque of the driving rope 4 corresponding to the wrist joint 23 or elbow joint 22 and the gravity torque, a method is established that considers the elastic characteristics of the driving rope 4 and ignores and simplifies the inertial characteristics of the driving rope 4. Therefore, while meeting the calculation accuracy, there is no need to divide the driving rope 4 into rope units. While retaining the dynamic characteristics of the driving rope 4, the modeling process and the complexity of the equations are simplified, which facilitates the controller design.

[0043] Moreover, the number of equations for the dynamic modeling of the rope cluster driven manipulator of the present application is relatively small, the equations are concise and intuitive, the numerical solution is simple, and the controller design is easy.

[0044] refer to Figure 3-Figure 5 As an optional implementation, step S102 includes sub-steps S121-S123.

[0045] In step S121, the contact point between the basic joint component 201 and the plane pure rolling joint component 202 is set as the base point P .

[0046] In step S122, the momentum theorem equation of the base point is set.

[0047] In step S123, the driving torque, gravity torque and inertia torque of the driving rope 4 are set corresponding to the position of the base point, and based on the driving torque, gravity torque and inertia torque, the momentum moment theorem equation is transformed to obtain the dynamic equation of the wrist joint 23 or the dynamic equation of the elbow joint 22.

[0048] In one embodiment, the wrist joint 23 is dynamically modeled using the method provided in step S102, such as Figure 3 The figure shows a schematic diagram of a single degree of freedom pure rolling of the wrist joint 23 .

[0049] Select the contact point between the basic joint component 201 and the planar pure rolling joint component 202 in the wrist joint 23 As a base point, set the momentum theorem equation for the base point (1) in, is the momentum moment about the base point in the wrist joint 23, is the moment about the base point of wrist joint 23, is the mass of the plane pure rolling joint component 202 in the wrist joint 23, is the velocity of the center of mass of the plane pure rolling joint component 202 of the wrist joint 23, It is the moving speed of the point where the base point in the wrist joint 23 coincides with the space. The coincidence point moves on the arc of the basic joint component 201. It cannot be considered that its speed is 0 because the point coincides with the instantaneous center of velocity of the plane pure rolling joint component 202 at an instant. The direction is along the paper facing inwards.

[0050] Then write down the rope driving torque and gravity torque of the driving rope 4 at the corresponding position of the wrist joint 23, and combine the formula (1) to transform it into

[0051] in, is the distance between the center of mass of the plane pure rolling joint component 202 of the wrist joint 23 and its own center of circle, is the center distance between the plane pure rolling joint component 202 and the basic joint component 201 in the wrist joint 23, is the rotation angle of the plane pure rolling joint component 202 of the wrist joint 23, w It is the distance between the two connection points of the drive cable 4 in the wrist joint 23 and the planar pure rolling joint component 202 in the wrist joint 23 . is the moment of inertia about the contact point P.

[0052] (2) in, is the moment of inertia of the planar pure rolling joint component 202 in the wrist joint 23 about its own center of mass. is the tension difference between the two ropes of the driving rope 4 at the wrist joint 23, and the specific expression is (3) in, for Figure 3 The roll radius in for Figure 3 The reel angle in is the preload force of the drive rope 4, It is the elastic force caused by the elastic deformation of a single cable of the drive cable 4 at the wrist joint 23.

[0053] (4)

[0054] in, is the elastic modulus of the drive cable 4 in the wrist joint 23, is the rope cross-sectional area of ​​the driving rope 4 in the wrist joint 23, is the length of the drive rope 4 in the wrist joint 23, is the damping coefficient.

[0055] again

[0056] in, is the distance between the center of mass of the plane pure rolling joint component 202 of the wrist joint 23 and the contact point P, is the angle between the velocity vector of the center of mass of the plane pure rolling joint component 202 of the wrist joint 23 and the velocity vector of the contact point movement, and , so

[0057] It can be obtained that the dynamic equation of the wrist joint 23 is: (5) in, is the moment of inertia of the plane pure rolling joint component 202 in the wrist joint 23 around its own center of mass, is the tension difference between the two ropes of the drive rope in the wrist joint 23, m is the mass of the planar pure rolling joint component 202 in the wrist joint 23, h is the center distance between the basic joint component 201 in the wrist joint 23 and the plane pure rolling joint component 202 in the wrist joint 23, e is the distance between the center of mass of the plane pure rolling joint component 202 in the wrist joint 23 and the center of the circle of the plane pure rolling joint component 202 in the wrist joint 23; θ is the rotation angle of the plane pure rolling joint component 202 in the wrist joint 23 relative to the wrist joint 23 component; w is the distance between the two connection points of the driving rope in the wrist joint 23 and the planar pure rolling joint component 202 in the wrist joint 23; g is the acceleration due to gravity.

[0058] In addition, is the contribution of centrifugal inertia force to the contact point torque.

[0059] In one embodiment, the method provided in step S102 is used to perform dynamic modeling on the elbow joint 22, such as Figure 4The figure shows a schematic diagram of the single degree of freedom pure rolling of the elbow joint 22. The difference between the embodiment of the embodiment of the dynamic modeling of the wrist joint 23 using the method provided in step S102 is that the pulling direction of the driving rope 4 in the elbow joint 22 is always tangent to the circumference of the plane pure rolling joint component 202 of the elbow joint 22, and the driving torque of the driving rope 4 in the wrist joint 23 is different from that of the wrist joint 23. , is the radius of the pure rolling circle.

[0060] Similar to the embodiment of using the method provided in step S102 to perform dynamic modeling on the wrist joint 23, the dynamic equation of the elbow joint 22 can be obtained as follows:

[0061] in, is the moment of inertia of the plane pure rolling joint component 202 in the elbow joint 22 around its own center of mass, is the tension difference between the two ropes of the drive rope in the elbow joint 22, m is the mass of the plane pure rolling joint component 202 in the elbow joint 22, h is the center distance between the basic joint component 201 in the elbow joint 22 and the plane pure rolling joint component 202 in the elbow joint 22, e is the distance between the center of mass of the plane pure rolling joint component 202 in the elbow joint 22 and the center of the circle of the plane pure rolling joint component 202 in the elbow joint 22; θ is the rotation angle of the plane pure rolling joint component 202 in the elbow joint 22 relative to the components of the elbow joint 22; w=2R , R is the radius of the circle of the plane pure rolling joint component 202 in the elbow joint 22; g is the acceleration due to gravity.

[0062] As an optional implementation, step S102 also includes S124.

[0063] In step S124, the rotation angle of the wrist joint 23 is set to be less than 5°, and the drive rope 4 at the wrist joint 23 or the elbow joint 22 is kept taut, and the dynamic equation of the wrist joint 23 or the elbow joint 22 is linearized into a micro-vibration equation.

[0064] For example, the embodiment of using the method provided in step S102 to perform dynamic modeling on the wrist joint 23 is continued. The dynamic equation of the wrist joint 23 obtained based on the momentum theorem shows that it is nonlinear. The source of the nonlinearity of the dynamic equation of the wrist joint 23 is that when the system corresponding to the wrist joint 23 performs a large-scale spatial rotation, the generalized force of the tension of the driving rope 4, the generalized force of gravity, and the generalized force of the external force contain nonlinear functions such as sin and cos. The pure rolling constraint makes The coefficient before is time-varying, and causes the centrifugal force to appear terms, and the discontinuous nonlinearity of the tension of the drive rope 4 caused by the inability of the drive rope 4 to be compressed.

[0065] Therefore, when the rotation angle of the system corresponding to the wrist joint 23 is less than 5° and the driving rope 4 at the wrist joint 23 is always tensioned, the equation can be linearized into a micro-vibration equation. The dynamic equation of the wrist joint 23 is optimized to reduce the complexity of the equation for easy design and application. The micro-vibration equation of the wrist joint 23 is (6) in, is the equivalent mass, is the equivalent damping, is the equivalent stiffness, and the expressions are , , .

[0066] Undamped natural circular frequency of wrist joint 23 (unit rad) is (7) Undamped natural frequency of wrist joint 23 (unit: Hz) is

[0067] System damping ratio of wrist joint 23 for

[0068] When the damping of the wrist joint 23 When the value of is 5000, the damping ratio About 0.14. Damped natural frequency for (8) refer to Figure 6 As an optional implementation, step S103 includes sub-steps S131-S132. In sub-step S131, the coordinate system of the multiple links 1 included in the rope cluster driven manipulator is determined, and relative coordinates with the same number of system degrees of freedom are selected to describe the rigid body motion of the rope cluster driven manipulator.

[0069] In sub-step S132, the established coordinate system is used to perform dynamic modeling of the rope cluster driven manipulator based on an improved iterative Newton-Euler method and / or an improved second-kind Lagrangian equation.

[0070] refer to Figure 6 and Figure 7 As an optional implementation, step S103 also includes sub-step S133 and sub-step S134.

[0071] In sub-step S133, the dynamic equation results of the rope cluster driven robotic arm dynamic modeling based on the improved iterative Newton-Euler method are compared with the dynamic equation results of the rope cluster driven robotic arm dynamic modeling based on the improved second-kind Lagrangian equation to verify the correctness of the two results.

[0072] In sub-step S134, two dynamic modeling methods based on the improved iterative Newton-Euler method and / or based on the improved second-kind Lagrangian equations are applied to at least one of the wrist joint 23 and the elbow joint 22 to verify whether the obtained dynamic equations of the wrist joint 23 or elbow joint 22 are consistent with the dynamic equations of the wrist joint 23 or elbow joint 22 dynamics 22 obtained based on the angular momentum theorem, thereby verifying or improving the accuracy of the method provided in the present application.

[0073] As an optional implementation, sub-step S131 includes determining the coordinate system origin and coordinate system direction of the plurality of connecting rods 1 according to a modified DH method, thereby determining the coordinate system of the plurality of connecting rods 1 .

[0074] According to the modified DH method (modified Denavit-Hartenberg method, a method of fixing a coordinate system on each link of the target and determining the origin and coordinate system direction of multiple coordinate systems), a modified DH coordinate system corresponding to multiple links 1 is established (modified Denavit-Hartenberg coordinate system, a fixed coordinate system of multiple links located at the drive shaft obtained by the above modified DH method). Each modified DH coordinate system on the traditional rigid arm is fixed to the corresponding link 1, while the rope cluster drive manipulator is different from the rigid arm, and only part of the DH coordinate system corresponds to the link 1. For example, Figure 7 A three-degree-of-freedom rope cluster driven robotic arm is shown, wherein the shoulder joint 21 is a rotational joint, the elbow joint 22 and the wrist joint 23 are single-degree-of-freedom planar pure rolling joints, and the No. 1, No. 3 and No. 5 coordinate systems correspond to and are fixed to the upper arm and the lower arm of the connecting rod 1, and the end tool 3, respectively. They are the main coordinate systems, the No. 0 coordinate system is fixed to the ground, and the No. 2 and No. 4 coordinate systems are only intermediate coordinate systems. In the robotic arm studied in this application, the mass of the corresponding components is usually much smaller than that of the connecting rod 1, and it can generally be considered that they do not correspond to the entity connecting rod 1.

[0075] refer to Figure 7-Figure 9 As an optional implementation, sub-step S132 includes sub-steps S1321-1324.

[0076] It should be noted that the two ends of the rope cluster driven manipulator are the end of the manipulator and the root of the manipulator, wherein the end of the rope cluster driven manipulator close to the ground is the root of the manipulator, and the other end is the end of the manipulator. From the root of the manipulator to the end of the manipulator is referred to as outward, from the end of the manipulator to the root of the manipulator is referred to as inward, the end close to the end of the manipulator is the outer side, and the end close to the root of the manipulator is the inner side.

[0077] In sub-step S1321 , the coordinate systems of the multiple connecting rods 1 are iterated outward to obtain the velocities, accelerations, angular velocities, and angular accelerations of the multiple connecting rods 1 , and then the inertia forces and inertia moments of the multiple connecting rods 1 are obtained.

[0078] The connecting rod 1 at the root of the rope cluster driven manipulator is usually fixed to the ground, and its motion is known, and the inertial force of each connecting rod 1 can be obtained by iterating outward in sequence. In order to calculate the inertial force of multiple connecting rods 1, it is first necessary to calculate the centroid linear acceleration, angular velocity, and angular acceleration of the coordinate system corresponding to each connecting rod 1.

[0079] The origin speed of the basic coordinate system (coordinate system 0) , origin acceleration , angular velocity , angular acceleration It should be noted that the superscript of a vector represents the number of the coordinate system into which the vector is projected.

[0080] is the number of the coordinate system, The angular velocity of the coordinate system is (9) The above formula represents Coordinate system angular velocity With Coordinate system angular velocity The conversion relationship between them is Indicates Coordinate system angular velocity Projection in its own coordinate system, similarly, Indicates Coordinate system angular velocity The projection in its own coordinate system is For Coordinate system to The direction cosine matrix of the coordinate system is is the joint angle, Indicates The coordinate system is relative to The relative angular velocity of the coordinate system is That is the Coordinate system Axis unit vector. Since the angular velocity and angular acceleration of the 0th coordinate system are known, the angular velocity and angular acceleration of any coordinate system can be obtained after multiple joint angles and joint angular velocities are given.

[0081] Taking the derivative of both ends of equation (9) we can get the angular acceleration transformation equation between coordinate systems: (10) According to the acceleration relationship between any two points on a rigid body, The linear acceleration of the origin of the coordinate system is (11) in, For the The linear acceleration of the origin of the coordinate system is For From the origin of the coordinate system to The vector at the origin of the coordinate system is The projection in the coordinate system is For the The angular velocity of the coordinate system is The projection in the coordinate system is For the The linear acceleration of the origin of the coordinate system.

[0082] No. The center of mass of link 1 in the coordinate system (when The linear acceleration of the connecting rod 1 in the coordinate system of the entity for (12) in, For From the origin of the coordinate system to The vector of the center of mass of connecting rod 1 is Projection in the coordinate system.

[0083] According to Newton's second law and D'Alembert's principle, the inertial force on connecting rod 1 for (13) in, For the The mass of connecting rod No. 1.

[0084] According to Euler's dynamic equation and D'Alembert's principle, the inertia moment on connecting rod 1 for (14) in, It represents the moment of inertia of connecting rod 1 in the center of mass coordinate system. Indicates that the The coordinate system is formed by translating the coordinate system to the center of mass of connecting rod 1.

[0085] In sub-step S1322, multiple links 1 are iterated inwardly, and the torque balance equation applicable to the plane pure rolling joint in the rope cluster driven manipulator is established to obtain the joint torque at multiple joints in the rope cluster driven manipulator. Among them, the plane pure rolling joint refers to the joint 2 that can simplify its own plane motion into pure rolling motion equivalently. For example, the wrist joint 23 and the elbow joint 22 in this application.

[0086] Since the force conditions at the end of the rope cluster driven robot are usually known, it is possible to iterate inward to obtain the joint torque of the rope cluster driven robot that is balanced with the driving torque of the rope cluster driven robot, as well as the torque balance equation of each link 1, and then obtain the dynamic equation of the entire rope cluster driven robot.

[0087] It is necessary to focus on the force condition of the connecting rod 1 with a plane pure rolling joint. The connecting rod 1 is taken as an isolated body. The force analysis in the motion plane is as follows: Fig. 9 shown.

[0088] According to D'Alembert's principle, write the moment balance equation of connecting rod 1 (15) in, (16) Set the number of Link 1 to , For Coordinate system to The direction cosine matrix of the coordinate system is For connecting rod The inertial force, For connecting rod The inner link of the revolute joint (the inner link of the revolute joint , for a planar pure rolling joint, the connecting rod ) For connecting rod In formula (15), for the outermost link at the end of the robot arm that is not subject to force, According to D'Alembert's principle, all forces and moments including inertial forces and inertial moments are calculated on the DH coordinate system on connecting rod 1. Take the moment of the axis and get the moment balance equation: (17) in, is the radius of the pure rolling joint on the outer plane of the current joint, is the radius of the inner plane pure rolling joint, (18) The above formula is different from the traditional iterative Newton-Euler method. This paper considers the torque contribution of the normal and tangential constraints at the plane pure rolling joint and obtains a new improved iterative Newton-Euler method, which is mainly reflected in the two terms in formula (17): and .

[0089] Rearrange the torque balance equation of the rope cluster drive manipulator to form an iterative relationship from high to low sequence numbers (19) (20) when , , it degenerates into the traditional iterative Newton-Euler method applicable to the rigid arm.

[0090] Therefore, the joint torque can be obtained by formula (20): for (twenty one) When there is gravity in the system, let the origin of the coordinate system 0 accelerate ( is the acceleration due to gravity), the gravity factor can be taken into account.

[0091] In sub-step S1323, the driving torques at multiple joints are calculated, and the driving torques at multiple joints are arranged to obtain the driving torque vector of the rope cluster driven manipulator.

[0092] Driving torque of wrist joint 23 for (twenty two) in, and is the tension of the driving rope 4 on both sides of the wrist joint 23, is the distance between the two rope driving points of the driving rope 4 at the wrist joint 23, It is the joint angle of wrist joint 23.

[0093] Driving torque of elbow joint 22 for (twenty three) in, and is the tension of the driving rope 4 on both sides of the elbow joint 22, is the pure rolling circle diameter of the elbow joint 22.

[0094] The driving torque of the shoulder joint 21 is defined as , given by the motor.

[0095] Arranging the driving torques of multiple joints 2 can obtain the driving torque vector (twenty four) In sub-step S1324, the dynamic equation of the rope cluster driven manipulator based on the iterative Newton-Euler method is formed according to the joint torque and the driving torque at the multiple joints 2.

[0096] Combining the joint torque and driving torque calculated above, the dynamic equation is as follows (25) in, is the joint torque (i.e. the inertia torque, external force torque and gravity torque in the Z-axis direction of coordinate systems 1, 3 and 5 obtained by the above-mentioned improved Newton-Euler method).

[0097] Taking the partial derivative of the joint torque with respect to the generalized acceleration, we can get the inertia matrix The above formula can be transformed into (26) Finally, the dynamic equation of the rope cluster driven manipulator based on the improved iterative Newton-Euler method is obtained as follows:

[0098] in, is the inertia matrix of the rope cluster driven manipulator, is a vector formed by multiple joint angles in the rope cluster driving robot arm, is the sum of the centrifugal inertia moment, Coriolis inertia moment, gravity moment and external force moment of the rope cluster driven manipulator, The driving torque of the rope cluster driving the mechanical arm. is the sum of the inertia moment, external force moment and gravity moment of the rope cluster driving manipulator, through The inertia moment in the figure reflects the inertial characteristics brought about by the rigid body motion of the rope cluster driven robotic arm.

[0099] In the dynamic modeling of the rope cluster driven manipulator based on the iterative Newton-Euler method, by defining symbolic variables corresponding to the system degrees of freedom, all modified DH coordinate systems in the rope cluster driven manipulator are iterated outwardly, and all the link 1s of the entities in the rope cluster driven manipulator are iterated inwardly to obtain the joint torque at each joint 2. Then, the terms of the multiplication of the joint torque of each joint 2 are expanded and combined with the driving torque group of the rope cluster driven manipulator to finally form a closed form group of dynamic equations for the system.

[0100] It can be seen that the present application establishes the dynamic iteration relationship of the planar pure rolling joint, and forms an iterative Newton-Euler method suitable for the rope cluster driven manipulator. Compared with the traditional iterative Newton-Euler method suitable for rigid arms, the traditional iterative Newton-Euler method does not consider the contribution of the tangential force and normal force at the planar pure rolling joint to the rotation axis, while the present application improves the traditional method, considers the force characteristics of the planar pure rolling joint, and obtains an iterative Newton-Euler method suitable for the rope cluster driven manipulator with a planar pure rolling joint.

[0101] refer to Figure 6 , Figure 7 , Fig. 9 and Fig.10 As an optional implementation, sub-step S133 includes sub-steps S1331-S1333.

[0102] In sub-step S1331, the homogeneous transformation matrix between the coordinate systems of two adjacent links 1 in the rope cluster driven manipulator and the homogeneous transformation matrix between the coordinate systems of multiple links 1 and the ground coordinate system are calculated according to the modified DH method, and the homogeneous transformation matrices corresponding to the physical links (excluding the links corresponding to the virtual rods connecting the centers of two circles in the planar pure rolling joint) are extracted and selected and reordered.

[0103] Traverse the modified DH coordinate systems of multiple link 1s, obtain the homogeneous transformation matrix between adjacent coordinate systems according to the modified DH method, and then obtain the homogeneous transformation matrix between each coordinate system and the base coordinate system. Next, it is necessary to extract the homogeneous transformation matrix corresponding to the physical link and reorder it. This step is different from the traditional rigid arm modeling method. Due to the existence of the planar pure rolling joint, the intermediate coordinate system needs to be eliminated and only the coordinate system corresponding to link 1 is retained. Figure 7 Taking the agile arm shown as an example, it is necessary to select the homogeneous transformation matrices of coordinate system No. 1, coordinate system No. 3, and coordinate system No. 5 from the homogeneous transformation matrices of coordinate system No. 0 to No. 5 (a total of 6, including coordinate system No. 0, coordinate system No. 1, coordinate system No. 2, coordinate system No. 3, coordinate system No. 4, and coordinate system No. 5) and rearrange them to coordinate system No. 1, coordinate system No. 2, and coordinate system No. 3.

[0104] Calculate the constant matrix describing the mass distribution of each solid link , (27) in, is the center of mass position of connecting rod 1, , , is the moment of inertia of connecting rod 1, , , is the inertia product of connecting rod 1.

[0105] In sub-step S1332, the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator are calculated according to the reordered homogeneous transformation matrix.

[0106] The kinetic energy of the entire rope cluster driving the robotic arm T for (28) in, is the homogeneous transformation matrix of the rope cluster driven manipulator, is the number of physical links of the rope cluster driving the manipulator, is the inertia matrix of the rope cluster driven manipulator.

[0107] Through the second kind of Lagrangian equation, the inertial force of the system corresponding to the rope cluster driving the manipulator is (29) in,

[0108]

[0109] When the rope cluster driven manipulator is in the gravitational field, the gravitational potential energy of the system is (30) in, , is the projection of gravitational acceleration in the 0 coordinate system.

[0110] According to the second kind of Lagrange equation, the generalized gravity G of the system is (31) in,

[0111] In sub-step S1333, the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator are assembled to form a dynamic equation of the rope cluster driven manipulator based on an improved second kind Lagrangian equation.

[0112] According to the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator, the dynamic equation of the rope cluster driven manipulator based on the second kind of Lagrangian equation is formed as follows: (32) in, is the generalized inertia force of the rope cluster driving the manipulator, is the inertia matrix of the rope cluster driven manipulator, is the velocity coupling matrix of the rope cluster driven manipulator, is the generalized gravity of the rope cluster driven manipulator, It is the generalized driving force of the rope cluster driven manipulator.

[0113] It can be seen that the present application has established a simplified modeling method for a rope cluster driven manipulator based on the second kind of Lagrangian equations. Considering the transformation relationship between multiple coordinate systems and joints 2, the traditional rigid arm modeling method based on the second kind of Lagrangian equations is modified, and a modeling method that can be applied to rope cluster driven manipulators is obtained. Different from the traditional second kind of Lagrangian equations applicable to rigid arms, the method proposed in this article crosses the intermediate coordinate system that does not correspond to the physical link, and obtains a modeling method based on the second kind of Lagrangian equations that is applicable to rope cluster driven manipulators.

[0114] This application describes the rigid body motion of the rope cluster driven robotic arm by selecting relative coordinates with the same number of system degrees of freedom, and establishes the system's dynamic equations through the second kind of Lagrangian equations or vector mechanics methods (Newton-Euler method and momentum moment theorem). The number of system equations is minimized, the equations are concise and intuitive, and are compatible with explicit and implicit numerical solution methods. The numerical solution is simple and easy to design the controller.

[0115] like Fig.11 and Fig.12 As shown, the low-dimensional equivalent dynamic model of the wrist joint 23 is verified.

[0116] In the free vibration of the wrist joint 23, in the case of no gravity and motor lock, the micro-vibration at the equilibrium position is considered, and the rope damping is given as 0. The dynamic response of the wrist joint 23 is as follows: Fig.11 The vibration period obtained by simulation is about 0.0135 s, and the theoretical value of the vibration period obtained by formula (7) is about 0.0137 s. The error between the two is about 1.4%. The simulation value is consistent with the theoretical value, which proves the correctness of the low-dimensional equivalent dynamic model of wrist joint 23.

[0117] In the sinusoidal drive of the wrist joint 23, given the low-speed sinusoidal drive of the wrist joint 23 reel, the dynamic response under the sinusoidal drive condition is calculated. The calculation result is as follows: Fig.12 As shown in the figure, theoretical analysis shows that at low speeds, the inertial force can be ignored and the dynamic response will be equal to the normalized drive angle, which is similar to Fig.12 The simulation results are consistent with those of , proving the correctness of the low-dimensional equivalent dynamics model.

[0118] like Figure 13-Figure 15 As shown, the low-dimensional equivalent dynamic model of the elbow joint 22 is verified.

[0119] In the free vibration of the elbow joint 22, under the condition of no gravity and motor locked, consider the micro-vibration at the equilibrium position, establish the dynamic equation of the elbow joint 22, and calculate the modal frequency. Give the system corresponding to the elbow joint 22 a weak disturbance, and the system will vibrate slightly. Given the initial angle is 0, the initial angular velocity is The undamped free vibration simulation results are as follows: Fig.13 The vibration period obtained by simulation is about 0.185 s, and the theoretical value of the vibration period calculated by formula (7) is about 0.186 s. The error between the two is about 0.58%, which shows the correctness of the simulation.

[0120] In the small angle slow sine drive of the elbow joint 22, the amplitude of the reel is given , small angle slow sine drive with frequency of 0.1 Hz, the simulation results are as follows Fig.14 The simulation results of the low-dimensional equivalent model of this paper (see Fig.13 The "low-dimensional model" curve in ) and the high-dimensional model simulation results based on differential algebraic equations in multibody dynamics simulation software (see Fig.13 Theoretical analysis shows that at this time is about 0.24, and the maximum value of the normalized drive angle is about Due to the slow motion, the angle response of the pure rolling element is almost equal to the normalized drive angle. The theoretical analysis results are consistent with Fig.13 It is consistent with the simulation results in .

[0121] In the small-angle fast sinusoidal drive of the elbow joint 22, a sinusoidal excitation with a frequency of 10 Hz is given, and the angle response (steady-state section) is as follows: Fig.15 As shown. At this time, the frequency ratio is about 2, the response amplitude will be smaller than the excitation amplitude, and the response phase lags the excitation phase by about 90 degrees. Fig.15 As shown, the two results are consistent.

[0122] like Figure 16-Figure 17 As shown, the low-dimensional equivalent dynamic model of the entire rope cluster driven robotic arm is verified.

[0123] In the free vibration of the whole arm of the rope cluster driven robot, the free vibration results of the dynamic model of the whole arm of the rope cluster driven robot are as follows: Fig.16 As shown, "Angle 1" represents the rotation angle of the boom relative to the ground, "Angle 2" represents the rotation angle of the forearm relative to the boom, and "Angle 3" represents the rotation angle of the end tool relative to the forearm. Given a certain angular velocity of the boom, forearm, and end tool, and a certain damping of the rope, the free vibration of the system will gradually decay over time. Fig.16 The angular response in the image gradually decays and eventually approaches the equilibrium position.

[0124] In the sinusoidal drive of the whole arm of the rope cluster driven manipulator, PD (proportional-differential) feedback control is applied to the shoulder drum in the dynamic model of the whole arm of the rope cluster driven manipulator. Given the sinusoidal drive of the elbow joint motor and the wrist joint 23 motor, the dynamic response is as follows: Fig.16 As shown, the lower arm and the upper arm will move in a sinusoidal manner.

[0125] like Fig.18 As shown, a high-agility controller 200 provided by the present application is presented in the form of a general-purpose computing device. The components of the controller 200 may include, but are not limited to: at least one processing unit 210, at least one storage unit 220, a bus 230 connecting different system components (including the storage unit 220 and the processing unit 210), a display unit 240, etc.

[0126] The storage unit stores program codes, which can be executed by the processing unit 210, so that the processing unit 210 executes the methods described in this specification according to various exemplary embodiments of the present application. For example, the processing unit 210 can execute the following: Figure 1 The method shown in .

[0127] The storage unit 220 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 2201 and / or a cache storage unit 2202 , and may further include a read-only storage unit (ROM) 2203 .

[0128] The storage unit 220 may also include a program / utility 2204 having a set (at least one) of program modules 2205, such program modules 2205 including but not limited to: an operating system, one or more application programs, other program modules, and program data, each of which or some combination may include an implementation of a network environment.

[0129] Bus 230 may represent one or more of several types of bus structures, including a memory unit bus or memory unit controller, a peripheral bus, an accelerated graphics port, a processing unit, or a local bus using any of a variety of bus architectures.

[0130] The controller 200 may also communicate with one or more external devices 300 (e.g., keyboards, pointing devices, Bluetooth devices, etc.), may also communicate with one or more devices that enable a user to interact with the controller 200, and / or communicate with any device that enables the controller 200 to communicate with one or more other computing devices (e.g., routers, modems, etc.). Such communication may be performed via an input / output (I / O) interface 250. In addition, the controller 200 may also communicate with one or more networks (e.g., a local area network (LAN), a wide area network (WAN), and / or a public network, such as the Internet) via a network adapter 260. The network adapter 260 may communicate with other modules of the controller 200 via the bus 230. It should be understood that, although not shown in the figure, other hardware and / or software modules may be used in conjunction with the controller 200, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0131] Through the description of the above implementation methods, it is easy for those skilled in the art to understand that the example implementation methods described here can be implemented by software, or by combining software with necessary hardware. The technical solution according to the implementation method of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including several instructions to enable a computing device (which can be a personal computer, a server, or a network device, etc.) to execute the above method according to the implementation method of the present application.

[0132] Those skilled in the art will appreciate that the above modules can be distributed in the device according to the description of the embodiment, or can be changed accordingly and only used in one or more devices different from the embodiment. The modules of the above embodiments can be combined into one module, or further divided into multiple sub-modules.

[0133] The present application provides a rope cluster driven robotic arm, comprising a robotic arm body and the above-mentioned controller, wherein the controller is used to control the movement of the rope cluster driven robotic arm.

[0134] The embodiments of the present application are described in detail above. Specific examples are used herein to illustrate the principles and implementation methods of the present application. The description of the above embodiments is only used to help understand the method and its core idea of ​​the present application. At the same time, changes or deformations made by those skilled in the art based on the ideas of the present application, the specific implementation methods and the scope of application of the present application, all belong to the scope of protection of the present application. In summary, the content of this specification should not be construed as a limitation on the present application.

Claims

1. A low-dimensional equivalent dynamics modeling method for a rope cluster driven manipulator, characterized in that: include: The planar motion of the wrist joint and the elbow joint of the rope cluster driven manipulator is equivalently simplified to pure rolling motion, wherein the wrist joint and the elbow joint both include a basic joint component and a planar pure rolling joint component; Based on the momentum moment theorem, a first dynamic modeling is performed on the wrist joint or the elbow joint in pure rolling motion in combination with the driving torque of the driving rope and the gravity torque; Performing a second dynamic modeling of the entire arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and an improved second-kind Lagrangian equation; The movement of the rope cluster driven manipulator is controlled by using the results of the first dynamics modeling and the second dynamics modeling.

2. The method according to claim 1, characterized in that Based on the momentum moment theorem, and in combination with the driving torque of the driving rope and the gravity torque, the first dynamic modeling of the wrist joint or the elbow joint in pure rolling motion includes: Setting the contact point between the basic joint component and the planar pure rolling joint component as a base point; Setting the momentum theorem equation of the base point; The driving torque, gravity torque and inertia torque of the driving rope are set corresponding to the position of the base point, and based on the driving torque, the gravity torque and the inertia torque, the momentum moment theorem equation is transformed to obtain the dynamic equation of the wrist joint or the dynamic equation of the elbow joint.

3. The method according to claim 2, characterized in that Based on the momentum moment theorem, and in combination with the driving torque of the driving rope and the gravity torque, the first dynamic modeling of the wrist joint or the elbow joint in pure rolling motion also includes: When the rotation angle of the wrist joint is set to be less than 5° and the driving rope at the wrist joint or the elbow joint is kept taut, the dynamic equation of the wrist joint or the elbow joint is linearized into a micro-vibration equation.

4. The method according to claim 2, characterized in that: The dynamic equation of the wrist joint is: in, is the moment of inertia of the plane pure rolling joint component in the wrist joint around its own center of mass, is the tension difference between the two ropes of the driving rope in the wrist joint, m is the mass of the planar pure rolling joint component in the wrist joint, h is the center distance between the basic joint component in the wrist joint and the plane pure rolling joint component in the wrist joint, e is the distance between the center of mass of the plane pure rolling joint component in the wrist joint and the center of the circle of the plane pure rolling joint component in the wrist joint; θ is the rotation angle of the plane pure rolling joint component in the wrist joint relative to the wrist joint component; w is the distance between the two connection points of the driving rope in the wrist joint and the planar pure rolling joint component in the wrist joint; g is the acceleration due to gravity.

5. The method according to claim 2, characterized in that: The dynamic equation of the elbow joint is: in, is the moment of inertia of the plane pure rolling joint component in the elbow joint around its own center of mass, is the tension difference between the two ropes of the drive rope in the elbow joint, m is the mass of the planar pure rolling joint component in the elbow joint, h is the distance between the center of the basic joint component in the elbow joint and the plane pure rolling joint component in the elbow joint, e is the distance between the center of mass of the plane pure rolling joint component in the elbow joint and the center of the circle of the plane pure rolling joint component in the elbow joint; θ is the rotation angle of the plane pure rolling joint component in the elbow joint relative to the elbow joint component; w=2R , R is the radius of the circle of the plane pure rolling joint component in the elbow joint; g is the acceleration due to gravity.

6. The method according to claim 1, characterized in that Performing a second dynamic modeling of the whole arm of the rope cluster driven manipulator based on at least one of an improved iterative Newton-Euler method and a second kind of Lagrangian equations includes: Determining a coordinate system of a plurality of links included in the rope cluster driven robot arm; and The coordinate system is used to perform dynamic modeling of the rope cluster driven manipulator based on the improved iterative Newton-Euler method and / or the improved second kind Lagrangian equations.

7. The method according to claim 6, characterized in that The second dynamic modeling of the whole arm of the rope cluster driven manipulator based on at least one of the improved iterative Newton-Euler method and the second kind of Lagrangian equations also includes: Comparing the dynamic equation results of the dynamic modeling of the rope cluster driven manipulator based on the improved iterative Newton-Euler method with the dynamic equation results of the dynamic modeling of the rope cluster driven manipulator based on the improved second-kind Lagrangian equation to verify the correctness of the results; or The improved iterative Newton-Euler method and / or the improved second-kind Lagrangian equations are applied to at least one of the wrist joint and the elbow joint to verify whether the obtained dynamic equation of the wrist joint or the elbow joint is consistent with the dynamic equation obtained based on the angular momentum theorem.

8. The method according to claim 6, characterized in that Determining the coordinate system of the plurality of links included in the rope cluster driven robotic arm comprises: The coordinate system origins and coordinate system directions of the plurality of connecting rods are determined according to the modified DH method, thereby determining the coordinate system of the plurality of connecting rods.

9. The method according to claim 8, characterized in that The dynamic modeling of the rope cluster driven manipulator based on the improved iterative Newton-Euler method includes: Iterate outwardly through the coordinate systems of the multiple connecting rods to obtain the velocities, accelerations, angular velocities, and angular accelerations of the multiple connecting rods, and then obtain the inertia forces and inertia moments of the multiple connecting rods; Iterate the coordinate systems of the multiple connecting rods inwardly, and obtain the joint torques at multiple joints in the rope cluster driven mechanical arm by establishing a torque balance equation applicable to the plane pure rolling joint in the rope cluster driven mechanical arm; Calculating the driving torques at the multiple joints, and arranging the driving torques at the multiple joints to obtain a driving torque vector of the rope cluster driven manipulator; According to the joint torques and driving torques at the multiple joints, a dynamic equation of the rope cluster driven robotic arm based on an improved iterative Newton-Euler method is formed.

10. The method according to claim 9, characterized in that The dynamic equation of the rope cluster driven manipulator based on the improved iterative Newton-Euler method is: in, is the inertia matrix of the rope cluster driven manipulator, is a vector formed by multiple joint angles in the rope cluster driving robot arm, is the sum of the centrifugal inertia moment, Coriolis inertia moment, gravity moment and external force moment of the rope cluster driven manipulator, is the driving torque vector of the rope cluster driving the manipulator.

11. The method according to claim 8, characterized in that The dynamic modeling of the rope cluster driven manipulator based on the improved second kind Lagrangian equation includes: Calculate the homogeneous transformation matrix between the coordinate systems of two adjacent links in the rope cluster driven manipulator according to the modified DH method, and the homogeneous transformation matrix between the coordinate systems of the multiple links and the ground coordinate system, and extract and select the homogeneous transformation matrix corresponding to the physical link and reorder it; Calculating the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven manipulator according to the reordered homogeneous transformation matrix; According to the generalized inertial force, generalized gravity and generalized driving force of the rope cluster driven robotic arm, a dynamic equation of the rope cluster driven robotic arm based on an improved second kind Lagrangian equation is formed.

12. The method according to claim 11, characterized in that The dynamic equation of the rope cluster driven manipulator based on the improved second kind Lagrangian equation is: in, is the generalized inertial force of the rope cluster driving the manipulator, is the inertia matrix of the rope cluster driven manipulator, is the velocity coupling matrix of the rope cluster driven manipulator, is the generalized gravity of the rope cluster driving the manipulator, It is the generalized driving force of the rope cluster driving the robotic arm.

13. A high-agility controller, characterized in that: include: processor; as well as A memory storing a computer program, which, when executed by the processor, enables the processor to perform the method according to any one of claims 1 to 12.

14. A rope cluster driven mechanical arm, characterized in that: include: Robotic arm body; as well as The controller as claimed in claim 13, wherein the controller is used to control the movement of the rope cluster driven robot arm.

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