Heterogeneous multi-branch rope-driven mechanical arm kinematics modeling method

Abstract

The invention relates to a kinematics modeling method for a heterogeneous multi-branch rope-driven mechanical arm, belongs to the technical field of kinematics modeling of robots and mechanical arms, solves the problem of performing kinematics modeling on the heterogeneous multi-branch rope-driven mechanical arm, and comprises the following steps: respectively establishing kinematics recursion relations of a large-span mechanical arm, a rope-driven agile mechanical arm and a rope-driven flexible mechanical arm; the kinematics recursion relations of the large-span mechanical arm, the rope-driven agile mechanical arm and the rope-driven flexible mechanical arm are integrated, so that a kinematics model of the large-span mechanical arm-the rope-driven agile mechanical arm and a kinematics model of the large-span mechanical arm-the rope-driven flexible mechanical arm are obtained; the model established through the method is simple in structure, the corresponding relation between the joint rotation angle and the tail end pose of the mechanical arm can be accurately reflected, the accuracy of the model is guaranteed, practicability is high, and the mechanical arm can be further controlled conveniently.

Description

Technical Field

[0001] The present invention belongs to the technical field of kinematic modeling of robots and robotic arms, and relates to a kinematic modeling method for a heterogeneous multi-branch cable-driven robotic arm. Background Art

[0002] In recent years, with the development of robot technology and the in-depth exploration of space, space robots are increasingly frequently used in space resource development. The cable-driven system has attracted extensive attention from workers in various fields due to its characteristics of small mass, large load ratio, good flexibility, and high safety performance in human-machine interaction. The cable-driven space robot currently plays an increasingly important role in space activities and has become a hot topic in the current space on-orbit system. The heterogeneous multi-branch cable-driven robotic arm has received more and more attention due to its flexible structure, diverse function designs, and rich application scenarios. To achieve high-precision control of the heterogeneous multi-branch cable-driven robotic arm, an accurate kinematic model thereof must be obtained. However, due to the complexity of its structural design, it is difficult to establish the kinematic model of the heterogeneous multi-branch cable-driven robotic arm. To meet the requirements of high-precision control of the robot, it is first required to establish an accurate kinematic model of the robot. To achieve this goal, problems in aspects such as the joint motion space and the structure of the heterogeneous multi-branch cable-driven robotic arm need to be solved. The kinematic modeling of the existing cable-driven space robot is a single-arm rod model, which does not consider the structural characteristics and motion range of the heterogeneous multi-branch cable-driven robotic arm, nor the multi-arm combined kinematic characteristics of the heterogeneous multi-branch cable-driven robotic arm, and cannot meet the kinematic requirements of the heterogeneous multi-branch cable-driven robotic arm. Summary of the Invention

[0003] The technical solution of the present invention is used to solve the problem of kinematic modeling of a heterogeneous multi-branch cable-driven robotic arm.

[0004] The present invention solves the above technical problems through the following technical solutions:

[0005] The present invention provides a kinematic modeling method for a heterogeneous multi-branch cable-driven manipulator. The heterogeneous multi-branch cable-driven manipulator includes: a large-span manipulator (10), a cable-driven agile manipulator (20), a cable-driven flexible manipulator (30), and a flexible or agile manipulator drive assembly (40). One end of the large-span manipulator (10) is connected to one end of the flexible or agile manipulator drive assembly (40), and the other end of the agile manipulator drive assembly (40) is respectively connected to the cable-driven agile manipulator (20) and the cable-driven flexible manipulator (30). The kinematic modeling method for the heterogeneous multi-branch cable-driven manipulator is as follows: establish the kinematic recurrence relations of the large-span manipulator, the cable-driven agile manipulator, and the cable-driven flexible manipulator respectively; integrate the kinematic recurrence relations of the large-span manipulator, the cable-driven agile manipulator, and the cable-driven flexible manipulator, so as to obtain the kinematic model of the large-span manipulator - cable-driven agile manipulator and the kinematic model of the large-span manipulator - cable-driven flexible manipulator.

[0006] Further, the transformation matrix of a certain link coordinate system of the large-span manipulator relative to the base coordinate system is as follows:

[0007]

[0008] Among them, represents the total transformation matrix from the initial point to the end point of the large-span manipulator, represents the transformation matrix from the initial point to the end point of the first link of the large-span manipulator, represents the transformation matrix from the end point of the first link to the end point of the second link of the large-span manipulator, represents the transformation matrix from the end point of the (N - 1)th link to the end point of the Nth link of the large-span manipulator;

[0009] The vector on the ith link of the large-span manipulator is represented relative to the base coordinate system as:

[0010]

[0011] Among them, is the initial vector on the first link of the large-span manipulator;

[0012] Derive the vector on the ith link of the large-span manipulator to obtain:

[0013]

[0014] Thus, the velocity derivation formula of the large-span manipulator is obtained as follows:

[0015]

[0016] Among them, is the joint angular velocity of the i-th joint of the large-span robotic arm,

[0017] Furthermore, the transformation matrix of a certain link coordinate system of the cable-driven agile robotic arm relative to the base coordinate system is as follows:

[0018]

[0019] where, represents the total transformation matrix from the initial point to the end point of the cable-driven agile robotic arm, represents the transformation matrix from the initial point to the end point of the first link of the cable-driven agile robotic arm, represents the transformation matrix from the end point of the first link to the end point of the second link of the cable-driven agile robotic arm, represents the transformation matrix from the end point of the (N - 1)-th link to the end point of the N-th link of the cable-driven agile robotic arm;

[0020] The vector on the i-th link of the cable-driven agile robotic arm is represented relative to the base coordinate system as:

[0021]

[0022] where, is the initial vector on the first link of the cable-driven agile robotic arm;

[0023] Taking the derivative of the vector on the i-th link of the cable-driven agile robotic arm gives:

[0024]

[0025] Thus, the velocity derivation formula of the cable-driven agile robotic arm is as follows:

[0026]

[0027] where, is the joint angular velocity of the i-th joint of the cable-driven agile robotic arm,

[0028] Furthermore, the end pose transformation matrix of the cable-driven flexible robotic arm is:

[0029]

[0030] where,

[0031] α ri+1 is the joint angle of the (i + 1)-th joint of the cable-driven flexible robotic arm, TrN represents the total transformation matrix from the initial point to the end point of the cable-driven flexible robotic arm, represents the transformation matrix from the initial point to the end point of the first arm segment of the cable-driven flexible robotic arm, represents the transformation matrix from the end point of the first arm segment to the end point of the second arm segment of the cable-driven flexible robotic arm, represents the transformation matrix from the end point of the second arm segment to the end point of the third arm segment of the cable-driven flexible robotic arm, represents the transformation matrix from the end point of the (N - 1)-th arm segment to the end point of the N-th arm segment of the cable-driven flexible robotic arm;

[0032] The vector on the i-th arm segment of the cable-driven flexible robotic arm is represented with respect to the base coordinate system as:

[0033]

[0034] where is the initial vector on the first arm segment of the cable-driven flexible robotic arm;

[0035] Taking the derivative of the vector on the i-th arm segment of the cable-driven flexible robotic arm gives:

[0036]

[0037] Thus, the velocity derivation formula of the cable-driven flexible robotic arm is as follows:

[0038]

[0039] where is the joint angular velocity of the i-th joint of the cable-driven flexible robotic arm,

[0040] Furthermore, the method for establishing the kinematic model of the large-span robotic arm - cable-driven agile robotic arm is as follows:

[0041] Multiplying the transformation matrix of a certain arm segment coordinate system of the large-span robotic arm with respect to the base coordinate system by the transformation matrix of a certain arm segment coordinate system of the cable-driven agile robotic arm with respect to the base coordinate system gives the kinematic derivation formula of the large-span robotic arm - cable-driven agile robotic arm as:

[0042] Adding the velocity derivation formula of the large-span robotic arm and the velocity derivation formula of the cable-driven agile robotic arm gives the velocity derivation formula of the large-span robotic arm - cable-driven agile robotic arm as:

[0043] Further, the method for establishing the kinematic model of the large-span robotic arm - cable-driven flexible robotic arm is as follows:

[0044] Multiply the transformation matrix of a certain arm coordinate system of the large-span robotic arm relative to the base coordinate system by the end pose transformation matrix T of the cable-driven flexible robotic arm rN to obtain the kinematic derivation formula of the large-span robotic arm - cable-driven flexible robotic arm as:

[0045] Add the velocity derivation formula of the large-span robotic arm to the velocity derivation formula of the cable-driven flexible robotic arm to obtain the velocity derivation formula of the large-span robotic arm - cable-driven flexible robotic arm as:

[0046] The present invention also provides an electronic device, including a memory and a processor. The memory is used to store a program that supports the processor to execute the above-mentioned kinematic modeling method of the heterogeneous multi-branch cable-driven robotic arm, and the processor is configured to execute the program stored in the memory.

[0047] The present invention also provides a storage medium, on which a computer program is stored. When the computer program is run by a processor, it executes the steps of the above-mentioned kinematic modeling method of the heterogeneous multi-branch cable-driven robotic arm.

[0048] The advantages of the present invention are as follows:

[0049] The present invention respectively establishes the kinematic recurrence relations of the large-span robotic arm, the cable-driven agile robotic arm, and the cable-driven flexible robotic arm; integrates the kinematic recurrence relations of the large-span robotic arm, the cable-driven agile robotic arm, and the cable-driven flexible robotic arm, so as to obtain the kinematic model of the large-span robotic arm - cable-driven agile robotic arm and the kinematic model of the large-span robotic arm - cable-driven flexible robotic arm; the model established by the method of the present invention has a simple structure, can accurately reflect the corresponding relationship between the joint angles of the robotic arm and the end pose, ensures the accuracy of the model, has strong practicability, and is convenient for further controlling the robotic arm. Description of the Drawings

[0050] Figure 1 is the structural diagram of the heterogeneous multi-branch cable-driven robotic arm according to the embodiment of the present invention;

[0051] Figure 2 is the schematic structural diagram of a single arm of the large-span robotic arm according to the embodiment of the present invention;

[0052] Figure 3 is the schematic structural diagram of the cable-driven agile robotic arm according to the embodiment of the present invention;

[0053] Figure 4It is a schematic diagram of the model structure of the cable-driven flexible robotic arm according to an embodiment of the present invention;

[0054] Figure 5 It is a schematic diagram of the model structure of the joint of the cable-driven flexible robotic arm according to an embodiment of the present invention;

[0055] Figure 6 It is a result diagram of the first simulation using Matlab according to an embodiment of the present invention;

[0056] Figure 7 It is a result diagram of the second simulation using Matlab according to an embodiment of the present invention. Detailed implementation manners

[0057] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0058] The technical solutions of the present invention will be further described below in conjunction with the accompanying drawings of the specification and specific embodiments:

[0059] Embodiment 1

[0060] As Figure 1 shown, the heterogeneous multi-branch cable-driven robotic arm according to the embodiment of the present invention includes: a large-span robotic arm (10), a cable-driven agile robotic arm (20), a cable-driven flexible robotic arm (30), and a flexible or agile robotic arm drive assembly (40). The end of the large-span robotic arm (10) is connected to one end of the flexible or agile robotic arm drive assembly (40), and the other end of the agile robotic arm drive assembly (40) is respectively connected to the cable-driven agile robotic arm (20) and the cable-driven flexible robotic arm (30).

[0061] The kinematic modeling method idea of the heterogeneous multi-branch cable-driven robotic arm according to the embodiment of the present invention is: respectively establish the kinematic recurrence relationships of the large-span robotic arm, the cable-driven agile robotic arm, and the cable-driven flexible robotic arm; integrate the kinematic recurrence relationships of the large-span robotic arm, the cable-driven agile robotic arm, and the cable-driven flexible robotic arm, so as to obtain the kinematic models of the large-span robotic arm - cable-driven agile robotic arm and the large-span robotic arm - cable-driven flexible robotic arm.

[0062] 1. Establish the kinematic recurrence relationship of the large-span robotic arm

[0063] As Figure 2As shown, it is a single-arm rod model of a large-span robotic arm. Among them, the length of the left half of each arm rod is L1, the length of the right half of each arm rod is L2, the length of the sling of each arm rod is h, the length of the rotating shaft is d, the rotating shaft is vertically fixed to the sling, the angle between the left half of each arm rod and the sling is θ1, and the angle between the right half of each arm rod and the sling is θ2. In the actual system motion control, the angles between the two arm rods and the sling of each joint are controlled to be equal, ignoring the slight inequality in the actual situation, that is, θ1 = θ2 = θ, and θ is the joint angle of each joint of the large-span robotic arm.

[0064] Any point in the space of the large-span robotic arm is expressed by a 3×1 position vector as follows:

[0065] A P d =[x d y d z d (1)

[0066] Among them, A P d represents the position vector of any point of the large-span robotic arm, x d represents the abscissa value of the position vector of this point of the large-span robotic arm, y d represents the ordinate value of the position vector of this point of the large-span robotic arm, z d represents the vertical coordinate value of the position vector of this point of the large-span robotic arm;

[0067] Then the attitude of the arm rod of the large-span robotic arm can be expressed by three unit vectors, and each column is the vector position reference of the coordinate axis:

[0068]

[0069] Among them, represents the attitude vector of the arm rod of the large-span robotic arm, r d11 、r d21 and r d31 respectively represent the abscissa value, ordinate value and vertical coordinate value of the first point of the arm rod position of the large-span robotic arm. Similarly, r d21 、r d22 and r d32 respectively represent the abscissa value, ordinate value and vertical coordinate value of the second point of the arm rod position of the large-span robotic arm, r d13 、r d23 and r d33 respectively represent the abscissa value, ordinate value and vertical coordinate value of the third point of the arm rod position of the large-span robotic arm.

[0070] From formula (1) and formula (2), the transformation matrix of the arm rod of the large-span robotic arm is obtained as follows:

[0071]

[0072] Among them, for the matrix there are three transformation rules: rotation about the x-axis, rotation about the y-axis, and rotation about the z-axis. Since the movement of the large-span robotic arm is in a plane, Equation (2) is rewritten as:

[0073]

[0074] Among them, from Formulas (3) and (4), we get:

[0075]

[0076] Among them, T d represents the arm rod transformation matrix of the large-span robotic arm, p dx represents the displacement vector along the x-axis, p dy represents the displacement vector along the y-axis, p dz represents the displacement vector along the z-axis.

[0077] Since there is a crossbeam at the joint of the large-span robotic arm, which is different from the structure of the traditional robotic arm, the single arm rod of the large-span robotic arm can be regarded as a combination of two end arm rods, and the joint angles between the two arm rods are equal. Taking the first arm rod of the large-span robotic arm as an example, the arm rod transformation matrix of the large-span robotic arm is divided into two parts for calculation:

[0078]

[0079] Among them, represents the arm rod transformation matrix of the front left part of the large-span robotic arm, represents the arm rod transformation matrix of the right half part of the large-span robotic arm.

[0080] Multiply the matrix and the matrix to obtain the transformation matrix

[0081]

[0082] Similarly, the transformation matrix of the large-span robotic arm is expressed by the above method for convenient further calculation. Multiply the transformation matrices of each arm rod to obtain the transformation matrix of a certain arm rod coordinate system relative to the base coordinate system as follows:

[0083]

[0084] Among them, represents the total transformation matrix from the initial point to the end point of the large-span robotic arm, represents the transformation matrix from the initial point to the end point of the first arm rod of the large-span robotic arm, The transformation matrix from the end point of the first arm segment of the large-span robotic arm to the end point of the second arm segment The transformation matrix from the end point of the (N - 1)-th arm segment of the large-span robotic arm to the end point of the N-th arm segment

[0085] Since the arm lengths and the lengths of the rotating shafts involved in formula (9) are all constant values, the transformation matrix is a function related to the joint angles. The vector on the i-th arm segment of the large-span robotic arm Expressed with respect to the base coordinate system as:

[0086]

[0087] Where Is the initial vector on the first arm segment of the large-span robotic arm;

[0088] For the vector on the i-th arm segment of the large-span robotic arm Taking the derivative gives:

[0089]

[0090] Thus, the velocity derivation formula of the large-span robotic arm is as follows:

[0091]

[0092] Where Is the joint angular velocity of the i-th joint of the large-span robotic arm,

[0093] 2. Establish the kinematic recurrence relationship of the cable-driven agile robotic arm

[0094] As Figure 3 Shown, the cable-driven agile robotic arm moves in a plane, so only three arm segments and the end gripper are considered. The arm lengths of the cable-driven agile robotic arm are L m1 , L m2 , L m3 , the gripper length is L m4 , the length of the intermediate linkage joint is d m1 , and the joint angles between the arm segments and between the arm segments and the gripper are θ m1 , θ m2 , θ m3 .

[0095] Any point in the space of the cable-driven agile robotic arm is expressed by a 3×1 position vector as follows:

[0096] A P m = [x m y m zm (13)

[0097] Among them, A P m represents the position vector of any point on the cable-driven agile robotic arm, and x m represents the abscissa value of the position vector of this point on the cable-driven agile robotic arm, y m represents the ordinate value of the position vector of this point on the cable-driven agile robotic arm, and z m represents the vertical coordinate value of the position vector of this point on the cable-driven agile robotic arm;

[0098] Then, the attitude in the cable-driven agile robotic arm is expressed by three unit vectors, and each column is the vector position reference of the coordinate axis:

[0099]

[0100] Among them, represents the attitude vector of the arm rod of the cable-driven agile robotic arm, r m11 , r m21 and r m31 respectively represent the abscissa value, ordinate value, and vertical coordinate value of the first point of the position of the arm rod of the cable-driven agile robotic arm. Similarly, r m21 , r m22 and r m32 respectively represent the abscissa value, ordinate value, and vertical coordinate value of the second point of the position of the arm rod of the cable-driven agile robotic arm, and r m13 , r m23 and r m33 respectively represent the abscissa value, ordinate value, and vertical coordinate value of the third point of the position of the arm rod of the cable-driven agile robotic arm.

[0101] The transformation matrix of the cable-driven agile robotic arm is obtained from Equation (13) and Equation (14) as follows:

[0102]

[0103] Among them, the transformation rules of the matrix are of three types: rotation about the x-axis, rotation about the y-axis, and rotation about the z-axis. Since the movement of the cable-driven agile robotic arm is in a plane, Equation (14) is rewritten as:

[0104]

[0105] Among them, θ mj is the joint angle of each joint of the cable-driven agile robotic arm, where j = 1, 2, or 3.

[0106] From Equation (15) and Equation (16), we get:

[0107]

[0108] Among them, T m represents the conversion matrix of the arm rod of the cable-driven agile manipulator, and p mx represents the displacement vector along the x-axis, and p my represents the displacement vector along the y-axis, and p mz represents the displacement vector along the z-axis.

[0109] Since there are linkage joints at the joints of the cable-driven agile manipulator, which is different from the structure of the traditional manipulator, the single-section arm rod of the cable-driven agile manipulator can be regarded as a combined body of two end arm rods, and the joint angles between the two arm rods are equal. Taking the first-section arm rod of the cable-driven agile manipulator as an example, the conversion matrix of the arm rod of the cable-driven agile manipulator is divided into two parts for calculation:

[0110]

[0111] Among them, represents the conversion matrix of the front half part of the arm rod of the cable-driven agile manipulator, represents the conversion matrix of the rear half part of the arm rod of the cable-driven agile manipulator.

[0112] Multiply the matrix and the matrix to obtain the conversion matrix of the first-section arm rod of the cable-driven agile manipulator as follows:

[0113]

[0114] Similarly, the conversion matrix of the cable-driven agile manipulator is expressed by the above method for convenient further calculation. Multiply the conversion matrices of each arm rod to obtain the conversion matrix of a certain arm rod coordinate system relative to the base coordinate system as follows:

[0115]

[0116] Among them, represents the total conversion matrix from the initial point to the end point of the cable-driven agile manipulator, represents the conversion matrix from the initial point to the end point of the first-section arm rod of the cable-driven agile manipulator, represents the conversion matrix from the end point of the first-section arm rod to the end point of the second-section arm rod of the cable-driven agile manipulator, represents the conversion matrix from the end point of the (N - 1)-th section arm rod to the end point of the N-th section arm rod of the cable-driven agile manipulator.

[0117] Since the arm rod length and the rotating shaft length involved in Equation (21) are both fixed values, the conversion matrix is a function related to the joint angle. The vector on the i-th arm rod of the cable-driven agile manipulator is represented relative to the base coordinate system as:

[0118]

[0119] Among them, is the initial vector on the first arm rod of the cable-driven agile robotic arm;

[0120] For the vector on the i-th arm rod of the cable-driven agile robotic arm, taking the derivative gives:

[0121]

[0122] Thus, the velocity derivation formula of the cable-driven agile robotic arm is as follows:

[0123]

[0124] Among them, is the joint angular velocity of the i-th joint of the cable-driven agile robotic arm,

[0125] 3. Establish the kinematic recurrence relationship of the cable-driven flexible robotic arm

[0126] As Figure 4 and Figure 5 shown, the arm rod part of the cable-driven flexible robotic arm is equivalent to a chain multi-rigid body system. The arm rod connection joint of the cable-driven flexible robotic arm is a "cross" joint with two degrees of freedom. Then, the kinematic recurrence formula from the (i + 1)-th joint to the i-th joint is:

[0127]

[0128] Among them, α ri is the joint angle of the i-th joint of the cable-driven flexible robotic arm, θ ri is the deflection angle of the i-th joint of the cable-driven flexible robotic arm, used to distinguish the joint angles of up and down and left and right. θ ri = [-90 0 90 0 … -90 …], l ri is the arm rod length of a single-segment cable-driven flexible robotic arm.

[0129] Then, the end pose transformation matrix of the cable-driven flexible robotic arm is:

[0130]

[0131] Among them,

[0132] α ri+1 is the joint angle of the (i + 1)-th joint of the cable-driven flexible robotic arm, T rN represents the total transformation matrix from the initial point to the end point of the cable-driven flexible robotic arm, represents the transformation matrix from the initial point to the end point of the first arm rod of the cable-driven flexible robotic arm, Represents the transformation matrix from the end point of the first arm rod of the cable-driven flexible manipulator to the end point of the second arm rod, Represents the transformation matrix from the end point of the second arm rod of the cable-driven flexible manipulator to the end point of the third arm rod, Represents the transformation matrix from the end point of the (N - 1)-th arm rod of the cable-driven flexible manipulator to the end point of the N-th arm rod.

[0133] Since the arm rod length and the rotating shaft length in Equation (26) are both constant values, the end pose transformation matrix of the cable-driven flexible manipulator is a function related to the joint angles. The vector on the i-th arm rod of the cable-driven flexible manipulator is expressed relative to the base coordinate system as:

[0134]

[0135] where, is the initial vector on the first arm rod of the cable-driven flexible manipulator;

[0136] For the vector on the i-th arm rod of the cable-driven flexible manipulator, taking the derivative gives:

[0137]

[0138] From this, the velocity derivation formula of the cable-driven flexible manipulator is obtained as follows:

[0139]

[0140] where, is the joint angular velocity of the i-th joint of the cable-driven flexible manipulator,

[0141] 4. Integrate the kinematic recurrence relations of the large-span manipulator, the cable-driven agile manipulator, and the cable-driven flexible manipulator, so as to obtain the kinematic models of the large-span manipulator - cable-driven agile manipulator and the large-span manipulator - cable-driven flexible manipulator

[0142] Multiply the transformation matrix of a certain arm rod coordinate system of the large-span manipulator relative to the base coordinate system by the transformation matrix of a certain arm rod coordinate system of the cable-driven agile manipulator relative to the base coordinate system to obtain the kinematic derivation formula of the large-span manipulator - cable-driven agile manipulator as:

[0143]

[0144] Add the velocity derivation formula of the large-span manipulator and the velocity derivation formula of the cable-driven agile manipulator to obtain the velocity derivation formula of the large-span manipulator - cable-driven agile manipulator as:

[0145]

[0146] Similarly, the transformation matrix of a certain arm coordinate system of the large-span manipulator relative to the base coordinate system is multiplied by the end pose transformation matrix T of the cable-driven flexible manipulator rN to obtain the kinematic derivation formula of the large-span manipulator - cable-driven flexible manipulator as:

[0147]

[0148] Adding the velocity derivation formula of the large-span manipulator and the velocity derivation formula of the cable-driven flexible manipulator gives the velocity derivation formula of the large-span manipulator - cable-driven flexible manipulator as:

[0149]

[0150] Simulation verification

[0151] Use Matlab to verify the obtained kinematic model.

[0152] Simulation 1, set the simulation parameters: the joint angles of the large-span manipulator are q d = [40; 60; -80; -80; 40] T , the joint angles of the cable-driven agile manipulator are q m = [0; 20; 20; 20; 20; 0; 10] T , the joint angles of the cable-driven flexible manipulator are q r = [0; -40; -20; -40; 0; -30] T , and the simulation of its manipulator arm type is as Figure 6 shown.

[0153] Simulation 2, set the simulation parameters: the joint angles of the large-span manipulator are q d = [40; -70; -80; -100; 90] T , the joint angles of the cable-driven agile manipulator are q m = [0; 50; 40; 50; 50; 0; 20] T , the joint angles of the cable-driven flexible manipulator are q r = [0; 20; 20; 20; 0; 30] T , and the simulation of its manipulator arm type is as Figure 7 shown.

[0154] It is verified that the forward mapping relationship between the joint rotation angles and the end poses of the heterogeneous multi-branch cable-driven manipulator is correct, proving that the derived kinematic model is correct.

[0155] Example 2

[0156] An electronic device includes a memory and a processor. The memory is used to store a program that supports the processor to execute a kinematic modeling method for a heterogeneous multi-branch cable-driven robotic arm in Embodiment 1. The processor is configured to execute the program stored in the memory.

[0157] Embodiment 3

[0158] A storage medium stores a computer program. When the computer program is run by a processor, it executes the steps of a kinematic modeling method for a heterogeneous multi-branch cable-driven robotic arm in Embodiment 1.

[0159] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. These modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A kinematic modeling method for a heterogeneous multi-branch rope-driven manipulator, characterized in that: The heterogeneous multi-branch rope-driven manipulator comprises: a long-span manipulator (10), a rope-driven agile manipulator (20), a rope-driven flexible manipulator (30), and a flexible or agile manipulator drive component (40). The end of the long-span manipulator (10) is connected to one end of the flexible or agile manipulator drive component (40), and the other end of the agile manipulator drive component (40) is respectively connected to the rope-driven agile manipulator (20) and the rope-driven flexible manipulator (30). The kinematic modeling method of the heterogeneous multi-branch rope-driven manipulator is as follows: the kinematic recursive relationship of the long-span manipulator, the rope-driven agile manipulator, and the rope-driven flexible manipulator is established respectively; the kinematic recursive relationship of the long-span manipulator, the rope-driven agile manipulator, and the rope-driven flexible manipulator is integrated, so as to obtain the kinematic model of the long-span manipulator-rope-driven agile manipulator and the kinematic model of the long-span manipulator-rope-driven flexible manipulator.

2. The kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator according to claim 1 is characterized in that: The transformation matrix of a certain arm coordinate system of a large-span manipulator relative to the base coordinate system is as follows: in, Represents the total transformation matrix from the initial point to the end point of the long-span manipulator, Represents the transformation matrix from the initial point of the long-span robot arm to the end point of the first arm segment, Represents the transformation matrix from the end point of the first arm section of the long-span robot arm to the end point of the second arm section, Represents the transformation matrix from the end point of the arm of the N-1th segment to the end point of the arm of the Nth segment of the long-span robot; The vector on the i-th arm of the long-span robot arm Relative to the base coordinate system, it is expressed as: in, is the initial vector on the first arm of the long-span robot; The vector on the i-th arm of the long-span robot arm The derivative is: The speed derivation formula of the large-span manipulator is as follows: in, is the joint angular velocity of the i-th joint of the long-span manipulator, 3. The kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator according to claim 2 is characterized in that: The transformation matrix of a certain arm coordinate system of the rope-driven agile manipulator relative to the base coordinate system is as follows: in, The total transformation matrix from the initial point to the end point of the rope-driven agile manipulator is expressed as: represents the transformation matrix from the initial point of the rope-driven agile manipulator to the end point of the first arm segment, represents the transformation matrix from the end point of the first arm section to the end point of the second arm section of the rope-driven agile manipulator, represents the transformation matrix from the end point of the arm of the rope-driven agile manipulator segment N-1 to the end point of the arm of the Nth segment; The vector on the i-th arm of the rope-driven agile manipulator Relative to the base coordinate system, it is expressed as: in, is the initial vector of the first arm of the rope-driven agile manipulator; The vector on the i-th arm of the rope-driven agile manipulator The derivative is: The speed derivation formula of the rope-driven agile manipulator is as follows: in, is the joint angular velocity of the i-th joint of the rope-driven agile manipulator, 4. The kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator according to claim 2 is characterized in that: The end position transformation matrix of the rope-driven flexible manipulator is: in, α ri+1 is the joint angle of the i+1th joint of the rope-driven flexible manipulator, T rN represents the total transformation matrix from the initial point to the end point of the rope-driven flexible manipulator, represents the transformation matrix from the initial point of the rope-driven flexible manipulator to the end point of the first arm segment, represents the transformation matrix from the end point of the first arm section to the end point of the second arm section of the rope-driven flexible manipulator, represents the transformation matrix from the end point of the second arm of the rope-driven flexible manipulator to the end point of the third arm, represents the transformation matrix from the end point of the arm of the rope-driven flexible manipulator segment N-1 to the end point of the arm of the segment N; The vector on the i-th arm of the rope-driven flexible manipulator Relative to the base coordinate system, it is expressed as: in, is the initial vector of the first arm of the rope-driven flexible manipulator; The vector on the i-th arm of the rope-driven flexible manipulator The derivative is: The velocity derivation formula of the rope-driven flexible manipulator is as follows: in, is the joint angular velocity of the i-th joint of the rope-driven flexible manipulator, 5. The kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator according to claim 3 is characterized in that: The kinematic model of the large-span manipulator-rope-driven agile manipulator is established as follows: The transformation matrix of a certain arm coordinate system of a large-span manipulator relative to the base coordinate system The transformation matrix of a certain arm coordinate system of the rope-driven agile manipulator relative to the base coordinate system The kinematics derivation formula of the large-span manipulator-rope-driven agile manipulator is obtained by multiplying: The speed derivation formula of the large-span manipulator and the speed derivation formula of the rope-driven agile manipulator are added together to obtain the speed derivation formula of the large-span manipulator-rope-driven agile manipulator:

6. The kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator according to claim 4 is characterized in that: The kinematic model of the large-span manipulator-rope-driven flexible manipulator is established as follows: The transformation matrix of a certain arm coordinate system of a large-span manipulator relative to the base coordinate system The end pose transformation matrix T of the rope-driven flexible manipulator is rN The kinematics derivation formula of the large-span manipulator-rope-driven flexible manipulator is obtained by multiplying: The speed derivation formula of the large-span manipulator and the speed derivation formula of the rope-driven flexible manipulator are added together to obtain the speed derivation formula of the large-span manipulator-rope-driven flexible manipulator:

7. An electronic device, comprising a memory and a processor, characterized in that: The memory is used to store a program that supports the processor to execute the kinematic modeling method of the heterogeneous multi-branch rope-driven manipulator described in any one of claims 1 to 6, and the processor is configured to execute the program stored in the memory.

8. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the kinematic modeling method of a heterogeneous multi-branch rope-driven manipulator as described in any one of claims 1 to 6 are executed.

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