Variable stiffness analysis method and system for accurate control of coaxial rope-driven robot, and computer storage medium

Abstract

The invention discloses a variable stiffness analysis method and system for precise control of a coaxial rope-driven robot and a computer storage medium. According to the invention, a stiffness model is established, and a variable stiffness analysis method for accurate control of the coaxial rope-driven robot is provided. The stiffness model modeling method comprises the following steps: establishing a kinematic model of a robot by using a biarc method; calculating a stiffness matrix of the central elastic skeleton by adopting a Moire integral method; calculating stiffness matrixes of other parts by adopting a virtual work principle; and calculating a total stiffness matrix and establishing a stiffness model. On the basis of given rope driving force and whole arm configuration, the total rigidity of the coaxial rope-driven robot can be calculated based on the established rigidity model; judging whether the difference value between the actual rigidity in a certain direction and the expected rigidity is smaller than a safety threshold value or not, and if not, adjusting the first section arc length and the rope driving force according to a rigidity model; if the judgment result is yes, the configuration, the rigidity and the rope driving force are output, and variable rigidity control is achieved.

Description

Technical Field

[0001] The present invention relates to the field of robot control, and in particular to an analytical variable stiffness method and system for precise control of a coaxial cable-driven robot, and a computer storage medium. Background Art

[0002] The cable-driven continuum robot adopts a cable-driven robotic arm structure, which has the advantages of small size and flexible movement, and is more suitable for working in a narrow space than traditional rigid robots. In the medical field, researchers have successfully developed various types of cable-driven continuum robots. These cable-driven continuum robots are respectively adapted to a variety of application environments, such as throat sampling, minimally invasive surgery, etc. For example: D. Caleb Rucker et al. designed a concentric tube continuum robot and established a model of its deformation under external loads, accurately describing the deformation caused by external loads. Zheng Li et al. designed a new type of constrained cable-driven flexible robotic arm, which expanded the working space without sacrificing the size and improved the dexterity. Junshi Zhang et al. designed a fiber-reinforced soft polymer flexible robotic arm, which has the advantages of active deformation, intelligent movement and adjustable stiffness. Xiaojie Ai et al. designed a multi-contact assisted continuum robotic arm, and introduced specific constraints to achieve anisotropy. Z Mu et al. proposed a spatial double circular arc planning method for coaxial cable-driven robots, which solved the problems of attitude determination and trajectory planning of coaxial cable-driven robots. Zhonghao Wu et al. designed a handle-optimized robotic surgical tool with a continuous wrist joint and kinematic optimization, which can reduce collisions and maintain an effective load capacity. D. Wu et al. designed a new type of ball-and-socket flexible robotic arm for minimally invasive surgery, which has high bending and torsional stiffness, excellent bending performance and strong load-bearing capacity.

[0003] The variable stiffness control of cable-driven continuum robots enables them to have the ability to avoid unnecessary damage at low stiffness and carry high-load tasks at high stiffness, and plays an increasingly important role in practical applications. However, due to the characteristics of high compliance and low stiffness of cable-driven continuum robots, relatively small forces often cause large deformations compared with conventional rigid robots, which has always been a difficult problem in practical applications. How to accurately establish the stiffness model of this type of robot and apply it to variable stiffness control has become a very attractive issue.

[0004] Compared with conventional rigid robots, the flexibility and redundancy of cable-driven continuum robots make it more difficult to establish their stiffness. To accurately establish the stiffness model of cable-driven continuum robots and conduct their variable stiffness control, many scholars have made contributions. For example: Allen Jiang et al. designed a composite particle variable stiffness flexible manipulator, which can achieve the stiffness control of the manipulator through particle parameters, etc. Huu Minh Le et al. proposed a new design concept using thermoplastic material PET and flexible stainless steel sheath as heating media and established its stiffness model, and this design realized the stiffness adjustment of the manipulator. Nan Ma et al. designed a type of two-degree-of-freedom tendon-driven parallel mechanism, which has the characteristics of low manufacturing and assembly difficulty and actively adjustable system stiffness. Kaitlin Oliver-Butler et al. established the deflection and stiffness models of tendon-driven or cable-driven continuum robots, providing a reference for the stiffness calculation of this type of robot. Bin Zhao et al. proposed a stiffness-adjustable two-section continuum manipulator based on continuous constrained bending curvature and established the tip stiffness model of the manipulator using Cosserat rod theory. This manipulator adopts the concept of a double continuum mechanism, further improves the stiffness of the manipulator through redundant skeleton arrangement, and uses the degree-of-freedom redundancy of the manipulator to achieve the control of stiffness change in the desired direction at the target position. Likun Gao et al. designed a flexible arm filled with particles and analyzed the variable stiffness characteristics of the flexible manipulator under particle interference, providing a reference for the analysis of the variable stiffness performance of the flexible arm. Xifeng Gao et al. established the stiffness model of multi-section continuum robots through the combination of geometric mechanics and mathematical analysis, improving the modeling accuracy of the stiffness models of this type of robot. Han Yuan et al. calculated the stiffness matrix of a cable-driven snake-like manipulator using analytical and numerical calculation methods respectively, contributing to the accuracy, calculation speed and real-time performance of the stiffness calculation. Peiyi Wang et al. designed a new type of variable stiffness built-in rope-winding continuum robot, which performs variable stiffness or "locking" functions by adjusting the friction between the winding rope and the rod, providing a new direction for variable stiffness research. Canberk Sozer et al. proposed a continuum manipulator robot module with variable stiffness joints, providing a highly compact, lightweight and low-cost solution for the variable stiffness of continuum robots. Most of these studies are only applicable to single-section cable-driven continuum robots, and there are some limitations in dealing with the effects of structural stiffness, configuration stiffness, driving force and external loads simultaneously. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems in the related art to some extent. To this end, an object of the present invention is to provide an analytical variable stiffness method and system for precise control of a coaxial cable-driven robot, and a computer storage medium, for realizing the precise control of the coaxial cable-driven robot.

[0006] The technical solution adopted by the present invention is: an analytical variable stiffness method for precise control of a coaxial cable-driven robot, comprising the following steps:

[0007] Using the double circular arc method to calculate the bending angle, radius, and the length of the second arc of the coaxial cable-driven manipulator, and determining the configuration of the coaxial cable-driven manipulator;

[0008] Calculating the stiffness of the central elastic skeleton and the rest except the central elastic skeleton respectively, and establishing the total stiffness matrix of the coaxial cable-driven manipulator;

[0009] Based on the stiffness model, drawing a stiffness contour map;

[0010] Judging whether the absolute value of the difference between the actual stiffness and the desired stiffness in a certain direction is less than the safety threshold. If the judgment result is yes, judging that the actual stiffness in a certain direction meets the expectation, and outputting the configuration, stiffness, and cable driving force.

[0011] Further, judging whether the absolute value of the difference between the actual stiffness and the desired stiffness in a certain direction is less than the safety threshold. If the judgment result is no, judging that the actual stiffness in a certain direction does not meet the expectation, and adjusting the length of the first arc and the cable driving force.

[0012] Further, the double circular arc method is based on the assumption of piecewise equal bending;

[0013] In the double circular arc method, the coaxial cable-driven robot has a total of three end pose constraints and four control degrees of freedom (bending and elongation of two segments) in planar motion. When the initial pose and the end pose are determined, there is still a redundant degree of freedom, and different arm shapes can be controlled by adjusting the length of the first circular arc.

[0014] Further, the flexibility matrix of the central elastic skeleton is established by the Mohr integral method, and the total flexibility matrix is obtained by serially adding the flexibility matrices of the two circular arc segments using the transformation matrix, and then the stiffness matrix is obtained;

[0015] Through the Mohr integral method, the small displacements in each direction of the circular arc segment under the external load are obtained, and then the flexibility matrix of a single circular arc segment in the local coordinate system is obtained through inverse kinematics, and then it is transformed into the flexibility matrix in the global coordinate system, and finally the stiffness matrix is obtained.

[0016] Furthermore, establish a relationship model between the rope length and the arm shape, establish the stiffness matrix of the remaining parts through the analytical method, establish a relationship model between the rope length and the arm shape, and use the principle of virtual work to conduct stiffness modeling of the coaxial cable-driven robot.

[0017] Another technical solution adopted by the present invention is: an analytical variable stiffness system for precise control of a coaxial cable-driven robot, including:

[0018] Rope driving force detection unit: used to detect the driving force of each rope;

[0019] Arm shape detection unit: used to detect the arm shape of the coaxial cable-driven robot, and further detect the rotation angle of each joint of the robotic arm;

[0020] Input unit: used to input parameters of the coaxial cable-driven robot, initial end pose, initial external force, initial rope driving force, etc. into the total stiffness calculation unit, and the parameters include the dimensions of multiple segments of the coaxial cable-driven robot, link weights, moments of inertia, etc.;

[0021] Stiffness calculation unit: used to calculate the stiffness according to the stiffness model;

[0022] Early warning unit: used to determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than or equal to the safety threshold. If the judgment result is yes, the stiffness in a certain direction meets the expectation;

[0023] Output unit: used to output calculation results such as arm shape, the length of the first arc, rope driving force, etc., so as to achieve the purpose of controlling the stiffness.

[0024] Another technical solution adopted by the present invention is: a computer storage medium, on which a computer program is stored, and when the program is executed by a processor, the following steps are implemented:

[0025] Use the double circular arc method to calculate the bending angle, radius, and the length of the second arc of the coaxial cable-driven robotic arm, and determine the configuration of the coaxial cable-driven robotic arm;

[0026] Calculate the stiffness of the central elastic skeleton and the remaining parts except the central elastic skeleton respectively, and establish the total stiffness matrix of the coaxial cable-driven robotic arm;

[0027] Based on the stiffness model, draw a stiffness cloud map;

[0028] Judge whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the judgment result is no, judge that the actual stiffness in a certain direction does not meet the expectation, and adjust the length of the first arc and the rope driving force;

[0029] Determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the determination result is yes, it is determined that the actual stiffness in a certain direction meets the expectation, and the configuration, stiffness, and rope driving force are output.

[0030] The beneficial effects of the present invention are:

[0031] The present invention discloses an analytical variable stiffness method and system for precise control of a coaxial cable-driven robot, and a computer storage medium. The present invention considers various factors such as rope driving force, manipulator configuration, elastic skeleton, and external load, establishes a comprehensive stiffness model, and proposes an analytical variable stiffness method for precise control of a coaxial cable-driven robot. The method includes: using the double arc method to determine the configuration of the coaxial cable-driven robot; calculating the total stiffness matrix of the coaxial cable-driven robot; based on the stiffness model, drawing a stiffness cloud map; determining whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the determination result is no, adjust the first arc length and rope driving force according to the stiffness cloud map; determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the determination result is yes, output the configuration, stiffness, and rope driving force to achieve variable stiffness control. Brief Description of the Drawings

[0032] Figure 1 It is a schematic diagram of the manipulator structure of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention;

[0033] Figure 2 It is a schematic diagram of the double arc planning method of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention;

[0034] Figure 3 It is a schematic diagram of the forward kinematics geometric relationship of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention;

[0035] Figure 4 It is a schematic diagram of the arc segment deformation analysis under the action of forces in each direction of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention;

[0036] Figure 5 It is a schematic diagram of the symbol definition for rope length calculation of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention;

[0037] Figure 6 It is a flowchart of the analytical variable stiffness method of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention. Detailed Embodiments

[0038] In order to enable those skilled in the art to better understand the technical solution of the present invention, the following will, in conjunction with embodiments, clearly and completely describe the specific technical solution of the present invention to help those skilled in the art further understand the present invention. Obviously, the embodiments described herein are only a part of the embodiments of the present invention, rather than all of the embodiments. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention and without conflict with each other, the embodiments in this application and the features in the embodiments can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of disclosure and protection of the present invention.

[0039] In addition, the terms "first", "second", "furthermore", etc. in the specification, claims and drawings of the present invention are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those described herein. At the same time, the terms "comprising" and "having" in the present invention and any variations thereof are intended to cover non-exclusive inclusion. In addition, for those of ordinary skill in the art, the specific meanings of the above terms in this case can be understood in combination with the prior art according to specific circumstances.

[0040] The multi-segment coaxial cable-driven robot is a strongly coupled, non-linear and under-actuated system. Since its movement is very slow in actual medical applications, its dynamic characteristics can often be ignored in research. This embodiment takes a two-segment coaxial cable-driven robot as an example to describe the analytical variable stiffness method for precise control of the multi-segment coaxial cable-driven robot. However, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the scope of disclosure and protection of the present invention. For convenience, the demonstrations in the embodiments are carried out in a plane, but the proposed method can also be extended to three-dimensional space.

[0041] Reference Figure 1 , Figure 1 is a schematic diagram of the mechanical arm structure of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention. The mechanical arm in this embodiment is divided into an internal cable drive mechanism and an external cable drive mechanism, which are respectively controlled by two cables. The joints of the mechanical arm are connected by concentric spherical pairs, making the robot more flexible and having a larger working space. An intermediate elastic body is installed at the center of the mechanical arm, making the robot have a certain rigidity and facilitating the control of the overall configuration of the multi-segment coaxial cable-driven robot.

[0042] Reference Figure 2 , Figure 2This is a schematic diagram of the double - arc planning method, which is a specific embodiment of the analytical variable - stiffness method for precise control of a coaxial cable - driven robot in the present invention. It can be seen from Figure 2 that P S , P e represent the starting coordinate and the ending coordinate respectively, the direction vectors L s , L e represent the initial attitude and the ending attitude, and S1 and S2 represent the lengths of the two arcs respectively.

[0043] 1. Kinematic model

[0044] Figure 2 In, l1 is the straight line where L s is located, l2 is the straight line where L e is located, l is the common tangent of the two arcs, and the tangent point is P. The intersection point of l1 and l is P1, and the intersection point of l2 and l is P2. It is easy to obtain:

[0045]

[0046] Let's set, then:

[0047]

[0048] Let then

[0049] |Z| = |L - λ1·L s - λ2·L e | = λ1 + λ2 (3)

[0050] Suppose O1 and O2 are the centers of the two arcs respectively, θ1 and θ2 are the rotation angles of the two arcs (counter - clockwise is positive), and R1 and R2 are the radii of the two arcs respectively, then there are

[0051]

[0052] In ΔO1P s P1 and ΔO2P e P2, there are:

[0053]

[0054] According to the geometric relationship, we can obtain:

[0055]

[0056] When the length of S1, the initial pose P s , L s the ending pose P e , L eWhen all are known, the rotation angles, arc lengths, and radii of the two arc segments of the coaxial cable-driven robot can be determined by equations (2), (3), (4), (5), and (6), and then the configuration of the coaxial cable-driven robotic arm can be determined.

[0057] Reference Figure 3 , Figure 3 is a schematic diagram of the forward kinematics geometric relationship of a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot. According to the coordinate transformation relationship, it is easy to know that the transformation from coordinate system R i to coordinate system R i-1 can be expressed as:

[0058]

[0059] where i = 1, 2. From Figure 3 it is easy to know that the and in equation (8) can be calculated as:

[0060]

[0061] In this embodiment, the global coordinate system coincides with the base coordinate system. Then, the transformation relationship between the global coordinate system of the coaxial cable-driven robot and the end-effector coordinate system of the robotic arm is:

[0062]

[0063] In this embodiment, we will calculate the stiffness matrix of the central elastic skeleton and the stiffness matrix of other parts except the central elastic skeleton respectively, and then obtain the total stiffness matrix of the coaxial cable-driven robot by parallel addition.

[0064] 2. Stiffness Matrix of Central Elastic Skeleton

[0065] For the calculation of the stiffness of the central elastic skeleton, in this embodiment, the flexibility matrices of the two arc segments are calculated respectively using the Mohr integral method, and then the flexibility matrices of the two arc segments are serially added using the transformation matrix to obtain the total flexibility matrix of the central elastic body, and then the stiffness matrix is obtained.

[0066] Reference Figure 4 , Figure 4 is a schematic diagram of the deformation analysis of the arc segment under the action of forces in each direction in a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot of the present invention.

[0067] From Figure 4 it is easy to know that the moment generated by F x , F y , M z at any position on the arc segment is:

[0068]

[0069] Unit load The moment generated at any position in the circular arc section is:

[0070]

[0071] In this embodiment, the angle is defined as a quantity with direction (counterclockwise is positive). Assuming the moment direction is counterclockwise as positive, for unified calculation, the following definitions are made:

[0072]

[0073] From Figure 4 It is easy to know that the infinitesimal displacements of the circular arc section in each direction under F x can be calculated by the following formula:

[0074]

[0075] where E and I z represent the Young's modulus and the product of inertia of the central elastic skeleton respectively. Similarly, from Figure 4 It is easy to know that the infinitesimal displacements of the circular arc section in each direction under F y and M z can be expressed as

[0076]

[0077]

[0078] According to the infinitesimal displacements in each direction under the external load, from Equation (11), we can obtain:

[0079]

[0080] From Equation (16), through the angles and radii calculated in inverse kinematics, the flexibility matrix of a single circular arc can be obtained:

[0081]

[0082] where represents the flexibility matrix of the first circular arc in the local coordinate system R1, represents the flexibility matrix of the second circular arc in the local coordinate system R2. And The flexibility matrices in the global coordinate system R G can be expressed as:

[0083]

[0084] Since the two circular arcs can be regarded as connected in series, the total flexibility matrix can be directly obtained by adding the two flexibility matrices:

[0085]

[0086] From the relationship between the stiffness matrix and the flexibility matrix, we can obtain:

[0087]

[0088] Finally, what we get is a 3×3 stiffness matrix. The flexibility matrix of the two arc segments is symmetric about the main diagonal, so the stiffness matrix of the central elastic skeleton obtained finally is also a symmetric matrix. These main diagonal elements reflect the stiffness levels of the robot in different directions and can be used to evaluate the stiffness characteristics of the robot. 3. Stiffness matrix of the rest part except the central elastic skeleton

[0089] (1) Rope length calculation

[0090] The coaxial cable-driven robot controls the bending of the arm shape through the stretching of the ropes. In order to accurately establish the stiffness matrix of the robot, a relationship model between the rope length of the robot and the arm shape needs to be established.

[0091] The joints of the outer cable-driven mechanism and the inner cable-driven mechanism have the same basic structure, and the only difference is the size. We use H to represent the height of the joint, and the outer cable-driven mechanism and the inner cable-driven mechanism are represented as H0 and H1 respectively; h represents the gap distance between adjacent joints, and the gaps between adjacent joints of the inner / outer cable-driven mechanisms are represented as h1 and h0 respectively. d represents the distance between the ropes, and the distances between the ropes of the inner / outer cable-driven mechanisms are represented as d1 and d0 respectively. We define the two ropes that control the outer cable-driven mechanism as rope 1 and rope 2, and the two ropes that control the inner cable-driven mechanism as rope 3 and rope 4.

[0092] Reference Figure 5 , Figure 5 is a schematic diagram of the symbol definition for the rope length calculation in a specific embodiment of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention. From Figure 5 it is easy to know that H O +h O =H I +h I . Assume that the central angles of the two arcs are θ1 and θ2 respectively; the lengths are S1 and S2 respectively. Then the bending angles of each joint of the two arcs can be expressed as:

[0093]

[0094] From Figure 5 the geometric relationship in it is easy to know that the rope length between the gaps of adjacent joints of the outer cable-driven mechanism is:

[0095]

[0096] where h O1 is the clearance length of rope 1, and h O2 is the clearance length of rope 2. Therefore, the lengths l1 and l2 of the two ropes of the outer rope drive mechanism are:

[0097]

[0098] For the inner rope drive mechanism, we study it in two parts: the overlapping part with the outer rope drive mechanism and the non - overlapping part with the outer rope drive mechanism. For the overlapping part with the outer rope drive mechanism, we have:

[0099]

[0100] where h IO3 is the clearance length of rope 3 in the overlapping part. h IO4 is the clearance length of rope 4 in the overlapping part. The clearance length of the non - overlapping part between the inner rope drive mechanism and the outer rope drive mechanism can be calculated by the following formula:

[0101]

[0102] Therefore, the rope lengths l3 and l4 of the inner rope drive mechanism can be expressed as:

[0103]

[0104] (2) Establishing the stiffness model based on the analytical method

[0105] In this embodiment, we use the principle of virtual work to perform stiffness modeling of the coaxial rope - driven robot.

[0106] In planar motion, the end of the coaxial rope - driven robot has 3 degrees of freedom: translation along x and y and rotation about the z - axis. The index for evaluating the stiffness of the coaxial rope - driven robot in this embodiment is the main diagonal elements. Therefore, when evaluating the stiffness of the coaxial rope - driven robot, we can calculate the stiffness of its translational degrees of freedom and rotational degrees of freedom respectively, and incorporate them into the main diagonal elements to form a complete stiffness matrix, which does not affect the stiffness evaluation of the main diagonal elements. Therefore, the stiffness matrix of the coaxial rope - driven robot except for the central elastic skeleton can be expressed as:

[0107]

[0108] When calculating K xy , the external load F ex = [F x , F y T , and the end position of the coaxial rope - driven robot is P xy = [P x , P y ; When calculating K​θ When F ex = M z . The end direction is p θ . The end position p xy The relationship with the angles θ1 and θ2 can be obtained by forward kinematics calculation. The end direction p θ = θ1 + θ2.

[0109] When the coaxial cable-driven robot is working, it will be affected by the external load at the end, the cable driving force, and its own gravity. Since the coaxial cable-driven robot moves slowly during operation, the working process can be regarded as a static equilibrium state, that is, the influence of acceleration is ignored. In this invention, only the planar motion of the coaxial cable-driven robot is considered, so each segment is controlled by two cables. The cable driving force F t = [F t1 , F t2 , F t3 , F t4 T . According to the principle of virtual work, we can get:

[0110] F ex T ·Δp - F t T ·Δl - G T ·Δh = 0 (28)

[0111] Where the cable length l = [l1, l2, l l3 , l l4 T , the center-of-gravity height h of each arm segment = [h1, h2] T , the gravity G received by each segment = [G1, G2] T . When the arc length of each segment changes, the gravity received is also different. The specific value of the gravity can be calculated by the following formula:

[0112]

[0113] Where ρ O and ρ I are the masses per unit arc length of the outer cable drive mechanism and the inner cable drive mechanism respectively, and g is the local acceleration due to gravity. For equation (28), we make the following transformation:

[0114]

[0115] Where θ is the rotation angle of each segment, θ = [θ1, θ2]. J p , J l , J h are the Jacobian matrices of the end position, cable length, and center-of-gravity height respectively. Substitute equation (30) and cancel out Δθ, then equation (31) can be written as: ​​

[0116]

[0117] Transposing (31) and taking the partial derivative with respect to θ gives:

[0118]

[0119] Since the gravity of each robotic arm segment of the coaxial cable-driven robot is only related to the elongation of the inner and outer cable-driven mechanisms and has nothing to do with the rotation angle of the cable-driven mechanism, so According to the definition of the Hessian matrix, we can easily obtain:

[0120]

[0121] Based on the relationship of partial derivatives, we can make the following transformation:

[0122]

[0123] Substituting equations (33) and (34) into equation (32) and moving the terms, we can get:

[0124]

[0125] According to the definition of stiffness The calculation method of the stiffness matrix is sorted out as:

[0126]

[0127] In the formula, from the definition of the rope stiffness, it can be known that is the stiffness K of the rope itself cable . From equation (36), K xy and K θ can be calculated respectively. Substituting K xy and K θ into equation (27), the stiffness K of the remaining part except the elastic skeleton can be obtained.

[0128] The bending angle, end force, and rope driving force of the coaxial cable-driven robot are interrelated. When the end force and bending angle are determined, the relationship between the rope driving forces can be calculated by equation (32) as:

[0129]

[0130] According to (37), when the driving force values of two ropes are given, the driving forces of the other two ropes will also be uniquely determined. The rope driving force refers to the average rope driving force of the four ropes.

[0131] 3. Calculate the total stiffness matrix of the coaxial cable-driven robotic arm

[0132] After obtaining the stiffness matrix K of the central elastic skeletonelasitic backbone After obtaining the stiffness matrix K of the parts other than the central elastic skeleton, since the elastic skeleton is in a parallel relationship with the connecting rods and ropes of the coaxial cable-driven robot, the stiffness matrices of all parts can be added to obtain the total stiffness matrix:

[0133] K robot = K elasitic backbone + K(38)

[0134] In this embodiment, we select the main diagonal elements of the stiffness matrix as the measurement standard for the stiffness of the coaxial cable-driven robot.

[0135] Reference Figure 6 , Figure 6 is a flow chart of an analytical variable stiffness method for precise control of a coaxial cable-driven robot in the present invention. The analytical variable stiffness method can achieve variable stiffness control of the cable-driven manipulator by adjusting the whole arm configuration and cable tension. The given conditions include the robot structure parameters, the initial end pose and the first arc length, the initial external force and the initial cable driving force, the desired stiffness and the safety threshold in a certain direction. The double arc method is used to calculate the bending angle, radius and the second arc length of the coaxial cable-driven manipulator to determine the configuration of the coaxial cable-driven manipulator; establish the link coordinate system of the coaxial cable-driven manipulator and give the coordinate transformation matrix between different coordinate systems; calculate the stiffness of the central elastic skeleton and the other parts, calculate the total stiffness matrix of the coaxial cable-driven manipulator and establish a stiffness model; judge whether the absolute value of the difference between the actual stiffness and the desired stiffness in a certain direction is less than the safety threshold. If the judgment result is no, it is judged that the actual stiffness in a certain direction does not meet the expectation, and the first arc length and the cable driving force are adjusted. Further, judge whether the absolute value of the difference between the actual stiffness and the desired stiffness in a certain direction is less than the safety threshold. If the judgment result is yes, it is judged that the actual stiffness in a certain direction meets the expectation, and the configuration, stiffness and cable driving force are output.

[0136] By repeating the above process, the most suitable stiffness can be calculated and selected to achieve the purpose of variable stiffness control. Similarly, an appropriate configuration can also be selected according to the actual application to achieve variable stiffness control, which can not only meet the pose task requirements of the end effector, but also achieve variable stiffness control, thus achieving the purpose of variable stiffness planning.

[0137] Based on the above method, the present invention also provides an analytical variable stiffness system for precise control of a coaxial cable-driven robot, including:

[0138] Cable driving force detection unit: used to detect the driving force of each cable;

[0139] Arm shape detection unit: used to detect the arm shape of the coaxial cable-driven robot, and further detect the rotation angle of each joint of the manipulator;

[0140] Input unit: It is used to input parameters of the coaxial cable-driven robot, initial end pose, initial external force, initial cable driving force, etc. into the total stiffness calculation unit. The parameters include dimensions of multiple segments of the coaxial cable-driven robot, link weights, moments of inertia, etc.

[0141] Stiffness calculation unit: It is used to calculate the stiffness according to the stiffness model.

[0142] Early warning unit: It is used to determine whether the absolute value of the difference between the actual stiffness in a certain direction and the expected stiffness is less than or equal to the safety threshold. If the judgment result is yes, the stiffness in a certain direction meets the expectation.

[0143] Output unit: It is used to output calculation results such as the arm shape, the length of the first arc, and the cable driving force, so as to achieve the purpose of controlling the stiffness.

[0144] In addition, the present invention also provides a computer storage medium, on which a computer program is stored. When the program is executed by a processor, the following steps are implemented:

[0145] Use the double circular arc method to calculate the bending angle, radius, and the length of the second arc of the coaxial cable-driven robotic arm, and determine the configuration of the coaxial cable-driven robotic arm.

[0146] Calculate the stiffness of the central elastic skeleton and the rest except the central elastic skeleton respectively, calculate the total stiffness matrix of the coaxial cable-driven robotic arm and establish a stiffness model.

[0147] Judge whether the absolute value of the difference between the actual stiffness in a certain direction and the expected stiffness is less than the safety threshold. If the judgment result is no, judge that the actual stiffness in a certain direction does not meet the expectation, and adjust the length of the first arc and the cable driving force.

[0148] Judge whether the absolute value of the difference between the actual stiffness in a certain direction and the expected stiffness is less than the safety threshold. If the judgment result is yes, judge that the actual stiffness in a certain direction meets the expectation, and output the configuration, stiffness, and cable driving force.

[0149] The working process of the computer program stored on the computer storage medium can refer to the specific description of the above-mentioned analytical variable stiffness method for precise control of coaxial cable-driven robots, and will not be elaborated here.

[0150] Meanwhile, in addition to being applicable to coaxial cable-driven robotic arms, the method of the present invention is also applicable to other various hyper-redundant robotic arms.

[0151] The above is a specific description of the preferred embodiments of the present invention. However, the present invention is not limited to the described embodiments. Those skilled in the art can also make various equivalent deformations or substitutions without departing from the spirit of the present invention. These equivalent deformations or substitutions are all included within the scope defined by the claims of this application.

Claims

1. An analytical variable stiffness method for precise control of a coaxial rope-driven robot, characterized in that: The following steps are involved: The double arc method is used to calculate the bending angle, radius, and second arc length of the coaxial rope-driven manipulator, and the configuration of the coaxial rope-driven manipulator is determined. The stiffness matrices of the central elastic skeleton and the rest of the skeleton are calculated respectively, and the total stiffness matrix of the coaxial rope-driven manipulator is obtained after parallel addition, and a stiffness model is established. Determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the judgment result is yes, it is determined that the actual stiffness in a certain direction meets expectations, and the configuration, stiffness, and rope driving force are output.

2. The analytical variable stiffness method for precise control of a coaxial rope-driven robot according to claim 1, characterized in that: Determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the judgment result is no, it is determined that the actual stiffness in a certain direction does not meet expectations, and adjust the first arc length and rope driving force according to the stiffness cloud map.

3. The analytical variable stiffness method for precise control of a coaxial rope-driven robot according to claims 1 to 2, characterized in that: The double arc method is based on the piecewise equal curvature assumption; In the double arc method, the coaxial rope-driven robot has three end-position constraints and four control degrees of freedom (bending and extension of two segments) in planar motion. After determining the initial and end-positions, there is still a redundant degree of freedom, which can be used to control different arm shapes by adjusting the length of the first arc.

4. The analytical variable stiffness method for precise control of a coaxial rope-driven robot according to any one of claims 1 to 3, characterized in that: The flexibility matrix of the central elastic skeleton is established by the Mohr integral method, and the two arc segment flexibility matrices are added in series using the transformation matrix to obtain the total flexibility matrix and then the stiffness matrix is ​​obtained; Through the Mohr integration method, the small displacement of the arc segment in each direction under the external load is obtained, and then the flexibility matrix of the single arc segment in the local coordinate system is obtained through inverse kinematics, which is then transformed into the flexibility matrix in the global coordinate system, and finally the stiffness matrix is ​​obtained.

5. The analytical variable stiffness method for precise control of a coaxial rope-driven robot according to any one of claims 1 to 4, characterized in that: A coupling model of the rope and the arm is established, the principle of virtual work is used to model the stiffness of the rope under this configuration, and the stiffness matrix of the remaining parts is established by analytical method; 6. An analytical variable stiffness system for precise control of a coaxial rope-driven robot, characterized in that: include, Rope driving force detection unit: used to detect the driving force of each rope; Arm shape detection unit: used to detect the arm shape of the coaxial rope-driven robot, and then detect the rotation angle of each joint of the robot arm; Input unit: used to input the coaxial rope-driven robot parameters, initial end position, initial external force, initial rope driving force, etc. into the total stiffness calculation unit. The parameters include the size of the multi-segment coaxial rope-driven robot, the weight of the connecting rod, the moment of inertia, etc.; Stiffness calculation unit: used to calculate stiffness according to the stiffness model; Early warning unit: used to determine whether the absolute value of the difference between the actual stiffness in a certain direction and the expected stiffness is less than or equal to the safety threshold. If the judgment result is yes, the stiffness in a certain direction meets expectations; Output unit: used to output the calculation results such as arm shape, first arc length, rope driving force, etc., in order to achieve the purpose of controlling stiffness.

7. A computer storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the following steps are implemented: The double arc method is used to calculate the bending angle, radius, and second arc length of the coaxial rope-driven manipulator, and the configuration of the coaxial rope-driven manipulator is determined. Establish the link coordinate system of the coaxial rope-driven manipulator and give the coordinate transformation matrix between different coordinate systems; Calculate the stiffness of the central elastic skeleton and the rest of the parts, and establish the total stiffness matrix of the coaxial rope-driven manipulator; Based on the stiffness model, draw the stiffness cloud diagram; Determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the determination result is no, it is determined that the actual stiffness in a certain direction does not meet expectations, and the first arc length and the rope driving force are adjusted; Determine whether the absolute value of the difference between the actual stiffness and the expected stiffness in a certain direction is less than the safety threshold. If the judgment result is yes, it is determined that the actual stiffness in a certain direction meets expectations, and the configuration, stiffness, and rope driving force are output.

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