Variable stiffness control method, device and medium for rope-driven flexible robot joints

Abstract

The present invention discloses a variable stiffness control method, device and medium for a rope-pulled flexible robot joint, belonging to the field of flexible robot control. The method comprises: step 1, deriving the material flexibility density matrix of the flexible control support in the body coordinate system; step 2, deriving a conversion formula for converting the material flexibility density matrix from the body coordinate system to the Cartesian coordinate system based on Lie theory; step 3, synthesizing all discrete units of the flexible control support using the conversion formula to obtain the stiffness matrix of the flexible control support; step 4, rotating the movable support ring shaft assembly of the flexible control support by inputting a rotation angle through a variable stiffness driving servo, changing the relative rotation angle between the flexible support sleeve assembly and the movable support ring shaft assembly, changing the material flexibility density matrix to control the stiffness matrix, and realizing variable stiffness adjustment of the joint. Based on Lie theory and improved material flexibility density matrix, the present invention establishes a full-space stiffness matrix of the robot joint, realizing efficient variable stiffness control of the flexible robot joint.

Description

Technical Field

[0001] The present invention relates to the field of flexible robot control, and in particular to a variable stiffness control method for a flexible robot joint pulled by a rope with variable stiffness. Background Art

[0002] A rope-pulled flexible robot is a robot whose end effector is pulled by multiple ropes. It can adapt to different working environments and task requirements. Its flexible joints allow for greater maneuverability during operation, reducing the need for precise data. It can better adapt to various unstructured environments and is less susceptible to damage from external impacts. It can complete complex tasks, especially in confined and unstructured environments.

[0003] Due to the unique stiffness characteristics of tethered flexible robots, establishing a stiffness model for them presents challenges. Stiffness models directly based on data acquisition are too coarse to meet the needs of practical applications. Dividing the tethered flexible robot into tiny discrete units and then solving the stiffness matrix based on the Jacobian matrix is ​​computationally intensive and inefficient. Therefore, achieving efficient and accurate joint stiffness modeling for tethered flexible robots, and thus achieving precise control of the robot's joints, is a pressing issue.

[0004] In view of this, the present invention is proposed. Summary of the Invention

[0005] The purpose of the present invention is to provide a variable stiffness control method, equipment and medium for the joints of a variable stiffness rope-traction flexible robot, which can achieve efficient and accurate modeling of the stiffness of the flexible robot joints, establish a full-space stiffness matrix, ensure efficient and accurate control of the joints of the rope-traction flexible robot, and thus solve the above-mentioned technical problems existing in the prior art.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A variable stiffness control method for a rope-driven flexible robot joint is provided, which is used for a rope-driven flexible robot joint consisting of an end motion platform, a flexible control support, a joint drive mechanism, a variable stiffness drive servo, and a fixed base. The flexible control support includes a flexible support sleeve assembly and a movable support ring shaft assembly, including:

[0008] Step 1: derive the material flexibility density matrix of the flexible control support in the body coordinate system;

[0009] Step 2: deriving a conversion formula for converting the material compliance density matrix from a body coordinate system to a Cartesian coordinate system based on Lie theory;

[0010] Step 3: Using the conversion formula to synthesize all discrete units of the flexible control support, the stiffness matrix of the flexible control support is derived;

[0011] Step 4: Rotate the movable support ring shaft assembly of the flexible control support body by inputting a rotation angle of the variable stiffness driving servo, thereby changing the relative rotation angle between the flexible support sleeve assembly of the flexible control support body and the movable support ring shaft assembly. The size of the flexible control support body is adjusted by changing the material flexibility density matrix of the flexible control support body to adjust the stiffness matrix of the flexible control support body, thereby realizing variable stiffness adjustment of the rope-traction flexible robot joint.

[0012] A processing device comprising:

[0013] at least one memory for storing one or more programs;

[0014] At least one processor is capable of executing one or more programs stored in the memory. When the one or more programs are executed by the processor, the processor is enabled to implement the method described in the present invention.

[0015] A readable storage medium stores a computer program, which can implement the method described in the present invention when the computer program is executed by a processor.

[0016] Compared with the prior art, the variable stiffness control method, device and medium for the variable stiffness rope pulling flexible robot joint provided by the present invention have the following beneficial effects:

[0017] Based on Lie theory and the improved material flexibility density matrix, the stiffness matrix of the robot joint in the entire space was established, avoiding the complex calculation of the Jacobian matrix, realizing the stiffness modeling of the variable stiffness rope-traction flexible robot joint, ensuring efficient and accurate control of the rope-traction flexible robot joint, and providing strong support for the practical application of the variable stiffness rope-traction flexible robot joint. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0019] Figure 1 This is a flow chart of the variable stiffness control method for the rope-traction flexible robot joint provided by an embodiment of the present invention.

[0020] Figure 2 Schematic diagram of the stiffness model of the rope-traction flexible robot joint provided in an embodiment of the present invention.

[0021] Figure 3 Schematic diagram of the cross-sectional structure of the flexible control support body of the rope-pulled flexible robot joint provided in an embodiment of the present invention.

[0022] Figure 4 A schematic diagram of the three-dimensional structure of a rope-traction flexible robot joint provided in an embodiment of the present invention.

[0023] Figure 5 This is a schematic diagram of the main structure of the rope-traction flexible robot joint provided by an embodiment of the present invention.

[0024] Figure 6 A schematic diagram of the three-dimensional exploded structure of a rope-traction flexible robot joint provided in an embodiment of the present invention.

[0025] Figure 7 Schematic diagram of the three-dimensional structure of the flexible control support body of the rope-traction flexible robot joint provided by an embodiment of the present invention.

[0026] Figure 8 Schematic diagram of the structure of a three-dimensional flexible support sleeve assembly of a flexible control support body for a rope-pulled flexible robot joint provided in an embodiment of the present invention.

[0027] Figure 9 Schematic diagram of the three-dimensional structure of the movable support ring shaft assembly of the flexible control support body of the rope-pulled flexible robot joint provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0028] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the specific content of the present invention. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments, and do not constitute a limitation of the present invention. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0029] First, the following terms may be used in this article:

[0030] The term “and / or” means that either or both of them can be realized at the same time. For example, X and / or Y includes both “X” or “Y” and “X and Y”.

[0031] The terms "include," "comprises," "contains," "has," or other similar expressions should be interpreted as non-exclusive. For example, "including certain technical features (such as raw materials, components, ingredients, carriers, dosage forms, materials, dimensions, parts, components, mechanisms, devices, steps, procedures, methods, reaction conditions, processing conditions, parameters, algorithms, signals, data, products, or manufactured articles)" should be interpreted as including not only the technical features explicitly listed, but also other technical features known in the art that are not explicitly listed.

[0032] The term "consisting of" excludes any technical features not explicitly listed. If used in a claim, this term renders the claim closed, excluding any technical features other than those explicitly listed, except for conventional impurities associated with them. If this term appears only in a clause of a claim, it limits only the elements explicitly listed in that clause; elements listed in other clauses are not excluded from the claim as a whole.

[0033] Unless otherwise specified or limited, the terms "mounted," "connected," "connect," and "fixed" should be interpreted broadly. For example, they can refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediary; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in this document based on specific circumstances.

[0034] When concentration, temperature, pressure, size or other parameters are expressed in the form of a numerical range, the numerical range should be understood to specifically disclose all ranges formed by the pairing of any upper limit, lower limit, or preferred value within the numerical range, regardless of whether the range is explicitly stated. For example, if a numerical range of "2 to 8" is stated, the numerical range should be interpreted as including ranges of "2 to 7," "2 to 6," "5 to 7," "3 to 4 and 6 to 7," "3 to 5 and 7," "2 and 5 to 7," etc. Unless otherwise specified, the numerical ranges stated herein include both their endpoints and all integers and fractions within the numerical range.

[0035] The terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings and are only for the convenience and simplification of description, and do not explicitly or implicitly indicate that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation, and therefore should not be understood as a limitation to this document.

[0036] The scheme provided by the present invention is described in detail below. The contents not described in detail in the examples of the present invention belong to the prior art known to professionals in this field. If specific conditions are not specified in the examples of the present invention, they are carried out according to conventional conditions in the field or conditions recommended by the manufacturer. If the manufacturer of the reagents or instruments used in the examples of the present invention is not specified, they are all conventional products that can be purchased commercially.

[0037] like Figure 1 As shown, an embodiment of the present invention provides a variable stiffness control method for a rope-pulled flexible robot joint, which is used to model the full-space stiffness matrix of a variable stiffness rope-pulled flexible robot joint. The method can be applied to the terminal stiffness control and force control of the variable stiffness rope-pulled flexible robot joint, and can realize automatic motion control of the variable stiffness rope-pulled flexible robot joint, and realize the execution of operation tasks in complex environments. The rope-pulled flexible robot joint used is composed of an end motion platform 1, a flexible control support body, a joint drive mechanism, a variable stiffness drive servo 10 and a fixed base 3, wherein the flexible control support body includes a flexible support sleeve assembly 6 and a movable support ring shaft assembly 9. The method includes the following steps:

[0038] Step 1: derive the material flexibility density matrix of the flexible control support in the body coordinate system;

[0039] Step 2: deriving a conversion formula for converting the material compliance density matrix from a body coordinate system to a Cartesian coordinate system based on Lie theory;

[0040] Step 3: Using the conversion formula to synthesize all discrete units of the flexible control support, the stiffness matrix of the flexible control support is derived;

[0041] Step 4: The flexible control support body's movable support ring shaft assembly is rotated by inputting a rotation angle through the variable stiffness driving servo 10, thereby changing the relative rotation angle between the flexible control support body's flexible support sleeve assembly and the movable support ring shaft assembly. The size of the flexible control support body is adjusted by changing the material flexibility density matrix of the flexible control support body to adjust the stiffness matrix of the flexible control support body, thereby realizing variable stiffness adjustment of the rope-traction flexible robot joint.

[0042] Preferably, in step 1 of the above method, the material flexibility density matrix of the flexibility control support in the body coordinate system is derived in the following manner, including:

[0043] The structure of the flexible control support is discretized into multiple discrete units in the Cartesian space coordinate system. The discrete unit at the origin is the first discrete unit, and the numbers are raised in sequence. The material flexibility density matrix of the discrete elements Expressed as:

[0044] (1);

[0045] Among them, the superscript Indicates the The expression of discrete units in the body coordinate system; represents the arc length from the bottom of the flexible control support along the central axis to the discrete unit; are the shear and stretch terms of the material flexibility density matrix; are the bending and torsion terms of the material flexibility density matrix, which are expressed in elastic parameter matrices as follows:

[0046] (2);

[0047] Among them, diag[] is a function for constructing a diagonal matrix; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis x; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis y; Indicates the The axial cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis z; represents the shear modulus, represents Young's modulus, , is the Poisson's ratio of the material; 、 、 Respectively represent The moment of inertia of each discrete unit relative to the coordinate axis x, the moment of inertia relative to the coordinate axis y, and the moment of inertia relative to the coordinate axis z.

[0048] Preferably, in the above method, the bending and torsion terms of the material flexibility density matrix In the corresponding elastic parameter matrix, Discrete units relative to the coordinate axis Moment of inertia With the Discrete units relative to the coordinate axis Moment of inertia The same, expressed as:

[0049] (3);

[0050] in, Indicates the Discrete units relative to the coordinate axis Moment of inertia or Discrete units relative to the coordinate axis Moment of inertia ; sin is to find the sine value, 、 are the polar diameter and polar angle of any position in the polar coordinate system when calculating the moment of inertia integral, 、 are respectively the inner and outer ring radii of the fan-shaped sleeve support column (61) of the flexible support sleeve assembly (6); is the radius of the core column (92) of the movable support ring shaft assembly (9); The relative rotation angle between the sleeve support column (61) and the core column support column (93) of the movable support ring shaft assembly (9) is 45° according to the central angle of the sector column and the symmetry of the design. ;No. Discrete units relative to the coordinate axis Moment of inertia Expressed as:

[0051] (4);

[0052] When the cross sections of the sleeve support column (61) and the core column support column (93) completely overlap, the relative rotation angle When the sleeve support column (61) and the core column support column (93) can provide axial support as a whole, the effective axial cross-sectional area is Expressed as:

[0053] (5);

[0054] When the cross sections of the sleeve support column (61) and the core column support column (93) do not completely overlap, the relative rotation angle When the sleeve support column (61) and the core column support column (93) do not overlap, the area that does not overlap cannot fully provide axial support. Only the overlapping area is the effective area for providing axial support. For axial stiffness, the effective axial cross-sectional area is Expressed as:

[0055] (6);

[0056] The material flexibility density matrix is ​​also composed of bending and shear parameters. Unlike the axial expansion parameter, the material flexibility density matrix of the discrete unit is not affected by the relative rotation of the sleeve support column (61) and the core column support column (93). Therefore, the shear cross-sectional area Expressed as:

[0057] (7);

[0058] in, For the The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis x or The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis y .

[0059] Preferably, in step 2 of the above method, a conversion formula for converting the material flexibility density matrix from a body coordinate system to a Cartesian coordinate system is derived based on Lie theory in the following manner, including:

[0060] In the Plücker coordinate system, the velocity spinor of the flexible control support and force screw The relationship is expressed as:

[0061] (8);

[0062] in, yes The flexibility matrix, yes The stiffness matrix of , the relationship between the two is expressed as:

[0063] (9);

[0064] In Lie algebra, the velocity spinor of the flexible control support Isomorphic matrix of and force screw Isomorphic matrix of The forms are as follows:

[0065] (10);

[0066] in, is the displacement velocity vector; is a three-dimensional angular velocity vector with subscripts 1, 2, and 3 Represent the three elements of the three-dimensional angular velocity vector, which are the angular velocity magnitudes in the three directions; is a spiral symmetric matrix, that is , and its inverse operation is expressed as: ; 、 are the three-dimensional transformation vector and three-dimensional rotation vector in Lie algebra respectively; The three-dimensional transformation vector to the three-dimensional transformation matrix of the Lie group The mapping is obtained by taking The exponential product of Get, that is:

[0067] (11);

[0068] in, is a three-dimensional rotation matrix involving Lie groups and displacement vector The homogeneous transformation matrix of is a three-dimensional rotation matrix with 3 rows and 3 columns, is a displacement vector of 3 rows and 1 column;

[0069] If the force rotation of the support body is flexibly controlled In two different coordinate systems , coordinate system The expressions are and ,but and The corresponding relationship is:

[0070] (12);

[0071] in, 、 The coordinate systems are To coordinate system The rotation matrix and displacement vector of ; Is the adjoint matrix determined by the rotation matrix and the displacement vector; according to the adjoint matrix The special properties of , according to formula (8) are:

[0072] (13);

[0073] in, Velocity spinor In the coordinate system Expression below; superscript Indicates the inverse of a matrix; superscript represents the inverse transpose of a matrix; is the flexibility matrix in the coordinate system The following expression;

[0074] Based on this, the conversion formula of the flexibility matrix from the body coordinate system to the Cartesian coordinate system is:

[0075] (14);

[0076] in, Represents the Cartesian space coordinate system To body coordinate system The adjoint matrix of Indicates the inverse transpose of the matrix, the superscript represents the inverse of a matrix;

[0077] It can be concluded that the conversion formula of the material flexibility density matrix from the body coordinate system to the Cartesian coordinate system is:

[0078] (15);

[0079] in, The material flexibility density matrix of the flexible control support body is converted from the body coordinate system to the Cartesian coordinate system; The material flexibility density matrix of the flexible control support body is in the coordinate system expression; The adjoint matrix representing the discrete unit coordinate system transformation of the flexible control support body, Indicates the inverse transpose of the matrix, the superscript Represents the inverse of a matrix.

[0080] Preferably, in step 3 of the above method, all discrete units of the flexible control support are synthesized using the conversion formula in the following manner to derive the stiffness matrix of the flexible control support, including:

[0081] The first The arc length of a discrete unit is , then in the body coordinate system The material flexibility density matrix of the discrete element is The entire flexible control support body is regarded as the synthesis of discrete units. When a force spinor Acting on the end of the joint of the rope-pulled flexible robot, the force is Will be transmitted to each discrete unit, and the influence on each discrete unit is determined by formula (12) With the force screw The relationship is expressed as:

[0082] (16);

[0083] From formula (13), we can get velocity spinor of discrete units The representation in Cartesian space is:

[0084] (17);

[0085] in, Indicates the The velocity spinor of each discrete unit in the body coordinate system;

[0086] The total deformation rotation of the entire flexible control support body is The representation in Cartesian space is:

[0087] (18);

[0088] in, represents the arc length from the bottom of the flexible control support along the central axis to the discrete unit; Represents the expression of parameters in Cartesian space; Indicates the total length of the central axis of the flexible control support body; due to the relative rotation angle of the active part of the flexible control support body , when integrating the material flexibility density matrix, it corresponds to left multiplication of the relative rotation matrix , the flexibility matrix of the flexible control support body is finally obtained:

[0089] (19);

[0090] Combining the above formula (19) with formula (9) can obtain the stiffness matrix of the flexible control support body.

[0091] For Equation (19), each segment of the flexibility matrix is ​​related to the relative rotation angle The rotation angle input of the steering gear 10 is driven by the variable stiffness, and the movable support ring shaft assembly 9 is rotated through the connecting flange to adjust the relative rotation angle. The size of the rope-traction flexible robot joint stiffness matrix is ​​controlled to complete the variable stiffness adjustment.

[0092] Preferably, in the structure of the rope-driven flexible robot joint in the above method, the lower end of the flexible control support body is connected to the fixed base 3, and the upper end of the flexible control support body is connected to the terminal motion platform 1;

[0093] The flexible support sleeve assembly 6 of the flexible control support body is nested in the movable support ring shaft assembly 9 and connected to form a flexible control support body structure;

[0094] The variable stiffness driving servo 10 is installed at the center of the fixed base 3, connecting and driving the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 to rotate relative to each other to change the stiffness of the flexible control support body;

[0095] The joint driving mechanism is installed on the fixed base 3, and pulls the terminal motion platform 1 through the rope to drive the flexible control support body to bend to realize the joint movement.

[0096] Preferably, in the rope-driven flexible robot joint of the above method, the flexible support sleeve assembly 6 is a sleeve structure, and at least one layer of sleeve support ring is provided in the inner hole of the sleeve structure; the sleeve support ring includes more than three fan-shaped sleeve support columns 61 uniformly distributed in the circumferential direction;

[0097] The movable support ring shaft assembly 9 includes a movable flange 91 and a core column 92. The lower end of the core column 92 is fixed to the center of the movable flange 91. The circumference of the core column 92 is provided with at least one layer of core column support ring on the movable flange 91; the core column support ring includes more than three fan-shaped core column support columns 93 uniformly distributed in the circumferential direction; the upper end of the core column 92 extends into the center hole formed by the inner arc surface of the sleeve support column 61; the sleeve support column 61 and the core column support column 93 are spaced apart and the end faces contact each other to support the flexible support sleeve assembly 6;

[0098] The lower end of the flexible support sleeve assembly 6 is connected to the fixed base 3, and the upper end of the flexible support sleeve assembly 6 is connected to the end motion platform 1;

[0099] The variable stiffness driving servo 10 is connected to and drives the movable support ring shaft assembly 9 to rotate relative to the flexible support sleeve assembly 6, adjusts the contact area between the end faces of the sleeve support column 61 and the core column support column 93, and changes the stiffness of the flexible control support body.

[0100] Preferably, in the rope-driven flexible robot joint of the above method, the sleeve of the flexible support sleeve assembly 6 includes two layers of sleeve support rings, the sleeve support column 61 of the upper layer is fixed to the inner wall and / or bottom surface of the sleeve; the sleeve support column 61 of the lower layer is fixed to the inner wall of the sleeve;

[0101] The movable support ring shaft assembly 9 and the core column 92 are provided with two layers of core column support rings around their circumferences. The core column support columns 93 of the upper layer are fixed to the outer wall of the core column 92; the core column support columns 93 of the lower layer are fixed to the outer wall of the core column 92 and / or the end face of the movable flange 91;

[0102] The axial spacing between the two layers of sleeve support columns 61 is the same as the axial height of the core column support column 93 of the upper layer, and the core column support column 93 of the upper layer is arranged between the two layers of sleeve support columns 61;

[0103] The axial spacing between the two layers of core column support columns 93 is the same as the axial height of the sleeve support columns 61 of the next layer, and the sleeve support columns 61 of the next layer are arranged between the two layers of core column support columns 93;

[0104] The end faces of the sleeve support column 61 and the core column support column 93 , which are arranged at intervals, contact each other to support the flexible support sleeve assembly 6 .

[0105] Preferably, the cross-sectional dimensions of the fan-shaped gaps between the adjacent sleeve support columns 61 of the next layer are adapted to the cross-sectional dimensions of the core column support columns 93 of the previous layer, and the core column support columns 93 of the previous layer pass through the fan-shaped gaps to between the two layers of sleeve support columns 61.

[0106] Preferably, the sleeve of the flexible support sleeve assembly 6 includes a sleeve support ring, and the sleeve support column 61 is fixed to the inner wall and / or bottom surface of the sleeve;

[0107] The movable support ring shaft assembly 9 and the core column 92 are provided with a layer of core column support ring around their circumferences, and the core column support column 93 is fixed to the outer wall of the core column 92 and / or the end face of the movable flange 91;

[0108] The end faces of the sleeve support column 61 and the core column support column 93 contact each other to support the flexible support sleeve assembly 6.

[0109] Preferably, the variable stiffness driving servo 10 is connected to the movable flange 91 via a rigid connecting flange 12 and drives the movable supporting ring shaft assembly 9 to rotate.

[0110] In addition, the diameter of the sleeve support column 61, the diameter of the core column 93, and the inner and outer ring diameters of the sleeve support ring (core column support ring) directly affect the size of the stiffness matrix and the size of the variable stiffness control range. Changing these design parameters can change the variable stiffness control ability of the variable stiffness rope traction flexible robot joint.

[0111] An embodiment of the present invention further provides a processing device, comprising:

[0112] at least one memory for storing one or more programs;

[0113] At least one processor can execute one or more programs stored in the memory, and when the one or more programs are executed by the processor, the processor can implement the above method.

[0114] The embodiments of the present invention further provide a readable storage medium storing a computer program, which can implement the above method when executed by a processor.

[0115] In summary, it can be seen that the control method of the embodiment of the present invention, based on Lie theory and improved material flexibility density matrix, establishes the stiffness matrix of the robot joint in the entire space, avoids the calculation of complex Jacobian matrix, realizes efficient variable stiffness rope-traction flexible robot joint stiffness modeling, and ensures efficient and accurate control of the rope-traction flexible robot joint.

[0116] In order to more clearly demonstrate the technical solution and technical effects provided by the present invention, the solution provided by the embodiment of the present invention is described in detail with reference to specific embodiments below.

[0117] Example 1

[0118] like Figure 1 As shown, this embodiment provides a variable stiffness control method for a rope-driven flexible robot joint, which is used for a variable stiffness rope-driven flexible robot joint consisting of an end motion platform 1, a flexible control support body, a joint drive mechanism, a variable stiffness drive servo 10, and a fixed base 3. The flexible control support body includes a flexible support sleeve assembly 6 and a movable support ring shaft assembly 9. The method specifically includes the following steps:

[0119] Step 1: Derive the flexibility density matrix of the flexible control support material in the body coordinate system:

[0120] like Figure 2 As shown in the figure, the flexible control support structure can be discretized into tiny discrete units, using the Cartesian space coordinate system. The discrete unit at the origin is the first discrete unit, and the numbers are raised in sequence. The material flexibility density matrix of the discrete elements It can be expressed as:

[0121] (1);

[0122] Among them, the superscript Represents the expression of discrete units in the body coordinate system; It represents the arc length from the bottom of the flexible control support structure along the central axis to the discrete unit; are the shear and stretch terms of the material flexibility density matrix; are the bending and torsion terms of the material flexibility density matrix, which can be expressed using the elastic parameter matrix as follows:

[0123] (2);

[0124] Among them, diag[] is a function for constructing a diagonal matrix; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis x; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis y; Indicates the The axial cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis z; represents the shear modulus, represents Young's modulus, , is the Poisson's ratio of the material; 、 、 Respectively represent The moment of inertia of each discrete unit relative to the coordinate axis x, the moment of inertia relative to the coordinate axis y, and the moment of inertia relative to the coordinate axis z.

[0125] The cross-sectional structure of the flexible control support is as follows Figure 3 As shown, the inner and outer ring radii of the fan-shaped sleeve support column 61 of the flexible support sleeve assembly 6 are and The radius of the core column 92 of the movable support ring shaft assembly 9 is The relative rotation angle between the sleeve support column 61 and the core column support column 93 is Since the central angle of the sector column is 45° and the symmetry is fully considered in the design, we only need to discuss The complete variable stiffness model can be established. Obviously, the cross sections of the sleeve support column 61 and the core column support column 93 completely overlap, that is, When the sleeve support column 61 and the core column support column 93 can provide axial support as a whole, the effective axial cross-sectional area is It can be expressed as:

[0126] (5);

[0127] When the cross sections of the sleeve support column 61 and the core column support column 93 do not completely overlap, that is, When the two do not overlap, the area that does not overlap cannot fully provide axial support. Only the overlapping area is the effective area that actually provides axial support. Therefore, for axial stiffness, the effective axial cross-sectional area It can be expressed as:

[0128] (6);

[0129] In addition, the material flexibility density matrix is ​​also composed of bending, shear and other parameter items. Unlike the axial expansion parameter item, the material flexibility density matrix of the discrete unit is not affected by the relative rotation of the sleeve support column 61 and the core column support column 93, so the shear cross-sectional area It can be expressed as:

[0130] (7);

[0131] in, For the The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis x or The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis y ;

[0132] From the symmetry, we know that Discrete units relative Moment of inertia of the coordinate axis Hedi Discrete units relative Moment of inertia of the coordinate axis The same can be expressed as:

[0133] (3);

[0134] in, Indicates the Discrete units relative Moment of inertia of the coordinate axis or Discrete units relative Moment of inertia of the coordinate axis ; 、 are the polar diameter and polar angle of any position in the polar coordinate system when calculating the moment of inertia integral;

[0135] Similarly, Discrete units relative Moment of inertia of the coordinate axis It can be expressed as:

[0136] (4).

[0137] Step 2: Based on Lie theory, derive the transformation formula of the flexibility matrix from the body coordinate system to the Cartesian coordinate system, as follows:

[0138] In the Plücker coordinate system, the velocity spinor of the flexible control support and force screw The relationship can be expressed as:

[0139] (8);

[0140] in, yes The flexibility matrix, yes The stiffness matrix of , the relationship can be expressed as:

[0141] (9);

[0142] In Lie algebra, two spinors can be written in the following isomorphic matrix form:

[0143] (10);

[0144] in, is the displacement velocity vector; is a three-dimensional angular velocity vector with subscripts 1, 2, and 3 Represent the three elements of the three-dimensional angular velocity vector, which are the angular velocity magnitudes in the three directions; is a spiral symmetric matrix, that is , and its inverse operation is expressed as: ; 、 are the three-dimensional transformation vector and three-dimensional rotation vector in Lie algebra respectively; The three-dimensional transformation vector to the three-dimensional transformation matrix of the Lie group The mapping is achieved by taking the isomorphic matrix The exponential product of Get, that is:

[0145] (11);

[0146] in, is a three-dimensional rotation matrix containing the Lie group and displacement vector The homogeneous transformation matrix of is a three-dimensional rotation matrix with 3 rows and 3 columns, is a displacement vector with 3 rows and 1 column.

[0147] If the force rotation of the support body is flexibly controlled In two different coordinate systems 、 Expression, the corresponding relationship can be expressed as:

[0148] (12);

[0149] in, 、 The coordinate systems are To coordinate system The rotation matrix and displacement vector, Is the adjoint matrix determined by them. According to the adjoint matrix The special properties of , combined with formula (8), can be obtained:

[0150] (13);

[0151] in, Velocity spinor In the coordinate system Expression below; superscript Indicates the inverse of a matrix; superscript represents the inverse transpose of a matrix; is the flexibility matrix in the coordinate system The following expression;

[0152] Based on this, the conversion formula of the flexibility matrix from the body coordinate system to the Cartesian coordinate system is:

[0153] (14);

[0154] Therefore, the conversion formula of the material flexibility density matrix from the body coordinate system to the Cartesian coordinate system is:

[0155] (15);

[0156] in, The material flexibility density matrix of the flexible control support body is converted from the body coordinate system to the Cartesian coordinate system; The material flexibility density matrix of the flexible control support body is in the coordinate system expression; The adjoint matrix representing the discrete unit coordinate system transformation of the flexible control support.

[0157] Step 3: Synthesize all discrete elements and derive the stiffness matrix of the flexible control support:

[0158] Order The arc length of a discrete unit is , then in the body coordinate system The material flexibility density matrix of the discrete element is The entire flexible control support body can be regarded as a synthesis of discrete flexible units. Figure 2 As shown, when a force screw Acting on the end of the flexible control support, this force torque will be transmitted to each discrete unit, and the influence on each discrete unit is determined by formula (12): With this spinor force The relationship is expressed as:

[0159] (16);

[0160] From formula (13), we can get the velocity spinor of each discrete unit: In Cartesian space it is represented as:

[0161] (17);

[0162] in, represents the velocity spinor of each discrete unit in the body coordinate system; therefore, the total deformation spinor of the entire flexible control support body is In Cartesian space it is represented as:

[0163] (18);

[0164] in, represents the arc length from the bottom of the flexible control support along the central axis to the discrete unit; Represents the expression of parameters in Cartesian space; Indicates the total length of the central axis of the flexible control support. Considering the relative rotation angle of the active part of the flexible control support , when integrating the flexibility matrix, the corresponding left multiplication relative rotation matrix is ​​required , and finally we can get:

[0165] (19);

[0166] Therefore, the stiffness matrix can be obtained directly without calculating the complex Jacobian matrix.

[0167] Step 4: Change the relative rotation angle between the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 Change the flexibility matrix of the joints of a rope-pulled flexible robot:

[0168] For Equation (19), each segment of the flexibility matrix is ​​related to the relative rotation angle The relative rotation angle is adjusted by inputting the rotation angle of the steering gear 10 through the variable stiffness drive and rotating the movable support ring shaft assembly 9 through the connecting flange. The size of the rope-traction flexible robot joint stiffness matrix is ​​controlled to complete the variable stiffness adjustment.

[0169] In the above method, the variable stiffness rope-driven flexible robot joint is as follows Figures 3 to 6 As shown, it includes an end motion platform 1, a flexible control support body, a joint traction mechanism, a variable stiffness traction servo 10 and a fixed base 3; the lower end of the flexible control support body is connected to the fixed base 3, and the upper end is connected to the end motion platform 1; the flexible control support body includes a flexible support sleeve assembly 6 and a movable support ring shaft assembly 9; the flexible support sleeve assembly 6 is nested outside the movable support ring shaft assembly 9 and connected to form a flexible control support body, and the variable stiffness traction servo 10 is installed at the center of the fixed base 3, connecting and pulling the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 to rotate relative to each other to change the stiffness of the flexible control support body; the joint traction mechanism is installed on the fixed base 3, and pulls the end motion platform 1 through a rope to drive the flexible control support body to bend, thereby realizing the bending movement of the joint robot. In this example, the active stiffness control can be achieved through the structural design of the flexible control support body inside the joint, without changing the external environmental conditions, thereby realizing the control of the joint stiffness.

[0170] In this embodiment, Figures 7 to 9As shown, the flexible control support body includes a flexible support sleeve assembly 6 and a movable support ring shaft assembly 9. The flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 are both made of flexible materials. The flexible materials have good plasticity and deformation properties and can be deformed under the action of external forces. Its main characteristics are softness, lightness, good elasticity, and large deformation capacity. Common flexible materials include rubber, plastic, etc. In this example, polyurethane elastomers, silicone, etc. can be used. Polyurethane elastomers, also known as thermoplastic polyurethane elastomers (TPU), are a type of elastomer that can be plasticized by heating and dissolved by solvents. They have excellent comprehensive properties such as high strength, high toughness, wear resistance, and oil resistance. They have good processing performance and are widely used in defense, medical, food and other industries. They are produced by processing methods such as injection molding, extrusion, and blow molding.

[0171] The lower end of the flexible control support body is connected to the fixed base 3, and the upper end is connected to the terminal motion platform 1; the flexible control support body includes a flexible support sleeve assembly 6 and a movable support ring shaft assembly 9; the flexible support sleeve assembly 6 is nested outside the movable support ring shaft assembly 9 and connected to form a flexible control support body, and the variable stiffness traction servo 10 is installed at the center of the fixed base 3, connecting and pulling the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 to rotate relative to each other to change the stiffness of the flexible control support body.

[0172] The joint traction mechanism is installed on the fixed base 3, and pulls the terminal motion platform 1 through the rope to drive the flexible control support body to bend, thereby realizing the movement of the joint robot.

[0173] Preferably, the flexible support sleeve assembly 6 is a sleeve structure, and at least one sleeve support ring is provided in the inner hole of the sleeve; the sleeve support ring includes more than three fan-shaped sleeve support columns 61 uniformly distributed in the circumferential direction;

[0174] The movable support ring shaft assembly 9 includes a movable flange 91 and a core column 92. The lower end of the core column 92 is fixed to the center of the movable flange 91. The circumference of the core column 92 is provided with at least one layer of core column support ring on the movable flange 91; the core column support ring includes more than three fan-shaped core column support columns 93 uniformly distributed circumferentially; the upper end of the core column 92 extends into the center hole formed by the inner arc surface of the sleeve support column 61; the sleeve support column 61 and the core column support column 93 are spaced apart and the end faces contact each other to support the flexible support sleeve assembly 6;

[0175] The lower end of the flexible support sleeve assembly 6 is connected to the fixed base 3, and the upper end is connected to the terminal motion platform 1; the variable stiffness traction servo 10 is connected and pulls the movable support ring shaft assembly 9 to rotate relative to the flexible support sleeve assembly 6, adjusting the contact area between the end faces of the sleeve support column 61 and the core column support column 93, and changing the stiffness of the flexible control support body.

[0176] Preferably, the sleeve of the flexible support sleeve assembly 6 includes two layers of sleeve support rings, the sleeve support columns 61 of the upper layer are fixed to the inner wall and / or bottom surface of the sleeve; the sleeve support columns 61 of the lower layer are fixed to the inner wall of the sleeve;

[0177] The movable support ring shaft assembly 9 and the core column 92 are provided with two layers of core column support rings around their circumferences. The core column support columns 93 of the upper layer are fixed to the outer wall of the core column 92; the core column support columns 93 of the lower layer are fixed to the outer wall of the core column 92 and / or the end face of the movable flange 91;

[0178] The axial spacing between the two layers of sleeve support columns 61 is the same as the axial height of the core column support column 93 of the upper layer, and the core column support column 93 of the upper layer is arranged between the two layers of sleeve support columns 61;

[0179] The axial spacing between the two layers of core column support columns 93 is the same as the axial height of the sleeve support columns 61 of the next layer, and the sleeve support columns 61 of the next layer are arranged between the two layers of core column support columns 93;

[0180] The end faces of the sleeve support column 61 and the core column support column 93 , which are arranged at intervals, contact each other to support the flexible support sleeve assembly 6 .

[0181] Preferably, the cross-sectional dimensions of the fan-shaped gaps between the adjacent sleeve support columns 61 of the next layer are adapted to the cross-sectional dimensions of the core column support columns 93 of the previous layer, and the core column support columns 93 of the previous layer pass through the fan-shaped gaps to between the two layers of sleeve support columns 61.

[0182] Preferably, the sleeve of the flexible support sleeve assembly 6 includes a sleeve support ring, and the sleeve support column 61 is fixed to the inner wall and / or bottom surface of the sleeve;

[0183] The movable support ring shaft assembly 9 and the core column 92 are provided with a layer of core column support ring around their circumferences, and the core column support column 93 is fixed to the outer wall of the core column 92 and / or the end face of the movable flange 91;

[0184] The end faces of the sleeve support column 61 and the core column support column 93 contact each other to support the flexible support sleeve assembly 6.

[0185] Preferably, the variable stiffness traction servo 10 is connected to the movable flange 91 via a rigid connection flange 12 and pulls the movable support ring shaft assembly 9 to rotate.

[0186] The variable stiffness drive servo 10 is connected to and drives the movable support ring shaft assembly 9 to rotate relative to the flexible support sleeve assembly 6, adjusting the contact area between the end faces of the sleeve support column 61 and the core column support column 93, thereby changing the stiffness of the flexible control support body. Specifically, the variable stiffness drive servo 10 is connected to the movable flange 91 via a rigid connection flange 12 and drives the movable support ring shaft assembly 9 to rotate. At the same time, the output shaft of the variable stiffness drive servo 10 can also be installed with a servo output flange 11. Specifically, the output shaft of the variable stiffness drive servo 10 and the servo output flange 11 adopt a universal connection method. Since the size of the output flange 11 is fixed, adding a rigid connection flange 12 can adapt to movable support ring shaft assemblies 9 of any diameter. The specific connection method will not be repeated here. The servo output flange 11 is installed with the rigid connection flange 12, and then connected to the movable flange 91. The servo output flange 11 and the rigid connection flange 12 are connected and fixed by a third bolt group 15. The servo-flange direct connection method makes the relative rotation response of the internal structure faster, thereby improving the response speed of the stiffness adjustment.

[0187] When the stiffness of the joint needs to be adjusted, the variable stiffness driving servo 10 is started. The variable stiffness driving servo 10 drives the movable support ring shaft assembly 9 to rotate through the servo output flange 11 and the rigid connection flange 12. It can be unidirectional or bidirectional. At the same time, the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9 are driven to rotate relative to each other. Then the end face contact area between the adjacent sleeve support column 61 and the core column support column 93 will change, and the spatial position between the sleeve support column 61 and the core column support column 93 will change, which changes the internal structure of the flexible control support body. The reconfigurable internal hollow structure of the flexible control support body brings the flexible robot joint the characteristics of variable stiffness while realizing the axial bending movement of the joint, and also ensures the ability of axial support. When the fan-shaped cross-sections of the sleeve support column 61 and the core support column 93 completely overlap, both of them can play an axial support role as a whole; when the fan-shaped cross-sections of the sleeve support column 61 and the core support column 93 do not completely overlap, the non-overlapping area cannot fully provide axial support. Only the overlapping area is the effective area that actually provides axial support. Therefore, the axial stiffness of the flexible control support body will change with the change of the internal structure. It can be seen that the internal structure of the flexible control support body will change with the relative changes of the flexible support sleeve assembly 6 and the movable support ring shaft assembly 9, which will also change the bending stiffness of the robot joint and achieve the adjustment of the overall stiffness of the joint.

[0188] In addition, the diameter of the sleeve support column 61, the diameter of the core column 93, and the inner and outer ring diameters of the sleeve support ring (core column support ring) directly affect the size of the stiffness matrix and the size of the variable stiffness control range. Changing these design parameters can change the variable stiffness control ability of the variable stiffness rope traction flexible robot joint.

[0189] In summary, for the stiffness control method of the variable stiffness rope-traction flexible robot joint, based on Lie theory and the improved material flexibility density matrix, the stiffness matrix of the robot joint in the entire space is established, which avoids the calculation of the complex Jacobian matrix and provides strong support for the practical application of the variable stiffness rope-traction flexible robot joint.

[0190] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware through a program. The program can be stored in a computer-readable storage medium. When executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0191] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or any form of implication that the information constitutes prior art already known to those skilled in the art.

Claims

1. A variable stiffness control method for a rope-driven flexible robot joint, which is used for a rope-driven flexible robot joint consisting of an end motion platform (1), a flexible control support, a joint drive mechanism, a variable stiffness drive servo (10) and a fixed base (3), wherein: The flexible control support body comprises a flexible support sleeve assembly (6) and a movable support ring shaft assembly (9), and is characterized by comprising: Step 1: derive the material flexibility density matrix of the flexible control support in the body coordinate system; Step 2: deriving a conversion formula for converting the material compliance density matrix from a body coordinate system to a Cartesian coordinate system based on Lie theory; Step 3: Using the conversion formula to synthesize all discrete units of the flexible control support, the stiffness matrix of the flexible control support is derived; Step 4, by inputting a rotation angle through the variable stiffness driving servo (10) to rotate the movable support ring shaft assembly of the flexible control support body, thereby changing the relative rotation angle between the flexible support sleeve assembly of the flexible control support body and the movable support ring shaft assembly. The size of the flexible control support body is adjusted by changing the material flexibility density matrix of the flexible control support body to adjust the stiffness matrix of the flexible control support body, thereby realizing variable stiffness adjustment of the rope-traction flexible robot joint.

2. The variable stiffness control method for the rope-driven flexible robot joint according to claim 1 is characterized in that: In step 1, the material flexibility density matrix of the flexible control support body in the body coordinate system is derived in the following manner, including: The structure of the flexible control support is discretized into multiple discrete units in the Cartesian space coordinate system. The discrete unit at the origin is the first discrete unit, and the numbers are raised in sequence. The material flexibility density matrix of the discrete elements Expressed as: （1）； Among them, the superscript Represents the expression of discrete units in the body coordinate system; represents the arc length from the bottom of the flexible control support along the central axis to the discrete unit; are the shear and stretch terms of the material flexibility density matrix; are the bending and torsion terms of the material flexibility density matrix, which are expressed in elastic parameter matrices as follows: （2）； Among them, diag[] is a function for constructing a diagonal matrix; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis x; Indicates the The shear cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis y; Indicates the The axial cross-sectional area of ​​the material of each discrete unit relative to the coordinate axis z; represents the shear modulus, represents Young's modulus, , is the Poisson's ratio of the material; 、 、 Respectively represent The moment of inertia of each discrete unit relative to the coordinate axis x, the moment of inertia of the coordinate axis y, and the moment of inertia of the coordinate axis z.

3. The variable stiffness control method for the rope-driven flexible robot joint according to claim 2, characterized in that: The bending and torsional terms of the material compliance density matrix In the corresponding elastic parameter matrix, Discrete units relative to the coordinate axis Moment of inertia With the Discrete units relative to the coordinate axis Moment of inertia The same, expressed as: （3）； in, Indicates the Discrete units relative to the coordinate axis Moment of inertia or Discrete units relative to the coordinate axis Moment of inertia ; sin is to find the sine value, 、 are the polar diameter and polar angle of any position in the polar coordinate system when calculating the moment of inertia integral; 、 are respectively the inner and outer ring radii of the fan-shaped sleeve support column (61) of the flexible support sleeve assembly (6); is the radius of the core column (92) of the movable support ring shaft assembly (9); The relative rotation angle between the sleeve support column (61) and the core column support column (93) of the movable support ring shaft assembly (9) is 45° according to the central angle of the sector column and the symmetry of the design. ;No. Discrete units relative to the coordinate axis Moment of inertia Expressed as: （4）； When the cross sections of the sleeve support column (61) and the core column support column (93) completely overlap, the relative rotation angle When the sleeve support column (61) and the core column support column (93) can provide axial support as a whole, the effective axial cross-sectional area is Expressed as: （5）； When the cross sections of the sleeve support column (61) and the core column support column (93) do not completely overlap, the relative rotation angle When the sleeve support column (61) and the core column support column (93) do not overlap, the area that does not overlap cannot fully provide axial support. Only the overlapping area is the effective area for providing axial support. For axial stiffness, the effective axial cross-sectional area is Expressed as: （6）； The material flexibility density matrix is ​​also composed of bending and shear parameters. Unlike the axial expansion parameter, the material flexibility density matrix of the discrete unit is not affected by the relative rotation of the sleeve support column (61) and the core column support column (93). Therefore, the shear cross-sectional area Expressed as: （7）； in, For the The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis x or The shear cross-sectional area of ​​the material of a discrete unit relative to the coordinate axis y .

4. The variable stiffness control method for a rope-driven flexible robot joint according to any one of claims 1 to 3, characterized in that: In step 2, a conversion formula for converting the material flexibility density matrix from the body coordinate system to the Cartesian coordinate system is derived based on Lie theory in the following manner, including: In the Plücker coordinate system, the velocity spinor of the flexible control support and force screw The relationship is expressed as: （8）； in, is a 6×6 flexibility matrix, is a 6×6 stiffness matrix, and the relationship between the two is expressed as: （9）； In Lie algebra, the velocity spinor of the flexible control support Isomorphic matrix of and force screw Isomorphic matrix of The forms are as follows: （10）； in, is the displacement velocity vector; is a three-dimensional angular velocity vector with subscripts 1, 2, and 3 Represent the three elements of the three-dimensional angular velocity vector, which are the angular velocity magnitudes in the three directions; is a spiral symmetric matrix, that is , and its inverse operation is expressed as: ; 、 are the three-dimensional transformation vector and three-dimensional rotation vector in Lie algebra respectively; The three-dimensional transformation vector to the three-dimensional transformation matrix of the Lie group The mapping is achieved by taking the isomorphic matrix The exponential product of Get, that is: （11）； in, is a three-dimensional rotation matrix involving Lie groups and displacement vector The homogeneous transformation matrix of is a three-dimensional rotation matrix with 3 rows and 3 columns, is a displacement vector with 3 rows and 1 column; If the force rotation of the support body is flexibly controlled In two different coordinate systems and coordinate system The expressions are and ,but and The corresponding relationship is: （12）； in, 、 The coordinate systems are To coordinate system The rotation matrix and displacement vector of ; Is the adjoint matrix determined by the rotation matrix and the displacement vector; according to the adjoint matrix The special properties of , according to formula (8) are: （13）； in, Velocity spinor In the coordinate system Expression below; superscript Indicates the inverse transpose of a matrix; the superscript represents the inverse of a matrix; Based on this, the conversion formula of the flexibility matrix from the body coordinate system to the Cartesian coordinate system is: （14）； in, represents the flexibility matrix for transforming from the body coordinate system to the Cartesian coordinate system; Represents the Cartesian space coordinate system To body coordinate system The adjoint matrix of Indicates the inverse transpose of the matrix, the superscript represents the inverse of a matrix; is the flexibility matrix in the coordinate system The following expression; It can be concluded that the conversion formula of the material flexibility density matrix from the body coordinate system to the Cartesian coordinate system is: （15）； in, The material flexibility density matrix of the flexible control support body is converted from the body coordinate system to the Cartesian coordinate system; The material flexibility density matrix of the flexible control support body is in the coordinate system expression; The adjoint matrix representing the discrete unit coordinate system transformation of the flexible control support body, Indicates the inverse transpose of the matrix, the superscript Represents the inverse of a matrix.

5. The variable stiffness control method for the rope-driven flexible robot joint according to claim 4 is characterized in that: In step 3, all discrete units of the flexible control support are synthesized using the conversion formula in the following manner to derive the stiffness matrix of the flexible control support, including: The first The arc length of a discrete unit is , then in the body coordinate system The material flexibility density matrix of the discrete element is The entire flexible control support body is regarded as the synthesis of discrete units. When a force spinor Acting on the end of the flexible control support, the force is Will be transmitted to each discrete unit, and the influence on each discrete unit is determined by formula (12) With the force screw The relationship is expressed as: （16）； From formula (13), the velocity spinor of each discrete unit is obtained The representation in Cartesian space is: （17）； in, Indicates the The velocity spinor of each discrete unit in the body coordinate system is the total deformation spinor of the entire flexible control support body. The representation in Cartesian space is: （18）； in, represents the arc length from the bottom of the flexible control support along the central axis to the discrete unit; Represents the expression of parameters in Cartesian space; Indicates the total length of the central axis of the flexible control support body, because the movable part of the flexible control support body has a relative rotation angle , when integrating the material flexibility density matrix, it corresponds to left multiplication of the relative rotation matrix , the flexibility matrix of the flexible control support body is finally obtained: （19）； Combining the above formula (19) with formula (9) can obtain the stiffness matrix of the flexible control support body.

6. The variable stiffness control method for a rope-driven flexible robot joint according to any one of claims 1 to 3, characterized in that: In the structure of the rope-driven flexible robot joint in the method, the lower end of the flexible control support body is connected to the fixed base (3), and the upper end of the flexible control support body is connected to the terminal motion platform (1); The flexible support sleeve assembly (6) of the flexible regulating support body is nested in the movable support ring shaft assembly (9) and is externally connected to form a flexible regulating support body structure; The variable stiffness driving servo (10) is installed at the center of the fixed base (3), connected to and drives the flexible support sleeve assembly (6) and the movable support ring shaft assembly (9) to rotate relative to each other to change the stiffness of the flexible control support body; The joint driving mechanism is mounted on a fixed base (3), and pulls the terminal motion platform (1) via a rope, thereby driving the flexible control support body to bend and realize joint movement.

7. The variable stiffness control method for the joints of a rope-driven flexible robot according to claim 6, characterized in that; The flexible support sleeve assembly (6) is a sleeve structure, and at least one layer of sleeve support ring is provided in the inner hole of the sleeve structure; the sleeve support ring includes more than three fan-shaped sleeve support columns (61) uniformly distributed in the circumferential direction; The movable support ring shaft assembly (9) includes a movable flange (91) and a core column (92), the lower end of the core column (92) is fixed to the center of the movable flange (91), and the circumference of the core column (92) is provided with at least one layer of core column support ring on the movable flange (91); the core column support ring includes more than three fan-shaped core column support columns (93) uniformly distributed in the circumferential direction; the upper end of the core column (92) extends into the center hole formed by the inner arc surface of the sleeve support column (61); the sleeve support column (61) and the core column support column (93) are spaced apart and their end faces contact each other to support the flexible support sleeve assembly (6); The lower end of the flexible support sleeve assembly (6) is connected to the fixed base (3), and the upper end of the flexible support sleeve assembly (6) is connected to the terminal motion platform (1); The variable stiffness driving servo (10) is connected to and drives the movable support ring shaft assembly (9) to rotate relative to the flexible support sleeve assembly (6), thereby adjusting the contact area between the end faces of the sleeve support column (61) and the core column support column (93), and changing the stiffness of the flexible control support body.

8. The variable stiffness control method for the joints of a rope-driven flexible robot according to claim 7, characterized in that; The flexible support sleeve assembly (6) includes two layers of sleeve support rings in the sleeve, wherein the sleeve support column (61) of the upper layer is fixed to the inner wall and / or bottom surface of the sleeve; and the sleeve support column (61) of the lower layer is fixed to the inner wall of the sleeve; The movable support ring shaft assembly (9) and the core column (92) are provided with two layers of core column support rings on their circumferences, wherein the core column support column (93) of the upper layer is fixed to the outer wall of the core column (92); and the core column support column (93) of the lower layer is fixed to the outer wall of the core column (92) and / or the end face of the movable flange (91); The axial spacing between the two layers of sleeve support columns (61) is the same as the axial height of the core column support column (93) of the upper layer, and the core column support column (93) of the upper layer is arranged between the two layers of sleeve support columns (61); The axial spacing between the two layers of core column support columns (93) is the same as the axial height of the sleeve support columns (61) of the next layer, and the sleeve support columns (61) of the next layer are arranged between the two layers of core column support columns (93); The end faces of the sleeve support column (61) and the core column support column (93) arranged at intervals contact each other to support the flexible support sleeve assembly (6).

9. A processing device, characterized in that: include: at least one memory for storing one or more programs; At least one processor is capable of executing one or more programs stored in the memory, and when the one or more programs are executed by the processor, the processor is capable of implementing the method according to any one of claims 1 to 8.

10. A readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 8 can be implemented.

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