A composite continuum robot arm control method, system and robot arm

Abstract

The application provides a kind of composite continuum mechanical arm control method, system and mechanical arm, consider friction loss, analyze drive wire node tension transmission relationship, obtain drive wire tension distribution, and then equivalent flexible beam deformation drive;The statics analysis is carried out to the cut continuum mechanical arm, the static model is established using Euler-Bernoulli beam theory, and the static model is solved using Taylor series expansion method;Based on the static model data, the end trajectory of the cut continuum mechanical arm is fitted using Kepler ellipse equation, and the relationship equation of the relative end coordinates of the concentric tube continuum mechanical arm is constructed;According to matrix coordinate conversion, the equation of the key parameters required for solving control parameters is established and iteratively solved, and the control parameter equation set is constructed to solve the control parameters of the composite continuum mechanical arm.The application can improve the timeliness of control response, improve the control accuracy and precision.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm control, specifically relating to a control method, system, and robotic arm for a composite continuum robotic arm. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] The super-redundant and flexible structure of the continuous robotic arm enables it to reach complex areas for surgical operations, and it has broad application prospects in surgery, especially for some high-precision surgeries, such as neurosurgery.

[0004] The composite continuous robotic arm is composed of a nested incision continuous robotic arm and a concentric tube continuous robotic arm. The outer incision continuous robotic arm has two degrees of freedom: bending and rotation. By pulling a drive wire, the incision continuous robotic arm deforms, thus achieving bending motion. The inner concentric tube continuous arm is made of nickel-titanium alloy tubing through bending and incision processing, and consists of straight and pre-bent sections, possessing two degrees of freedom: rotation and feed. The composite continuous robotic arm combines the structural features of both incision and concentric tube continuous robotic arms, expanding the workspace, enhancing flexibility, and achieving a smaller size within a certain range. In the application of surgical robotic arms, accurate and efficient inverse motion solutions are crucial for real-time control. In particular, while current static models of continuous robotic arms can achieve good accuracy, they suffer from low solution efficiency.

[0005] Due to the flexible, multi-joint structure of continuum manipulators, solving the super-redundant inverse kinematics of continuum manipulators is a challenging task. The traditional method for solving the inverse kinematics problem of continuum robots is the Jacobi method, which iterates based on the pseudo-inverse of the Jacobi. However, when the number of joints is large, it requires extensive computation and inevitably suffers from non-convergence and singularities, significantly complicating the control of the manipulator and impacting its timeliness, accuracy, and precision. Summary of the Invention

[0006] To address the aforementioned problems, this invention proposes a control method, system, and robotic arm for a composite continuum robotic arm. This invention establishes a static model of the composite continuum robotic arm and introduces Kepler elliptic curve fitting to the end-effector trajectory of the cut continuum robotic arm to simplify the model. This ensures accuracy while achieving efficient inverse kinematics solution, thereby improving control response timeliness and enhancing control accuracy and precision.

[0007] According to some embodiments, the present invention adopts the following technical solution:

[0008] A method for controlling a composite continuum robotic arm includes the following steps:

[0009] Considering frictional losses, the tension transmission relationship of the driving wire nodes is analyzed to obtain the tension distribution of the driving wire, and then the deformation driving of the equivalent flexible beam is obtained.

[0010] Static analysis was performed on the slit continuum manipulator. A static model was established using Euler-Bernoulli beam theory, and the static model was solved using Taylor series expansion.

[0011] Based on static model data, the Kepler ellipse equation is used to fit the end trajectory of the cut continuum robot arm, and the relationship equation between the relative end coordinates of the concentric tube continuum robot arm is constructed.

[0012] Based on matrix coordinate transformation, equations for the key parameters required to solve the control parameters are established and solved iteratively. A set of control parameter equations is constructed to solve the control parameters of the composite continuum robot arm.

[0013] In practical applications, the robotic arm is controlled using the obtained control parameters.

[0014] As an alternative implementation method, considering frictional losses, the process of analyzing the tension transmission relationship of the drive wire nodes and obtaining the drive wire tension distribution includes: the drive wire tension, frictional force and support force of each node of the drive wire are in balance with each other.

[0015] Furthermore, the loss of tension in the drive wire is caused solely by friction.

[0016] Establish local coordinate systems for each node and scalarize the forces to achieve mutual equilibrium.

[0017] The two beams at any joint are equivalent to one beam, and a coordinate system is established to create an expression for the deflection angle of each equivalent beam.

[0018] By adding the tension transmission coefficient of the corresponding node, which is only related to the deflection angle of the drive wire at the node and the direction of the drive wire movement, the relationship between the tension of the drive wire is established.

[0019] As an alternative implementation, the deformation-driven process of the equivalent flexible beam includes: the force on the i-th segment of the flexible beam is F. i Treating the first i flexible beam segments as a whole, the force on the i-th flexible beam segment is the vector sum of the tensions of the driving wires at the action nodes. Substituting this into the relationship between the tensions of the driving wires, we obtain the force F on the end of the i-th flexible beam segment. i To express the tension of the driving wire at the end node of the beam segment, without considering the torsion and shear of the beam, the tension of the driving wire at the node is equivalent to the deformation drive at the end of the beam, thus forming the expression for the force and torque acting on the end of the i-th flexible beam segment.

[0020] As an alternative implementation, static analysis is performed on the slit continuum manipulator. A static model is established using Euler-Bernoulli beam theory, and the process of solving the static model using Taylor series expansion includes: modeling the flexible beam using Euler-Bernoulli beam theory;

[0021]

[0022] In the formula, E is the Young's modulus of the material, I is the moment of inertia of the beam's cross-sectional area (I remains constant during beam bending), and point s is any point on the beam. Point s on the i-th beam relative to Z i The rotation angle of the shaft, M(s) is the bending moment acting on point s on the beam, F Zi F Ri The force acting on the end of the beam is differentiated to obtain the characteristic equation of the Euler-Bernoulli beam theory. After adding boundary conditions, a third-order Maclaurin series of the bending angle at any point on each beam segment is established and simplified. The relationship between beam deformation and deformation driving force is established through the beam model, and then the unknowns in the expression are solved.

[0023] As an alternative implementation, the process of fitting the end-effector trajectory of the cut continuum robot arm using the Keplerian elliptic equation includes fitting the Z-coordinate of the end-effector of the cut continuum with the bending angle using a polynomial. The relationship between the Z-coordinate and R-coordinate of the end of the cut continuum is fitted using the Kepler ellipse equation, simplifying the complex end trajectory into a mathematical model.

[0024] As a further defined implementation, when the length of the slicing continuum robotic arm is constant, its end-effector Z-coordinate and bending angle are... The relationship is obtained through polynomial fitting, and the polynomial coefficients are determined by the least squares method.

[0025] As a further defined implementation, the major and minor radii of the Keplerian ellipse equation are obtained by fitting the end-effector trajectory of the cut continuum using the least squares method.

[0026] As an alternative implementation, the process of constructing the relational equation between the relative end coordinates of the concentric tube continuum robot arm includes: combining the feed length, deflection angle, and pre-bending curvature of the concentric tube continuum robot arm to establish a mathematical relationship between the end coordinates of the concentric tube and the end coordinates of the cut continuum, wherein the end coordinates of the concentric tube continuum robot arm are determined by its feed length L. t Deflection angle φ t The pre-bending curvature K is determined and the kinematic constraints of the concentric tube continuum manipulator are satisfied.

[0027] As an alternative implementation method, the process of establishing equations for the key parameters required to solve the control parameters based on matrix coordinate transformation and iteratively solving them, and constructing a set of control parameter equations to solve the control parameters of the composite continuum manipulator, includes: establishing the transformation relationship between the basic coordinate system and the relative coordinate system based on matrix coordinate transformation; using Newton's iterative method to solve the key parameter equations, and then solving the control parameters of the composite continuum manipulator, including the deflection angle of the slit continuum manipulator, the feed length and deflection angle of the concentric tube continuum manipulator.

[0028] A composite continuous robot arm control system includes:

[0029] The tension distribution calculation module is configured to consider friction loss, analyze the tension transmission relationship of the drive wire nodes, obtain the tension distribution of the drive wire, and then the deformation drive of the equivalent flexible beam.

[0030] The static model building and solution module is configured to perform static analysis on the cut continuum manipulator, build the static model using Euler-Bernoulli beam theory, and solve the static model using Taylor series expansion.

[0031] The end-point trajectory module is configured to fit the end-point trajectory of the cut continuum robot arm based on static model data using the Kepler ellipse equation, and to construct the relationship equation between the relative end-point coordinates of the concentric tube continuum robot arm.

[0032] The control parameter solving module is configured to establish equations for the key parameters required to solve the control parameters based on matrix coordinate transformation and iteratively solve them, thereby constructing a set of control parameter equations to solve the control parameters of the composite continuum robot arm.

[0033] A composite continuum robotic arm includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, complete the steps in the above method;

[0034] It may include the aforementioned systems.

[0035] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0036] (1) This invention considers friction loss, analyzes the tension transmission relationship of the drive wire node, obtains the tension distribution of the drive wire, and then drives the deformation of the equivalent flexible beam; performs static analysis on the cut continuum robot arm, establishes a static model using Euler-Bernoulli beam theory, and solves the accurate static model using Taylor series expansion.

[0037] (2) This invention addresses the inverse kinematics problem of a composite continuum manipulator. Based on a static model, it introduces Kepler elliptic curve fitting to the end trajectory of the cut continuum segment to simplify the inverse kinematics model. The implicit relationships between control parameters of the first cut continuum segment are transformed into explicit relationships. Therefore, the complex inverse kinematics problem is transformed into a simple problem of solving the control parameters by simultaneously solving explicit equations. This invention can achieve efficient solutions by combining an accurate static model, meeting the accuracy and speed requirements in practical control.

[0038] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0039] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0040] Figure 1 This is a schematic diagram of the overall structure of the composite continuum robotic arm according to Embodiment 1 of the present invention;

[0041] Figure 2 This is a schematic diagram of the inverse kinematics mapping establishment process in Embodiment 1 of the present invention;

[0042] Figure 3 This is a schematic diagram of the tension transmission of the drive wire in the slit continuum robotic arm according to Embodiment 1 of the present invention;

[0043] Figure 4 This is a schematic diagram of the force analysis of the drive wire node of the slit continuum robotic arm according to Embodiment 1 of the present invention;

[0044] Figure 5 This is a schematic diagram of the deflection angle of the slit continuum robotic arm beam according to Embodiment 1 of the present invention;

[0045] Figure 6 This is a schematic diagram of the stress condition of the slit continuum robotic arm beam according to Embodiment 1 of the present invention;

[0046] Figure 7 This is a schematic diagram of the coordinate establishment of the composite continuum robot arm according to Embodiment 1 of the present invention;

[0047] Figure 8 This is a schematic diagram of the Kepler elliptic curve at the end of the cut continuum in Embodiment 1 of the present invention;

[0048] Figure 9 This is a flowchart of the Newton-based iteration method algorithm for solving the problem according to Embodiment 1 of the present invention;

[0049] Figure 10 This is a flowchart of the inverse kinematics algorithm according to Embodiment 1 of the present invention;

[0050] Among them, 1. Incision continuous robotic arm, 2. Drive wire, 3. Concentric tube continuous robotic arm, 4. Straight tube, 5. Pre-bent tube, 6. Surgical instruments. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0052] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0053] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0054] Where there is no conflict, the embodiments and features described in this application may be combined with each other.

[0055] Example 1

[0056] As described in the background section, existing methods for solving the inverse kinematics of continuum manipulators require extensive computation and inevitably suffer from non-convergence and singularities. To address these technical problems, this invention proposes a control method for a composite continuum manipulator.

[0057] The structure of the composite continuum robotic arm is as follows: Figure 1 As shown. The incision continuous robotic arm 1 is nested outside the concentric tube continuous robotic arm 3 and has two degrees of freedom. The extension and retraction of the two drive wires 2 enable the incision continuous robotic arm 1 to bend in the plane, and the rotational motion of the incision continuous robotic arm enables it to bend in any direction in space. The surgical instrument 6 passes through the central cavity of the concentric tube continuous robotic arm 3 and is fixed at its end. The concentric tube continuous robotic arm 3 consists of a straight tube 4 and a pre-bending section 5, and has two degrees of freedom. The feed range of the concentric tube continuous robotic arm 3 is from the position where the pre-bending section 5 coincides with the incision continuous robotic arm to the position where the straight tube 4 coincides with the incision continuous robotic arm.

[0058] like Figure 10 As shown, a control method for a composite continuum robotic arm includes the following steps:

[0059] S101: Considering frictional losses, analyze the tension transmission relationship of the driving wire nodes to obtain the tension distribution of the driving wire, and then the deformation drive of the equivalent flexible beam.

[0060] In this embodiment, as Figure 3 As shown, the nodes of drive wire 1 and drive wire 2 with the slit continuum are located on both sides of the threading hole of the rigid disk. Since the force analysis at each node is similar, ... Taking the node as an example, the tension of the driving wire friction support force The four forces are in equilibrium, as shown in equation (2).

[0061]

[0062] Where n is the number of the driving wire, n = 1, 2. i is the number of the flexible beam, i = 1, 2, ..., 14. Since the tension loss of the driving wire is only caused by friction, the following relationship can be obtained:

[0063]

[0064] Where μ is a constant coefficient of friction. For Nodes, establishing a local coordinate system as follows Figure 4 As shown, scalarizing the vector equation (2) yields:

[0065]

[0066] in For support With local coordinate system The included angle, The deflection angle of the driving wire is equal to the deflection angle of the driving wire at corresponding nodes on the two driving wires.

[0067] like Figure 5 and Figure 6 As shown, the two beams at any joint can be considered as a single beam, and a coordinate system is established. The deflection angle of the equivalent beam in the i-th segment is... For nodes Establish the following relationship.

[0068]

[0069] Where r i and z i The coordinates are in the coordinate system of the equivalent beam. It is the bending angle of the i-th flexible beam segment.

[0070] for Node, tension transmission coefficient is (direction in which the driving wire length decreases) or (Direction of increasing driving filament length), node With nodes The situation is similar. and The expression is shown in equation (7).

[0071]

[0072] Substituting equation (7) into equations (3) and (4) yields the tension transfer coefficient. or The expression.

[0073]

[0074] Where σ1 is used to simplify the tension transmission coefficient. and The symbol of the expression. The expression for σ1 is shown in (9).

[0075]

[0076] From the above formula, we can see that the tension transmission coefficient and It depends only on the deflection angle of the driving wire at the node and the direction of the driving wire's movement. When the driving wire moves in the positive direction (the direction in which the length of the driving wire decreases), the relationship between the driving wire tensions satisfies equation (10).

[0077]

[0078] When the driving wire moves in the opposite direction (the direction in which the length of the driving wire increases), in the formula... and Then replace with and From equation (10), we can obtain the vector relationship shown in equation (11).

[0079]

[0080] The force on the i-th flexible beam is F. i Considering the first i-th flexible beam segments as a whole, the force on the i-th flexible beam segment is the vector sum of all forces on the flexible beam segments from the i-th to the 14th, that is, the vector sum of the tension of the driving wire at the action node, F i The expression for is shown in equation (12).

[0081]

[0082] Substituting equation (11) into equation (12) and simplifying, we can obtain the force F at the end of the i-th flexible beam segment. iThe tension of the driving wire at the end node of the beam segment is shown in equation (13).

[0083]

[0084] Considering the general case where both driving wires on the continuum apply force, the force F acting at the end of the i-th segment of the flexible beam is... i The expression is shown in equation (14).

[0085]

[0086] When the tension acting on the beam end at the node is translated, bending moments in different directions will be generated. Since the torsional and shear stiffness of the beam in the continuum designed in this paper is much greater than its bending stiffness, the torsional and shear stiffness of the beam are not considered. Figure 6 As shown, the tension of the driving wire at the node is equivalent to the deformation drive at the end of the beam, and the force and torque on the end of the i-th flexible beam segment can be expressed as Equation (15).

[0087]

[0088] in It is the force that drives wire 1 to act on the i-th segment of the beam. This is the force exerted by the driving wire 2 on the i-th beam segment. Combining the previous equations, when the tension transmission coefficient is known, the force at the end of the i-th beam segment can be related to the initial tension applied to the driving wire. Therefore, the expressions for the force and torque acting on the end of the i-th beam segment include z. i r i Since there are two unknowns, the relationship between beam deformation and deformation driving force can be established by using a suitable beam model, thereby solving for z. i With r i .

[0089] S102: Perform static analysis on the cutting continuum robot arm, establish a static model using Euler-Bernoulli beam theory, and solve the static model using Taylor series expansion.

[0090] In this embodiment, the key to solving the motion of a flexible beam in a continuum under deformation-driven conditions lies in modeling the flexible beam structure. The displacement of each point in a flexible beam during bending is very small relative to the beam's dimensions and satisfies the assumptions and conditions of the Euler-Bernoulli beam theory. Therefore, this paper uses the Euler-Bernoulli beam theory to model the flexible beam. The beam is assumed to be initially a straight line, and the presence of pre-bending curvature is not considered. The constitutive equation of the Euler-Bernoulli beam is equation (17).

[0091]

[0092] In the formula, E is the Young's modulus of the material, I is the moment of inertia of the beam's cross-sectional area (I remains constant during beam bending), and point s is any point on the beam. Point s on the i-th beam relative to Z i The rotation angle of the shaft, M(s), is the bending moment acting on point s on the beam. F Zi F Ri It is the force acting on the end of the beam (s=L). M(s) can be expressed as equation (18).

[0093] M(s)=F Ri (z i (L)-z i (s))-F Zi (r i (L)-r i (s))+M i (17)

[0094] Where M i It is the initial bending moment acting on the beam. Substituting equation (17) into equation (16) yields:

[0095]

[0096] Differential equation (18) yields:

[0097]

[0098] Equation (19) is the characteristic equation of the Euler-Bernoulli beam theory. By analyzing the conditions when s = 0 and s = l, we can obtain the boundary conditions of the above differential equation, as shown in equation (20).

[0099]

[0100] Establish the bending angle at any point on each beam segment. The 3rd order Maclaurin series:

[0101]

[0102] According to equation (19), the following equation can be obtained:

[0103]

[0104] Differentiating equation (21) yields:

[0105]

[0106] Substituting equation (22) into equation (23), and combining it with the second boundary condition in equation (20), we can obtain the following about... The equation is:

[0107]

[0108] Simplify to get The expression:

[0109]

[0110] Substituting equation (25) into equation (21) yields θ. i The expression for (s):

[0111]

[0112] The coordinate r of the end of the i-th beam segment i z i It can be represented as:

[0113]

[0114] Combining equations (21), (25), and (27), we can obtain a result containing only r. i and z i Two equations with two unknowns can be used to solve for r. i and z i Then, substituting into equation (21) to solve for θ i (s).

[0115] S103: Based on static model data, the Kepler ellipse equation is used to fit the end trajectory of the cut continuum robot arm, and the relationship equation between the relative end coordinates of the concentric tube continuum robot arm is constructed.

[0116] In this embodiment, the coordinate system establishment and control parameters of the composite continuum robot are as follows: Figure 7 As shown, where L n It is the total length of the cutting continuum robotic arm, φ n It is the deflection angle of the cutting continuum robotic arm. L is the total bending angle of the slicing continuum robotic arm. t It is the feed length of the concentric tube continuum robotic arm, φ t It is the deflection angle of the concentric tube continuum robotic arm. The total bending angle of the concentric tube continuum robot arm is given by K, where K is the pre-bending curvature of the concentric tube continuum robot arm. The coordinates of the end effector of the cutting continuum robot arm in the basic coordinate system are (x...). M ,y M ,z M It can be seen that when the length of the cutting continuum robotic arm is constant, z M Only with bending angle Related. Using polynomial fitting for z. M and Relationship:

[0117] z M =a1θ n 8 +b1θ n 6 +c1θ n 4 +d1θ n 2 +e1 (28)

[0118] Where a1, b1, c1, d1, and e1 are obtained using the least squares method. For the slicing continuum robot arm, its workspace is a surface formed by rotating about the Z-axis:

[0119] F(x M ,y M ,z M )=0 (29)

[0120] The generatrix of a surface of revolution can be represented as:

[0121] G(r M ,z M )=0 (30)

[0122] The end effector trajectory of the robotic arm, which is a continuous cut surface, is fitted using Kepler elliptic curves, with the center point being C. i (z i ,r i The equation for the Keplerian ellipse can be expressed as:

[0123]

[0124] Where a, b, and c are the major radius, minor radius, and radius of symmetry of the Keplerian ellipse, respectively. Figure 8 As shown, taking segment P0P1 as an example, the Kepler fitting curve equation for segment P0P1 is:

[0125]

[0126] Where b can be obtained using the least squares method. When θ n <θ p1 r M The value of can be calculated using equation (21).

[0127]

[0128] The coordinates of the end effector of the concentric tube continuum robot arm in the relative coordinate system are: The coordinates of the end effector of the concentric tube continuum robot relative to the reference coordinate system {M}:

[0129]

[0130] Relative coordinates of a concentric tube continuum robotic arm Satisfy the following equation:

[0131]

[0132] S104: Based on matrix coordinate transformation, establish equations for the key parameters required to solve the control parameters and solve them iteratively, construct a set of control parameter equations to solve the control parameters of the composite continuum robot arm.

[0133] Rotation matrix between base coordinate system {B} and relative coordinate system {M} x can be used M ,y M ,z M and It means that P E Let P be the coordinate of the end of the composite continuum relative to the basic coordinate system {B}. M P E and The relationship between them can be represented as:

[0134]

[0135] Combining the above relationships, we can obtain:

[0136]

[0137] Relative coordinates of a concentric tube continuum robotic arm Satisfy the following equation:

[0138]

[0139] in Combining equations (28), (32), (37), and (38), we can obtain information about x. M The equation:

[0140] H(x M )=0 (39)

[0141] When P E (x E ,y E ,z E )and Given a value, use Newton's iteration method to solve for x. M Control parameter φ n L t φ t Solve using the following system of equations:

[0142]

[0143] Example 2

[0144] A composite continuous robot arm control system includes:

[0145] The tension distribution calculation module is configured to consider friction loss, analyze the tension transmission relationship of the drive wire nodes, obtain the tension distribution of the drive wire, and then the deformation drive of the equivalent flexible beam.

[0146] The static model building and solution module is configured to perform static analysis on the cut continuum manipulator, build the static model using Euler-Bernoulli beam theory, and solve the static model using Taylor series expansion.

[0147] The end-point trajectory module is configured to fit the end-point trajectory of the cut continuum robot arm based on static model data using the Kepler ellipse equation, and to construct the relationship equation between the relative end-point coordinates of the concentric tube continuum robot arm.

[0148] The control parameter solving module is configured to establish equations for the key parameters required to solve the control parameters based on matrix coordinate transformation and iteratively solve them, thereby constructing a set of control parameter equations to solve the control parameters of the composite continuum robot arm.

[0149] Example 3

[0150] A composite continuum robotic arm includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, they complete the steps in the method provided in Embodiment 1.

[0151] It may include the system provided in Embodiment 2.

[0152] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0153] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0154] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0155] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0156] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A control method for a composite continuum robotic arm, characterized in that, Includes the following steps: Considering frictional losses, the tension transmission relationship of the driving wire nodes is analyzed to obtain the tension distribution of the driving wire, and then the deformation driving of the equivalent flexible beam is obtained. Static analysis was performed on the slit continuum manipulator. A static model was established using Euler-Bernoulli beam theory, and the static model was solved using Taylor series expansion. Based on static model data, the Kepler ellipse equation is used to fit the end trajectory of the cut continuum robot arm, and the relationship equation between the relative end coordinates of the concentric tube continuum robot arm is constructed. Based on matrix coordinate transformation, equations for the key parameters required to solve the control parameters are established and solved iteratively. A set of control parameter equations is constructed to solve the control parameters of the composite continuum robot arm. Considering frictional losses, the process of analyzing the tension transmission relationship at the drive wire nodes and obtaining the tension distribution of the drive wire includes the balance between the drive wire tension, friction force, and support force at each node of the drive wire. Furthermore, the loss of tension in the drive wire is caused solely by friction. Establish local coordinate systems for each node and scalarize the forces to achieve mutual equilibrium. The two beams at any joint are equivalent to one beam, and a coordinate system is established to create an expression for the deflection angle of each equivalent beam. Add the tension transmission coefficient of the corresponding node. The tension transmission coefficient is only related to the deflection angle of the drive wire at the node and the direction of the drive wire movement, thereby establishing the relationship between the tension of the drive wire. No. i The force on the flexible beam segment is F. i , will go i The flexible beam segment is considered as a whole. i The force on the flexible beam segment is the vector sum of the tensions of the driving wires at the action nodes. Substituting this into the relationship between the tensions of the driving wires, we obtain the first... i The force F at the end of the flexible beam segment i To control the tension of the driving wire at the end node of the flexible beam, without considering the torsion and shear of the beam, the tension of the driving wire at the node is equivalent to the deformation drive at the end of the beam, forming the first... i Expressions for the forces and moments acting on the ends of a flexible beam segment; in The driving wire 1 acts on the first i Forces on the segment beam The driving wire 2 acts in the first i Forces on the segment beam F Zi , F Ri It is the force acting on the end of the flexible beam, of which M i It is the initial bending moment acting on the flexible beam; Static analysis of the cutting continuum manipulator was performed, and a static model was established using Euler-Bernoulli beam theory. The process of solving the static model using Taylor series expansion included: modeling the flexible beam using Euler-Bernoulli beam theory. ； The constitutive equations for an Euler-Bernoulli beam are: ； In the formula E It is the Young's modulus of the material. I It is the moment of inertia of the beam's cross-sectional area during the bending process of the flexible beam. I remain unchanged. s A point is any point on the flexible beam. It is the first i On a flexible beam s Point relative to Z i The rotation angle of the shaft, M(s) It is the point acting on the flexible beam s Bending moment, l For the end of the beam, we differentiate it to obtain the characteristic equation of the Euler-Bernoulli beam theory. After adding boundary conditions, we establish the third-order Maclaurin series of the bending angle at any point on each flexible beam segment and simplify it. We then establish the relationship between beam deformation and deformation driving through the beam model, and finally solve for the unknowns in the expression.

2. The composite continuum robot arm control method as described in claim 1, characterized in that, The process of fitting the end-effector trajectory of a robotic arm using the Kepler elliptic equation includes fitting the Z-coordinate and bending angle of the end-effector using a polynomial. θ n The relationship between the Z-coordinate and R-coordinate of the end of the cut continuum is fitted using the Kepler ellipse equation, simplifying the complex end trajectory into a mathematical model.

3. The composite continuous robot arm control method as described in claim 2, characterized in that, When the length of the slicing continuum robotic arm is constant, its end-effector Z-coordinate and bending angle are related. θ n The relationship is obtained through polynomial fitting, and the polynomial coefficients are determined by the least squares method. Alternatively, the major and minor radii of the Keplerian ellipse equation can be obtained by fitting the end-effector trajectory of the cut continuum using the least squares method.

4. The composite continuum robot arm control method as described in claim 1, characterized in that, The process of constructing the relational equation between the relative end-effector coordinates of the concentric tube continuum robot arm includes: combining the feed length, deflection angle, and pre-bending curvature of the concentric tube continuum robot arm to establish the mathematical relationship between the end-effector coordinates of the concentric tube and the end-effector coordinates of the cut continuum, wherein the end-effector coordinates of the concentric tube continuum robot arm are determined by its feed length. L t Deflection angle ϕ t and pre-bending curvature K Determine and satisfy the kinematic constraints of the concentric tube continuum manipulator.

5. The composite continuous robot arm control method as described in claim 1, characterized in that, Based on matrix coordinate transformation, the process of establishing equations for the key parameters required to solve the control parameters and solving them iteratively, and constructing a set of control parameter equations to solve the control parameters of the composite continuum manipulator includes: establishing the transformation relationship between the basic coordinate system and the relative coordinate system based on matrix coordinate transformation; using Newton's iteration method to solve the key parameter equations, and then solving the control parameters of the composite continuum manipulator, including the deflection angle of the slit continuum manipulator, and the feed length and deflection angle of the concentric tube continuum manipulator.

6. A composite continuous robotic arm control system, employing the method described in claim 1, characterized in that, include: The tension distribution calculation module is configured to consider friction loss, analyze the tension transmission relationship of the drive wire nodes, obtain the tension distribution of the drive wire, and then the deformation drive of the equivalent flexible beam. The static model building and solution module is configured to perform static analysis on the cut continuum manipulator, build the static model using Euler-Bernoulli beam theory, and solve the static model using Taylor series expansion. The end-point trajectory fitting module is configured to fit the end-point trajectory of the cut continuum robot arm based on static model data using the Kepler ellipse equation, and to construct the relationship equation between the coordinates of the concentric tube continuum robot arm and the end-point coordinates. The control parameter solving module is configured to establish equations for the key parameters required to solve the control parameters based on matrix coordinate transformation and iteratively solve them, thereby constructing a set of control parameter equations to solve the control parameters of the composite continuum robot arm.

7. A composite continuous robotic arm, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-5.

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