Flexible continuum manipulator and damped jacobian pseudo-inverse control method for manipulators

Abstract

The application discloses a flexible continuum manipulator and a damping Jacobian pseudo-inverse control method of the manipulator, and the method comprises the following steps: S1, a mapping relationship from a joint space to an operation space is established, and a homogeneous transformation matrix of an end relative to a reference coordinate system is obtained; S2, a mapping relationship from the joint space of the flexible continuum manipulator to a driving space is established; S3, a forward kinematics relationship from the driving space to the joint space is established; S4, a Jacobian matrix from the driving space to the operation space is established based on a chain rule; S5, a step factor and a damping factor initial value are set, and an improved damping least square Jacobian pseudo-inverse control model is established; S6, initial and final positions are differentiated by interpolation, and a driving space increment is iteratively solved; and S7, two flexible joints of the flexible continuum manipulator are controlled to reach a target position according to the driving space increment obtained by solving. On the basis of realizing high-precision control, the application avoids great changes of driving amount of the continuum manipulator at singular points.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control technology, and in particular to a flexible continuum robotic arm and a damped Jacobian pseudo-inverse control method for the robotic arm. Background Technology

[0002] Due to their unique structural characteristics, continuous robotic arms possess extremely high flexibility and environmental adaptability, enabling them to adapt to complex, narrow, and irregular working environments. They can achieve complex motion and posture adjustments, fulfilling the needs of complex path planning. Their highly redundant structure gives them near-infinite continuous deformation capabilities; under significant external forces, they can deform in the direction of the force and quickly recover after the force disappears, achieving flexible and safe operation. Their drive method is generally cable-driven, with the drive motors centrally located on a fixed base, allowing for a highly lightweight design with a simple mechanical structure while simultaneously enhancing the load-bearing capacity of the continuous robotic arm.

[0003] However, the continuous deformation characteristics of continuum manipulators increase the difficulty of modeling and control. Currently, researchers have proposed many methods for modeling continuum manipulators, among which the most widely used is the piecewise constant curvature assumption model, but it has not been analyzed, compared, or adaptively adjusted for actual systems. Due to the super-redundant structural characteristics of continuum manipulators, in the case of multiple joints, it is impossible to linearly describe the mapping relationship between the operation space and the drive space. Therefore, its control requires the design of corresponding optimized control models. Commonly used inverse kinematics control models include particle swarm optimization, Jacobi pseudo-inverse, and neural network-based control methods. However, particle swarm optimization is prone to getting trapped in local optima, and its convergence speed is affected by control accuracy. Jacobi pseudo-inverse is prone to severe jitter at singular points, and neural networks require a large amount of data for training and have poor generalization ability. Summary of the Invention

[0004] This invention provides a flexible continuum robotic arm and a damping Jacobian pseudo-inverse control method for the robotic arm to solve the technical problems mentioned in the background art.

[0005] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0006] This invention provides a damped Jacobian pseudo-inverse control method for a flexible continuum manipulator, comprising the following steps:

[0007] S1. Establish the mapping relationship from joint space to operation space under the constant curvature model, and obtain the homogeneous transformation matrix of the end effector of the continuum robot relative to the reference coordinate system.

[0008] S2. Based on the bending posture of the flexible continuum manipulator, establish the mapping relationship from the joint space to the drive space of the flexible continuum manipulator.

[0009] S3. Establish the positive kinematic relationship between the drive space and the joint space based on the mapping relationship between the joint space and the drive space of the flexible continuum robot arm.

[0010] S4. Establish the Jacobian matrix from the driving space to the operation space based on the chain rule;

[0011] S5. Set the initial values ​​of the step size factor and damping factor, and establish an improved damped least squares Jacobian pseudo-inverse control model based on the Jacobian matrix from the driving space to the operating space.

[0012] S6. The initial and final positions of the interpolation differentiation are determined iteratively based on the improved damped least squares Jacobi pseudo-inverse control model, the homogeneous transformation matrix of the end of the continuous manipulator relative to the reference coordinate system, and the positive kinematic relationship from the drive space to the joint space to solve the drive space increment.

[0013] S7. Based on the solved driving space increment, control the two flexible joints on the flexible continuum robot arm to reach the target position.

[0014] In another aspect, the present invention provides a flexible continuum robotic arm, controlled using the above-mentioned damped Jacobian pseudo-inverse control method, including:

[0015] The control mechanism includes a control box, two sets of first control units and second control units installed inside the control box;

[0016] The visual perception module is installed on the end face of the control box;

[0017] The flexible continuous arm includes two flexible joints: a first flexible joint mounted on the end face of the control box and a second flexible joint mounted on the first flexible joint. The first and second flexible joints are driven by two sets of first control units to realize the rotation and bending of the first and second flexible joints. Each set of first control units includes two first control units.

[0018] The end gripper, mounted on the second flexible joint, is driven by the second control unit to grasp the target object.

[0019] The beneficial effects of this invention are:

[0020] 1. This invention discloses a damped Jacobian pseudo-inverse control method for a flexible continuum manipulator, wherein the Jacobian matrix from the driving space to the operating space of the multi-joint continuum manipulator is established using the chain rule, which simplifies the model complexity and the difficulty of solving.

[0021] Furthermore, this invention sets a single-step amplitude and differentiates the initial and final positions based on the single-step amplitude interpolation. The initial and final positions are then divided into multiple process points. Between each process point, the step size factor and damping factor in the improved damped least squares Jacobi pseudo-inverse control model are dynamically adjusted based on error fluctuations. During the iteration process, while satisfying the control accuracy, it achieves smooth motion that avoids singularities.

[0022] 2. In another aspect, the present invention discloses a flexible continuum robotic arm, comprising two flexible joints, namely a first flexible joint and a second flexible joint. The flexible joints adopt an embedded double spring structure, and the bending posture conforms to the constant curvature model. The rigid material has high force transmission efficiency and rapid response; the linear range of force characteristics is large, the motion accuracy is high, and the load capacity is large. Attached Figure Description

[0023] Figure 1 This is a flowchart of the damped Jacobian pseudo-inverse control method in this invention;

[0024] Figure 2 This is a layout diagram of the coordinate systems on the second flexible joint in this invention;

[0025] Figure 3 This is a layout diagram of the coordinate systems of the two flexible joints in this invention;

[0026] Figure 4 This is a diagram showing the planar error results of the circular trajectory in the accuracy verification experiment of this invention embodiment;

[0027] Figure 5 This is a graph showing the axial error results of the circular trajectory in the accuracy verification experiment of this invention embodiment;

[0028] Figure 6 This is a diagram showing the planar error results of the square trajectory in the accuracy verification experiment of this invention embodiment;

[0029] Figure 7 This is a graph showing the axial error results of the square trajectory in the accuracy verification experiment of this invention embodiment;

[0030] Figure 8 This is a diagram showing the planar error results of the triangle trajectory in the accuracy verification experiment of this invention.

[0031] Figure 9 This is a graph showing the axial error results of the triangular trajectory in the accuracy verification experiment of this invention.

[0032] Figure 10 This is a schematic diagram of the flexible continuum robotic arm in this invention.

[0033] Explanation of reference numerals in the attached figures:

[0034] 1. Tension spring; 2. Compression spring; 3. Drive wheel; 4. Pulley block; 5. Drive rope; 6. First disk; 7. Second disk; 8. Third disk; 9. Threading hole; 10. End gripper. Detailed Implementation

[0035] To facilitate understanding of the present invention, a more complete description will be given below with reference to the accompanying drawings. Preferred embodiments of the invention are shown in the drawings. However, the invention can be implemented in many other different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a thorough and complete understanding of the disclosure of the invention.

[0036] It should be noted that when a component is referred to as being "fixed to" or "set on" another component, it can be directly on or indirectly on that other component. When a component is referred to as being "connected to" another component, it can be directly connected to or indirectly connected to that other component.

[0037] It should be understood that the terms "length", "width", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the present invention.

[0038] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0039] It should also be noted that in the embodiments of this application, the same reference numerals are used to represent the same component or part. For the same part in the embodiments of this application, the reference numerals may only be used to mark one part or component as an example in the figure. It should be understood that the reference numerals are also applicable to other identical parts or components.

[0040] Reference Figure 1This application provides a damping Jacobian pseudo-inverse control method for a flexible continuum manipulator. Specifically, this method is a control method for a flexible continuum manipulator. The flexible continuum manipulator has two sequentially connected flexible joints, each mainly comprising a tension spring 1 and a compression spring 2. The tension spring 1 is embedded in the center of the compression spring 2. One end of both springs is fixed to a second disk 7, and the other end is fixed to a first disk 6 and a third disk 8, forming an embedded double-spring structure. Compared to traditional flexible materials, the selected tension spring 1 and compression spring 2 are made of 45 steel, which has a high elastic modulus, low energy loss after deformation, and a faster response speed. Simultaneously, the regular helical structure of the springs can disperse external forces through uniform deformation, ensuring consistent deformation of each differential segment when the spring bends. These properties ensure that the flexible joint with the embedded double-spring structure satisfies the constant curvature model during bending deformation. The constant curvature model is a mathematical model where the shape of the bending deformation is an arc, and the deformation angle of each differential segment of the arc is the same.

[0041] The damped Jacobian pseudo-inverse control method includes the following steps:

[0042] S1. Establish the mapping relationship from joint space to operation space under the constant curvature model, and obtain the homogeneous transformation matrix of the end effector of the continuum robot relative to the reference coordinate system.

[0043] S2. Based on the bending posture of the flexible continuum manipulator, establish the mapping relationship from the joint space to the drive space of the flexible continuum manipulator.

[0044] S3. Establish the positive kinematic relationship between the drive space and the joint space based on the mapping relationship between the joint space and the drive space of the flexible continuum robot arm.

[0045] S4. Establish the Jacobian matrix from the driving space to the operation space based on the chain rule;

[0046] S5. Set the initial values ​​of the step size factor and damping factor, and establish an improved damped least squares Jacobian pseudo-inverse control model based on the Jacobian matrix from the driving space to the operating space.

[0047] S6. The initial and final positions of the interpolation differentiation are determined iteratively based on the improved damped least squares Jacobi pseudo-inverse control model, the homogeneous transformation matrix of the end of the continuous manipulator relative to the reference coordinate system, and the positive kinematic relationship from the drive space to the joint space to solve the drive space increment.

[0048] S7. Based on the solved driving space increment, control the two flexible joints on the flexible continuum robot arm to reach the target position.

[0049] This invention designs an improved damped least-squares Jacobian pseudo-inverse control model. The flexible joint with an embedded double-spring structure experiences more uniform force, making the deformation of each differential segment of the flexible joint tend to be consistent. The control system incorporates damping and step size factors that adaptively adjust with error fluctuations, achieving high-precision control while avoiding significant changes in the drive quantity of the continuous robotic arm at singular points, which could lead to control instability.

[0050] In some embodiments, refer to Figure 2 and Figure 3 S1 specifically includes the following steps:

[0051] S11. Establish the mapping relationship between joint space and operating space under the constant curvature model; the constant curvature model is a mathematical model in which the shape is arc when bending and deforming, and the deformation angle of each differential segment of the arc is the same.

[0052] S12. Based on the mapping relationship from joint space to operating space, establish the homogeneous transformation matrix T of the i-th flexible joint end relative to its own fixed coordinate system. i ;reference Figure 3 If it is the first flexible joint, its own fixed coordinate system is the coordinate system O1X1Y1Z1 established with the center of the second disk 7; if it is the second flexible joint, its own fixed coordinate system is the coordinate system O2X2Y2Z2 established with the center of the third disk 8.

[0053] S13, then based on the homogeneous transformation matrix T of the i-th flexible joint end relative to its own fixed coordinate system. i The homogeneous transformation matrix T of the end effector of the continuum robot relative to the reference coordinate system is obtained. q The reference coordinate system is the coordinate system O0X0Y0Z0 established with the center of the first disk 6; specifically as follows:

[0054]

[0055] Where n represents the total number of flexible joints within the flexible continuum manipulator. Since n = 2, the homogeneous transformation matrix T of the end effector of the continuum manipulator relative to the reference coordinate system is... q =T1@T2, where @ represents matrix multiplication.

[0056] In some embodiments, refer to Figure 2 The mapping relationship from joint space to operating space under the constant curvature model in S11 is as follows:

[0057]

[0058] Where, x i y i , z iθ represents the positional changes of the i-th flexible joint end-effector coordinate system relative to its own fixed coordinate system OXYZ on the x, y, and z axes, respectively. x θ y θ z θ represents the pose changes of the i-th flexible joint's end coordinate system relative to its fixed coordinate system OXYZ along the x, y, and z axes, respectively; ρ represents the bending radius of the tension spring 1 in the i-th flexible joint; θ i This represents the bending angle of tension spring 1 in the i-th flexible joint; represents the torsional angle of the i-th flexible joint relative to its own fixed coordinate system x-axis; · represents the dot product.

[0059] In some embodiments, the homogeneous transformation matrix T of the i-th flexible joint end relative to its own fixed coordinate system in S12 i The details are as follows:

[0060]

[0061] Where c represents the cosine function cos(.) and s represents the sine function sin(.).

[0062] In some embodiments, in the constant curvature model, the bending posture of the flexible joint is an arc shape, and the curvature of each differential segment is the same. Simultaneously, because the tension spring 2 in the embedded double-spring structure restricts the axial change of the flexible joint, the arc length formed by the spring contact point in the bending direction remains unchanged during bending deformation. Based on the assumption of continuous material deformation, the length changes of the drive rope 5 corresponding to the holes in the four directions can be obtained. Since the length changes of the ropes with relative to the center-symmetric holes are the same in magnitude but opposite in direction, they can be driven by the same motor. Therefore, each flexible joint is driven by two motors, and the continuous body manipulator is driven by four motors. The first flexible joint is closer to the reference coordinate system and its movement is controlled by drive quantities l1 and l2. The second flexible joint, connected sequentially, is controlled by drive quantities l3 and l4. However, since the drive rope 5 controlling the movement of the second joint passes through the first flexible joint, changes in the first flexible joint will affect changes in l3 and l4, requiring decoupling. Finally, the changes in the drive variables relative to the initial pose before bending deformation are obtained, i.e., the mapping relationship from the joint space to the drive space of the flexible continuous body manipulator, as follows:

[0063]

[0064] Where l1 and l2 are the driving variables of the two motors on the first flexible joint, respectively; l3 and l4 are the driving variables of the two motors on the second flexible joint, respectively; θ1, θ2 represents the bending angle and torsional angle of the first flexible joint, respectively. These are the bending angle and torsional angle of the second flexible joint, respectively. r1 is the radius of the compression spring 2, and r2 is the radius of the tension spring 1.

[0065] In some embodiments, the positive kinematic relationship from the drive space to the joint space is specifically as follows:

[0066]

[0067] In some embodiments, S4 specifically includes the following steps:

[0068] S41. Establish the mapping relationship from the driving space to the operation space through the chain rule. The specific mapping relationship from the driving space to the operation space is as follows:

[0069]

[0070] in, These represent the velocity changes in the operating space, joint space, and drive space, respectively; J qx J is the Jacobian matrix from joint space to operation space; lq The Jacobian matrix from the drive space to the joint space; Let be the Jacobian pseudo-inverse matrix from joint space to driving space;

[0071] S42. Solve for the Jacobian matrix J from joint space to operation space using the mapping relationship from driving space to operation space. qx And the Jacobian pseudo-inverse matrix from joint space to drive space

[0072] S43. The Jacobian matrix J that maps joint space to operation space. qx And the Jacobian pseudo-inverse matrix from joint space to drive space Performing a dot product yields the Jacobian matrix J from the driving space to the operating space. lx The specific formula is as follows:

[0073]

[0074] In some embodiments, S5 specifically includes the following steps:

[0075] S51. Set the initial values ​​for the step size factor and damping factor;

[0076] S52, Based on the Jacobian matrix J from the driving space to the operating space lx An improved damped least squares Jacobian pseudo-inverse control model is established to solve for the drive space increment corresponding to each process point. The specific details of the improved damped least squares Jacobian pseudo-inverse control model are as follows:

[0077]

[0078] Where α is the step size factor, λ is the damping factor, I is the identity matrix, Δx is the operation space increment, i.e., the motion increment of the end effector gripper 10 on the flexible continuum robot arm; Δl is the drive space increment, i.e., the change in the rotation angle of the four motors on the two flexible joints; and T is the transpose of the matrix.

[0079] In some embodiments, S6 specifically includes the following steps:

[0080] S61. Introduce the ClampMag method and set the single-step amplitude; then, based on the single-step amplitude, perform interpolation differentiation on the initial and final positions of the flexible continuum robot to obtain multiple process points;

[0081] S62. The two flexible joints on the flexible continuum manipulator are solved by the improved damped least squares Jacobi pseudo-inverse control model to determine the required drive space increment to move to the next process point. Then, based on the drive space increment, the homogeneous transformation matrix of the end of the continuum manipulator relative to the reference coordinate system, and the forward kinematic relationship from the drive space to the joint space, the position of the end gripper 10 of the flexible continuum manipulator after motion is determined.

[0082] S63. Calculate the error Xd between the position of the end effector gripper 10 of the flexible continuous manipulator after motion and the target position. Calculate the error difference between the error between the position of the end effector gripper 10 of the flexible continuous manipulator after motion and the set error Xc. ε ;

[0083] S64. Based on the error difference between the position of the end effector gripper 10 of the flexible continuous robotic arm after motion and the target position, and the set error. ε The step size factor and damping factor are dynamically adjusted.

[0084] S65, repeat S62 to S64, iteratively solve the driving space increment for each process point.

[0085] In the improved damped least squares Jacobi pseudo-inverse control model, the damping factor enhances numerical stability, especially when the Jacobi matrix approaches singularities. The damping term allows the continuum manipulator to smoothly traverse singularities. However, an excessively small damping factor λ cannot effectively suppress singularities, potentially preventing a stable and smooth transition at singularities. Conversely, an excessively large damping factor λ reduces convergence speed, leading to slow end effector response. The step size factor primarily controls the magnitude of the update increment. Multiplying the step size factor by the motion increment obtained from the pseudo-inverse control model means only the portion of the motion increment at that moment is used as the actual motion step size, thus improving the accuracy of the motion increment. A larger step size factor results in a larger update increment, accelerating convergence but potentially causing system instability or oscillations; a smaller step size factor increases stability and improves convergence accuracy but may slow down convergence.

[0086] To balance control stability and accuracy, the designed improved damped least squares Jacobi pseudo-inverse control model adaptively adjusts the step size factor and damping factor based on error fluctuations to improve motion stability while maintaining control accuracy. Specifically, it sets two adjustment states for the step size factor and damping factor based on the error accuracy at each interpolation position (i.e., process point). Before each iteration, it checks if the current error is less than a set error value. When the distance to the interpolation position is far, i.e., the error is greater than the set error value, a larger step size factor and damping factor are set to achieve rapid approximation. After the current error is less than the set error value, the step size factor and damping factor are adjusted to smaller values. Simultaneously, dynamic adjustments are made based on the fluctuation amplitude and direction of the error, according to a certain mapping relationship. Specifically, when the error increases, the step size factor and damping factor change proportionally; when the error decreases and the decrease reaches more than half, the step size factor and damping factor are adjusted to 0.8 times their previous value.

[0087] The damping factor and step size factor are adaptively adjusted based on the error value. The end effector motion increment is obtained through iterative solution. Finally, the continuous robot is controlled to reach the target position based on the obtained drive increment. If no stable solution is found after the maximum number of iterations, the initial values ​​of the step size factor and damping factor need to be reset. Ultimately, the motion stability of the continuous robot arm is achieved while meeting the control accuracy requirements.

[0088] The technical results of the above solution are described in detail below based on two flexible joint continuous manipulators. The main geometric parameters of the continuous manipulators are as follows: l = 80 mm; r1 = 16 mm; r2 = 4 mm; The solution of the present invention is analyzed using three trajectory tracking methods as shown in the table.

[0089] Table 1: Data set for three trajectories in the accuracy verification experiment;

[0090] Trajectory parameters radius r = 100mm Side length a = 70mm Side length b = 170mm RMSE error 0.07mm 0.015mm 0.036mm Maximum error 2.1mm 1.75mm 1.85mm accuracy 0.088％ 0.019％ 0.045％

[0091] Table 1 shows the trajectory parameters, root mean square error (Z-axis direction), maximum error, and accuracy set in the accuracy verification experiment. Specifically, the circular trajectory has a radius of 100mm, a root mean square error of 0.07mm, a maximum error of 2.1mm, and an accuracy (RMSE ratio to the length of the continuous robotic arm) of 0.088%; the square trajectory has a side length of 70mm, a root mean square error of 0.015mm, a maximum error of 1.75mm, and an accuracy (RMSE ratio to the length of the continuous robotic arm) of 0.019%; and the triangular trajectory has a side length of 170mm, a root mean square error of 0.036mm, a maximum error of 1.85mm, and an accuracy (RMSE ratio to the length of the continuous robotic arm) of 0.045%. Here, RMSE represents the root mean square error.

[0092] Experimental results are as follows Figures 4 to 9 As shown, the dashed line represents the desired trajectory, and the solid line represents the actual trajectory. By comparing the tracking errors under different trajectories, the maximum error occurs in the Z-axis direction, with a maximum value of less than 2.5 mm. It can be seen that the experimental results meet the control requirements of various trajectories very well, proving that the proposed control method can effectively improve the control accuracy.

[0093] Reference Figure 10 In another aspect, the present invention provides a flexible continuum robotic arm, controlled using the above-mentioned damped Jacobian pseudo-inverse control method, including:

[0094] The control mechanism includes a control box, two sets of first control units and second control units installed inside the control box;

[0095] The visual perception module is installed on the end face of the control box;

[0096] The flexible continuous arm includes two flexible joints: a first flexible joint mounted on the end face of the control box and a second flexible joint mounted on the first flexible joint. The first and second flexible joints are driven by two sets of first control units to realize the rotation and bending of the first and second flexible joints. Each set of first control units includes two first control units.

[0097] The end gripper 10 is mounted on the second flexible joint and driven by the second control unit to grasp the target object.

[0098] The flexible continuum robotic arm disclosed in this invention is similar to the underactuated flexible continuum robotic arm CN118769296A (hereinafter referred to as the reference document). The only difference is that the inventor has optimized the driving method and the structure of the first flexible joint and the second flexible joint in the reference document. Specifically, the difference in the driving method is that the first flexible joint and the second flexible joint in the reference document are driven by three first control modules, and each first control module in the reference document includes a motor, that is, the first flexible joint and the second flexible joint in the reference document are driven by three motors; while in this application, the first flexible joint and the second flexible joint are driven by four first control units, and the four first control units are paired up to drive the first flexible joint and the second flexible joint respectively, that is, the first flexible joint and the second flexible joint are both driven by two first control units; the structure of one of the first control units on the first flexible joint is described below;

[0099] Specifically, the first control unit includes a motor, a drive wheel 3, three pulley groups 4, and two drive ropes 5: the three pulley groups 4 are the first pulley group to the third pulley group respectively; wherein the second pulley group is located between the first pulley group and the third pulley group;

[0100] The motor is mounted inside the control box via a motor support frame; the drive wheel 3 is fixedly mounted on the output shaft of the motor; the first disk 6, the second disk 7, and the third disk 8 each have four wire holes 9 arranged in a square shape, and two pulley groups 4 are symmetrically installed inside the control box; one end of one drive rope 5 is fixed in one wire hole 9 on the second disk 7, and the other end passes through the wire holes 9 on the first disk 6, around the first and second pulley groups, and is fixed to one side of the drive wheel 3; one end of another drive rope 5 is fixed in another wire hole 9 on the second disk 7, and the other end passes through the wire holes 9 on the first disk 6, around the third disk 8 and the second pulley group, and is fixed to the other side of the drive wheel 3; and the two drive ropes 5 are fixedly connected to the two farthest wire holes 9 on the second disk 7 (on the opposite diagonal of the square).

[0101] The structure of the other first control unit on the first flexible joint is the same as that of the first control unit described above. The only difference is that the two drive ropes 5 are fixedly connected to the other two wire holes 9 of the second disk 7, and the two drive ropes 5 also pass through the other two wire holes 9 of the first disk 6 and are finally connected to the drive wheel 3.

[0102] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A damped Jacobian pseudo-inverse control method for a flexible continuum robotic arm, characterized in that, Includes the following steps: S1. Establish the mapping relationship from joint space to operation space under the constant curvature model, and obtain the homogeneous transformation matrix of the end effector of the continuum robot relative to the reference coordinate system. S2. Based on the bending posture of the flexible continuum manipulator, establish the mapping relationship from the joint space to the drive space of the flexible continuum manipulator. S3. Establish the positive kinematic relationship between the drive space and the joint space based on the mapping relationship between the joint space and the drive space of the flexible continuum robot arm. S4. Establish the Jacobian matrix from the driving space to the operation space based on the chain rule; S5. Set the initial values ​​of the step size factor and damping factor, and establish an improved damped least squares Jacobian pseudo-inverse control model based on the Jacobian matrix from the driving space to the operating space. S6. The initial and final positions of the interpolation differentiation are determined iteratively based on the improved damped least squares Jacobi pseudo-inverse control model, the homogeneous transformation matrix of the end of the continuous manipulator relative to the reference coordinate system, and the positive kinematic relationship from the drive space to the joint space to solve the drive space increment. S7. Based on the solved driving space increment, control the two flexible joints on the flexible continuum robot arm to reach the target position. S1 specifically includes the following steps: S11. Establish the mapping relationship between joint space and operating space under the constant curvature model; the constant curvature model is a mathematical model in which the shape is an arc when bending and deforming, and the deformation angle of each differential segment of the arc is the same. S12. Establish the first step based on the mapping relationship from joint space to operation space. Homogeneous transformation matrix of the end of a flexible joint relative to its own fixed coordinate system If it is the first flexible joint, its own fixed coordinate system is the coordinate system established with the center of the second disk; if it is the second flexible joint, its own fixed coordinate system is the coordinate system established with the center of the third disk. S13, then according to the first Homogeneous transformation matrix of the end of a flexible joint relative to its own fixed coordinate system The homogeneous transformation matrix of the end effector of the continuum robot relative to the reference coordinate system is obtained. The reference coordinate system is the coordinate system established with the center of the first disk; specifically as follows: in, n This represents the total number of flexible joints within a flexible continuum robotic arm. The mapping relationship from joint space to operating space under the constant curvature model in S11 is as follows: in, They represent the first i The coordinate system of the flexible joint end face relative to its own fixed coordinate system x , y , z Changes in position of the three axes The first i The coordinate system of the flexible joint end effector relative to its own fixed coordinate system x , y , z Three-axis pose changes; Indicates the first i The bending radius of the tension spring in a flexible joint; Indicates the first i The bending angle of the tension spring in a flexible joint; Indicates the first i A flexible joint relative to its own fixed coordinate system x The angle of torsion of the shaft; This indicates dot product.

2. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 1, characterized in that, The S12 in Homogeneous transformation matrix of the end of a flexible joint relative to its own fixed coordinate system The details are as follows: in, Let s denote the cosine function cos(.), and let s denote the sine function sin(.).

3. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 2, characterized in that, The mapping relationship from the joint space to the drive space of the flexible continuum robotic arm is as follows: in, These are the driving variables for the two motors on the first flexible joint; These are the driving variables for the two motors on the second flexible joint, respectively. These represent the bending angle and torsional angle of the first flexible joint, respectively. These represent the bending angle and torsional angle of the second flexible joint, respectively. The radius of the compression spring, The radius of the tension spring.

4. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 3, characterized in that, The specific positive kinematic relationship from the drive space to the joint space is as follows: 。 5. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 4, characterized in that, S4 specifically includes the following steps: S41. Establish the mapping relationship from the driving space to the operation space through the chain rule. The specific mapping relationship from the driving space to the operation space is as follows: in, These are the velocity changes in the operating space, joint space, and drive space, respectively. Let be the Jacobian matrix from joint space to operation space; The Jacobian matrix from the drive space to the joint space; Let be the Jacobian pseudo-inverse matrix from joint space to driving space; S42. Solve for the Jacobian matrix from joint space to operation space using the mapping relationship from driving space to operation space. And the Jacobian pseudo-inverse matrix from joint space to drive space ; S43. Jacobian matrix for translating joint space to operand space. And the Jacobian pseudo-inverse matrix from joint space to drive space Performing a dot product yields the Jacobian matrix from the driving space to the operating space. The specific formula is as follows: 。 6. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 5, characterized in that, S5 specifically includes the following steps: S51. Set the initial values ​​for the step size factor and damping factor; S52, Based on the Jacobian matrix from the driving space to the operating space An improved damped least squares Jacobian pseudo-inverse control model is established to solve for the drive space increment corresponding to each process point. The specific details of the improved damped least squares Jacobian pseudo-inverse control model are as follows: in, Step size factor The damping factor, It is the identity matrix. This refers to the increment of the operating space, i.e., the increment of motion of the end effector gripper on the flexible continuum robotic arm. To drive the spatial increment, that is, the change in the rotation angle of the four motors on the two flexible joints; T This is the transpose of the matrix.

7. The damping Jacobian pseudo-inverse control method for a flexible continuum manipulator according to claim 6, characterized in that, S6 specifically includes the following steps: S61. Introduce the ClampMag method and set the single-step amplitude value; then, based on the single-step amplitude value, perform interpolation differentiation on the initial and final positions of the flexible continuum robot to obtain multiple process points; S62. The two flexible joints on the flexible continuum manipulator are solved by the improved damped least squares Jacobi pseudo-inverse control model to find the drive space increment required to move to the next process point. Then, based on the incremental drive space, the homogeneous transformation matrix of the end of the continuous manipulator relative to the reference coordinate system, and the positive kinematic relationship from the drive space to the joint space, the position of the gripper at the end of the flexible continuous manipulator after motion is solved. S63. Calculate the error Xd between the position of the end effector gripper of the flexible continuous manipulator after motion and the target position. Calculate the error difference between the error between the position of the end effector gripper of the flexible continuous manipulator after motion and the set error Xc. ; S64. Based on the error difference between the position of the end effector gripper of the flexible continuous robotic arm after motion and the target position, and the set error. The step size factor and damping factor are dynamically adjusted. S65, repeat S62 to S64, iteratively solve the driving space increment for each process point.

8. A flexible continuous robotic arm, characterized in that, Controlling using the damped Jacobian pseudo-inverse control method according to any one of claims 1 to 7 includes: The control mechanism includes a control box, two sets of first control units and second control units installed inside the control box; The visual perception module is installed on the end face of the control box; The flexible continuous arm includes two flexible joints: a first flexible joint mounted on the end face of the control box and a second flexible joint mounted on the first flexible joint. The first and second flexible joints are driven by two sets of first control units to realize the rotation and bending of the first and second flexible joints. Each set of first control units includes two first control units. The end gripper, mounted on the second flexible joint, is driven by the second control unit to grasp the target object.

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