A stiffness control and compensation method for continuum robots

Abstract

The present invention provides a method for stiffness control and compensation of a continuum robot, comprising: constructing a kinematic model of the continuum robot, the kinematic model being used to provide information on the length variation of the continuum robot's drive rope; constructing a stiffness model of the continuum robot's manipulator arm based on the kinematic model; obtaining a rope stiffness model based on the manipulator arm stiffness model; and adjusting the rope tension using the rope stiffness model to achieve stiffness control and compensation for the continuum robot. This method can adjust the robot's overall stiffness without the need for an external stiffness adjustment device, evaluate the manipulator arm's stiffness adjustment strategy in real time, and improve the robot's overall stiffness and positioning accuracy. The modeling method is applicable to various types of rope-driven parallel robots and exhibits high generalization capabilities.

Description

Technical Field

[0001] The invention belongs to the technical field of rope-driven continuum robot control, and in particular relates to a stiffness control and compensation method for a continuum robot. Background Art

[0002] To operate within confined spaces, slender structures with large length-to-diameter ratios are typically employed, resulting in low stiffness for robotic arms. These arms can adjust their shape to deliver specialized end-effectors (such as grippers and grinders) deep within infrastructure. However, because continuum robots are designed with very small diameters and lengths, the system stiffness is very low, making it difficult to meet practical requirements. For example, a small, flexible, tether-driven continuum robot was constructed for endoscopic navigation operations in medical applications. However, its low stiffness makes it difficult to perform high-precision operations. Furthermore, a series of continuum robots have been developed for endoscopic operations such as aircraft engine maintenance and nuclear power plant overhaul. Because continuum robots are driven by tethers, the stiffness of the system is significantly affected. As can be seen from the above cases, given the growing demand for high-precision inspection and operation in high-value infrastructure, there is an urgent need to improve the precision of robots operating in confined spaces (such as abdominal surgery and engine combustion chamber maintenance). There is an urgent need to adopt stiffness adjustment strategies to enhance the operational accuracy of such specialized robotic systems.

[0003] The patent "Actively Variable Stiffness Underactuated Redundant Robot Based on Joint Stiffness Amplification Device" (Application Number: CN202111345876.6) designs an actively variable stiffness redundant robot in conjunction with a drive mechanism and a stiffness amplification device. Stiffness-adjusting amplification devices are installed on the robot arm and the drive end to adjust the stiffness of the rope. This complex structure makes it difficult to apply to continuum robots with slender structures, such as those used in minimally invasive surgery. Furthermore, due to the influence of the robot arm's own weight, the tension required to drive the rope in different configurations varies. This device does not consider the influence of the robot arm's own weight on the rope tension in different configurations, resulting in poor stiffness adjustment.

[0004] The patent "Decoupling Control Method for Rope-Driven Parallel Variable-Stiffness Robot Joints" (Application Number: 202210241367.7) proposes a variable stiffness device. A permanent magnet variable stiffness device is connected to the rope that drives the robot to adjust the robot's stiffness. The drive motor compensates for the deformation of the variable stiffness module and the change in rope length. However, because the permanent magnet variable stiffness device consists of two magnets, one above the other, it is susceptible to interference from other magnetic fields, causing deviations in its stiffness adjustment and affecting the robot's end-point accuracy.

[0005] From the above content, it can be seen that the current stiffness adjustment method of most rope-driven robots is to add an elastic element to the mechanism and use the elastic deformation of the elastic element to achieve the variable stiffness capability of the robot arm. It has the characteristics of complex structure and it is difficult to fully consider the influence of friction and gravity on the stiffness of the robot arm. Summary of the Invention

[0006] To solve the above technical problems, the present invention proposes a stiffness control and compensation method for a continuum robot. By decoupling the stiffness of the manipulator arm, the stiffness of the manipulator arm is divided into joint stiffness and rope stiffness. The influence of rope friction and manipulator arm gravity on rope stiffness under different postures is fully considered, and a new high-precision comprehensive stiffness adjustment strategy is developed. The stiffness of the manipulator arm is adjusted without adding other elastic elements. The strategy has the characteristics of simple structure and high generalization ability. The stiffness of the manipulator arm is adjusted in real time by adjusting the stiffness of the rope, which can significantly improve the stiffness of the manipulator arm.

[0007] To achieve the above objectives, the present invention provides a stiffness control and compensation method for a continuum robot, comprising:

[0008] Constructing a kinematic model of the continuum robot, wherein the kinematic model is used to provide a change in the length of a driving rope of the continuum robot;

[0009] Based on the kinematic model, constructing a static model of the continuum robot;

[0010] Based on the statics model, a stiffness model of the manipulator arm of the continuum robot is constructed. Based on the stiffness model of the manipulator arm, the stiffness model of the rope is obtained. The tension of the rope is adjusted by the stiffness model to complete the stiffness control and compensation of the continuum robot.

[0011] Optionally, constructing the kinematic model of the continuum robot includes:

[0012] Obtaining trajectory planning of the continuum robot;

[0013] Based on the trajectory planning, obtaining the joint angle change driving the joint movement;

[0014] Based on the changes in the joint angles, a kinematic model of the continuum robot is established.

[0015] Optionally, constructing a statics model of the continuum robot includes:

[0016] Based on the kinematic model, obtaining a sub-model of a driving rope length change under different configurations of the continuum robot;

[0017] Static modeling is performed on the continuum robot based on the driving rope length change sub-model to obtain the static model.

[0018] Optionally, the statics model includes: a friction sub-model, a gravity sub-model and an additional force resultant sub-model.

[0019] Optionally, the kinematic model is:

[0020]

[0021] in, is the i-th joint coordinate system O i In the i-1th joint coordinate system O i-1 The homogeneous transformation matrix in , i is the i-th joint of the robotic arm, i = 1, 2, ...10.

[0022] Optionally, the driving rope length change sub-model is:

[0023]

[0024] Among them, l i,j is the i-th joint, the length of the j-th rope, m is the number of joints, l m,j To drive the rope in the local coordinate system {O i} and {O i+1} position vector.

[0025] Optionally, the statics model is:

[0026]

[0027] in, is the driving force of the jth rope of the i-th joint, is the normal pressure of the jth rope at the i+1th joint, is the force on the central support of each joint i, F i is the force applied to the i-th joint, M i is the torque applied to the i-th joint, is the position vector from the center of the i-th joint universal joint to the fixed point of the j-th rope of the i-th joint, is the position vector from the center of the universal joint of the i-th joint to the fixed point of the j-th cable of the i+1-th joint.

[0028] Optionally, the friction sub-model is:

[0029]

[0030] in, The driving force provided to the motor; is the force acting on the rigid disk of the ith joint, is the friction force of the entire drive rope from the drive side to the robot arm side;

[0031] The graviton model is:

[0032]

[0033] Among them, G i,lower is the gravity vector of the lower part of the i-th 2-DoF joint, G i,upper is the gravity vector on the upper part of the i-th 2-DoF joint, m i,lower and m i,upper are the masses of the lower and upper parts of the i-th 2-DoF joint, respectively, and g is the gravitational constant;

[0034] The resultant sub-model of the additional force generated by the driving rope is:

[0035]

[0036] in, is the resultant force of the rope driving the i-th joint, is the tension of the first driving cable of the i-th joint, is the tension of the second driving cable of the i-th joint, is the tension of the third driving cable of the i-th joint.

[0037] Optionally, the mechanical arm stiffness model is:

[0038]

[0039] Among them, W i is the static model of the i-th joint, s i is the rotation pose vector of the i-th joint, K i is the stiffness matrix of the 2-DoF joint, K i,1 is the rope stiffness model, K i,2 is the structural stiffness, f i is the driving force matrix composed of three ropes, is the Jacobian matrix of the i-th joint;

[0040] The rope stiffness model is:

[0041]

[0042] Among them, k i,1 ,k i,2 and k i,3 are the stiffness of the three driving ropes, J iis the Jacobian matrix of the i-th joint rope.

[0043] Compared with the prior art, the present invention has the following advantages and technical effects:

[0044] This paper presents the first attempt to adjust the stiffness of a continuum manipulator by adjusting the tension of the drive cables. This approach provides a convenient and efficient method for adjusting the stiffness of long continuum robots (composed of modular sections and multiple drive cables). Using the proposed cable tension adjustment algorithm, the additional force required to increase the drive cable tension can be calculated under different system configurations and external loads without affecting system equilibrium.

[0045] 2. This paper proposes a comprehensive statics model for the continuum robot. This model consists of modeling friction (i.e., the drive cable with the guide system), the induced net force (caused by the controlled tension of the drive cable), and an updated stiffness model (accounting for both the stiffness and tension of the drive cable). This improved statics model enables the prediction of the continuum robot's deformed shape and the evaluation of developed tension control strategies.

[0046] 3. In order to develop the driving cable tension adjustment algorithm, a comprehensive statics model including friction, external load and gravity is proposed. By controlling the tension of the three ropes that drive the joint movement, the influence of gravity and friction on the stiffness of the manipulator arm can be compensated in real time, thereby improving the accuracy of the stiffness control algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0048] Figure 1 Schematic diagram of a flow chart of a stiffness control and compensation method for a continuum robot according to an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram of the structure of a continuum robot according to an embodiment of the present invention;

[0050] Figure 3 Schematic diagram of the kinematic model of a continuum robot according to an embodiment of the present invention;

[0051] Figure 4 Schematic diagram of a static model of a continuum robot according to an embodiment of the present invention;

[0052] Figure 5 Schematic diagram of the external load sub-model of the continuum robot according to an embodiment of the present invention. DETAILED DESCRIPTION

[0053] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0054] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0055] Example

[0056] This embodiment provides a stiffness control and compensation method for a continuum robot, including:

[0057] Constructing a kinematic model of the continuum robot, wherein the kinematic model is used to provide a change in the length of a driving rope of the continuum robot;

[0058] Based on the kinematic model, constructing a static model of the continuum robot;

[0059] Based on the statics model, a stiffness model of the manipulator arm of the continuum robot is constructed. Based on the stiffness model of the manipulator arm, the stiffness model of the rope is obtained. The tension of the rope is adjusted by the stiffness model to complete the stiffness control and compensation of the continuum robot.

[0060] Furthermore, constructing the kinematic model of the continuum robot includes:

[0061] Obtaining trajectory planning of the continuum robot;

[0062] Based on the trajectory planning, obtaining the joint angle change driving the joint movement;

[0063] Based on the changes in the joint angles, a kinematic model of the continuum robot is established.

[0064] Furthermore, constructing the statics model of the continuum robot includes:

[0065] Based on the kinematic model, obtaining a sub-model of a driving rope length change under different configurations of the continuum robot;

[0066] Static modeling is performed on the continuum robot based on the driving rope length change sub-model to obtain the static model.

[0067] Furthermore, the statics model includes: a friction sub-model, a gravity sub-model and an additional force resultant sub-model.

[0068] The present embodiment will be described in further detail below with reference to the accompanying drawings. Figure 1 As can be seen from the stiffness control flow chart in the figure, trajectory planning is first used to calculate the joint angle of the driving joint motion. Then, the change in the length of the driving space rope is calculated through the kinematic model to establish the static model of the system. The influence of the parasitic load of the driving rope and the change in the joint angle caused by the deadweight of the manipulator on the stiffness of the robot is fully considered. The stiffness model of the system is established, and the comprehensive stiffness of the manipulator is decomposed into structural stiffness and rope stiffness. The developed rope stiffness adjustment algorithm is used to adjust the stiffness of the rope in real time, predict the actual deformation of the manipulator, adjust and compensate for the overall stiffness of the manipulator, and improve the accuracy of the robot. The rope stiffness adjustment algorithm refers to the change in the rope tension caused by the end load, which leads to the change in the rope stiffness. According to Hooke's law, the rope change caused by the change in rope stiffness can be compensated, thereby improving the end position accuracy of the manipulator.

[0069] The overall stiffness adjustment strategy of this embodiment is to construct a robot stiffness model based on the statics model of the continuum robot. The robot stiffness model can be divided into two parts: the structural stiffness of the manipulator arm and the stiffness of the flexible rope. Compared to the structural stiffness of the manipulator arm, the stiffness of the flexible rope is smaller, and the stiffness of the manipulator arm is primarily affected by the stiffness of the flexible rope, which is elastic. Therefore, to adjust the overall stiffness of the robot, simply adjust the rope tension, thereby adjusting the rope stiffness and thus improving the overall stiffness of the manipulator arm. This method can meet the needs of different environments. For example, when the robot is performing high-precision operations, adjusting the rope stiffness can improve the robot's overall stiffness. Conversely, to improve the interaction between the human and the robot, or between the robot and the environment, adjusting the rope tension can reduce the stiffness of the manipulator arm.

[0070] The specific implementation steps of the stiffness control and compensation method of a continuum robot proposed in this embodiment are as follows:

[0071] Step 1: Establish the kinematic model of the robot to obtain the change of the driving rope length under different configurations of the given continuum robot. The structure of the continuum robot is as follows: Figure 2 shown.

[0072] Combined with attachment Figure 3 The kinematic model of the robot is established. According to the working principle and structural design (taking a continuum robot with 20 degrees of freedom as an example), 10 local coordinate systems ({O i}, i=1,2,...,10) are built on the bottom of 10 2-DoF joints to define their shape changes. Specifically, the i,j} to {O i,j+1} is defined as follows: First, {O i,j} means moving from its origin to O i,j to O i,j+1 , along Z ij Axis moves; then {O ij Around Y i,j+1 Axis rotation θ ij Angle. Therefore, the homogeneous transformation matrix can be expressed as:

[0073]

[0074] where R X (θ i,j ) is from {O i,j+1}Coordinate system around Y i,j+1 Axis rotation θ ij The rotation matrix generated by the angle, D i,j Is from {O i,j}O ij to O i,j+1 Since universal joints are usually used as rotation joints when constructing continuum robots, it can be further expressed as rotating around two orthogonal axes θ i,1 and θ i,2 The rotation matrix of the angle is as follows:

[0075]

[0076] Among them, T z (l i,1 ) and T z (l i,2 ) is along the coordinate system {O i}'s z-axis is translated by l i,1 and l i,2 The transformation matrix of i,1 and l i,2 are the lengths of the rigid axes of the upper and lower platforms respectively. x (π / 2) and T x (-π / 2) are the transformation matrices for rotating π2 and -π / 2 along the x-axis respectively. y (π / 2) and T z (-π2) is defined as the rotation transformation matrix around the y-axis and the z-axis respectively. z (θ i,1 ) and T z (θ i,2 ) are defined as the rotation θ around the cross-joint axis. i,1 and θ i,2 The transformation matrix.

[0077] By substituting the parameters into the equation, the rotation matrix R(θ i,1 ,θ i,2 ) and position vector P(θi,1 ,θ i,2 ) can be expressed as:

[0078]

[0079] Among them, sθ=sinθ, cθ=cosθ is a concise expression of trigonometric functions.

[0080] After obtaining the explicit expression of the transformation matrix of the i-th segment of the continuum robot, the entire kinematic model of the multi-segment continuum can be established by multiplying the 10 segment transformation matrices.

[0081]

[0082] To drive the shape change of the i-th 2-DoF joint (i.e., the rotation angle θ i,1 and θ i,2 ), the length of the driving rope needs to be calculated based on the inverse kinematics of the system. The closed-loop vector of the j-th rope of the i-th 2-DoF joint can be expressed as:

[0083] l i,j =R(θ i,1 ,θ i,2 )(l i,2 +r i,j )+l i,1 -b i,j

[0084] where l i,j is the position vector of the driving rope in the manipulator coordinate system {O}; l i,1 and l i,2 are the position vectors of the upper and lower rigid axes in their coordinate systems; r i,j Yes i b is the position vector of the rope fixing point in the coordinate system moving platform; i,j The rope fixing point is i} Position vector on the static platform in the coordinate system.

[0085] Since there are two actuation strategies for the design of continuum robots with multiple 2-DoF joints: coupling (i.e., Sections 1–7) and decoupling (i.e., Sections 8–10), the length of the actuation rope can be expressed as:

[0086]

[0087] For the coupled 2-DoF part, since the driving rope of the front part will pass through the rear part, the length change of the j-th driving rope of the i-th joint will be the sum of the length changes of the ropes of all the joints in the rear part; while for the decoupled 2-DoF part, since the driving rope is directly connected to the motor through a flexible spring tube (similar to the brake cable of a bicycle), the length change will be the geometric distance difference between the moving platform and the static platform.

[0088] Step 2: Static Modeling of the 20-DoF Continuum Robot

[0089] By the attached Figure 4 It can be seen that, taking the i-th 2-DoF joint as an example, due to the characteristics of coupled drive, the rope driving the motion of the i+1-th joint will pass through the i-th joint. Therefore, three more driving ropes need to be added when establishing the static equation. Among them, a static coordinate system {O i}, external load (F i and M i ) is applied to the moving platform of the i-th joint. Three drive cables pass through the guide holes and are connected to the upper plate at one end and the linear motor at the other end. In addition, the two central shafts extending from the base and the upper plate are connected by a universal joint. Therefore, in order to construct the static equations, it is necessary to consider three drive cables (with a tension of and ), three passive drive ropes (tension and ) and center support force.

[0090] For the i-th joint of a multi-segment continuum robot, the static equation can be expressed as:

[0091]

[0092] in, is the driving force of the jth rope at the i-th joint, is the normal pressure of the jth rope at the i+1th joint, is the force on the central support of each joint i, F i,e is the force applied to the i-th joint, M i,e is the torque applied to the i-th joint, The position vector from the center of the universal joint of the i-th joint to the fixed point of the j-th rope of the i-th joint, The position vector from the center of the universal joint of the i-th joint to the fixed point of the j-th cable of the i+1-th joint.

[0093] Combined Force The driving force vector on one side of the rigid disk at section i is generated by the j-th driving rope (on the rigid disk at section i, the driving force vector on one side is The driving force vector on the other side is ) can be expressed as:

[0094]

[0095] As the drive cable passes and slides along the holes in the rigid disk, friction is generated, which reduces the efficiency of force transmission (from the base to the tip). Therefore, friction analysis is necessary. Because long continuum robots are typically composed of multiple 2-DoF joints, each of which can rotate about its two orthogonal axes, the angle between the drive cable and the rigid disk varies significantly with the different configurations of the continuum robot. Therefore, it is necessary to calculate the direction vector of the drive cable to calculate the magnitude of the friction force.

[0096]

[0097] in and The driving force vectors and The module length. i.j and l i+1.j They are the driving rope in the local coordinate system {O i} and {O i+1}. In order to obtain the magnitude of the friction force, it is necessary to calculate the normal pressure relative to the guide hole. It can be expressed as:

[0098]

[0099] Among them, n i is the unit normal vector of the rigid disk (coordinate system {O i+1} plane XOY).

[0100] Friction can be expressed as:

[0101]

[0102] Where μ is the friction coefficient between the drive rope and the rigid disk. |·| represents the modulus of the vector. Based on the rope friction force calculated above, the friction loss of the drive rope from the i-th segment to the i+1-th segment can be expressed as:

[0103]

[0104] Where ± represents the direction of the friction force between the drive cable and the rigid disk. For example, when the drive cable slides toward the tip, the negative sign is valid, and vice versa. Therefore, the friction force equation for the entire drive cable from the drive side (i.e., the motor) to the manipulator side (i.e., the fixed point of the rigid disk) can be expressed as:

[0105]

[0106] in The driving force provided to the motor; is the force acting on the rigid disk of the ith joint.

[0107] Due to the slender structure of the continuum robot, the tension distribution of the actuation cable will be greatly affected by the loads (e.g., internal load: gravity of the joints; external load: environmental forces during task completion), resulting in a large deviation of the robotic arm from its ideal shape.

[0108] Based on the structural design of the multi-DOF continuum robot (i.e., each 2-DoF joint is composed of two rigid parts and connected by a rigid universal joint in the center) and the definition of the coordinate system (i.e., a motion coordinate system is established at the bottom of each 2-DoF segment joint to describe the shape change of the entire continuum robot), in their local coordinate systems, the gravity vectors of the two parts (i.e., G i,lower and G i,upper ) can be expressed as:

[0109]

[0110] where m i,lower and m i,upper are the masses of the lower and upper parts of the i-th 2-DoF joint. g is the gravitational constant.

[0111] By using the transformation matrix, the coordinate system {O i} represents the intrinsic mass of the lower and upper parts of the 2-DoF joint:

[0112]

[0113] in and In the local coordinate system {O i The mass vectors of the lower and upper parts represented by}. and They are respectively from the coordinate system {O i}upper to {O i,joint}Transformation matrix of the lower center of mass. is from the coordinate system {O i} to the joint coordinate system {O i,joint}'s transformation matrix.

[0114] Similarly, the external load (i.e., F i and M i ) can also be used in the coordinate system {O i} is represented as:

[0115]

[0116] in, and Represented as a local coordinate system {O i} in the external load. Represents the coordinate system {{O i,joint}} to coordinate system {O i+1}'s transformation matrix.

[0117] Since the gravity vector is moved to the local coordinate system {O i} will produce adjoint moments, which can be expressed as:

[0118]

[0119] in and is the local coordinate system {O i The lower mass and upper mass of the 2-DoF joint represented by

[0120] Similarly, the external force F i The resulting torque can be expressed as:

[0121]

[0122] Step 3: Calculate the additional load on the drive rope;

[0123] Depend on Figure 5 As can be seen, a multi-DOF continuum robot is composed of multiple 2-DOF joints connected in series. The front drive cable passes through the rear section, causing complex force coupling in the rear 2-DOF segment (that is, the resultant force of the front drive cable generates additional torque on the rear 2-DOF segment), which greatly affects the kinematic accuracy of the system.

[0124] The i-th 2-DoF joint (i.e., θ i,1 and θ i,2 For example, the three driving cables of the adjacent i+1 joint pass through the rigid disk of the i joint. Since the i+1 2-DOF joint is not in a straight line with the i joint, the driving cable of the i+1 joint will generate an additional force on the i joint (i.e. and ):

[0125]

[0126] Since each 2-DoF part can have independent motion, the adjacent i+1th joint may have a different configuration than the i-th joint, resulting in the point where the force is applied. Not in the center of the rigid disk. The new force point ( For example) can be calculated by combining the following two equations:

[0127]

[0128] in, and is the unit vector of the rope attached to the rigid disk. and are the unit vectors of the driving rope at the i-th joint and the i+1-th joint respectively.

[0129] The resultant of the three additional forces generated by the driving rope It can be expressed as:

[0130]

[0131] By transforming the matrix, the resultant force and its corresponding moment in the coordinate system {O i} can be expressed as:

[0132]

[0133] in and It is expressed in the coordinate system {O i The resultant force in is applied at point The force vector

[0134] Step 4: Rope Tension Adjustment Strategy

[0135] Since the stiffness of the drive rope (characteristics: small diameter, long length) is usually lower than the stiffness of the rigid components (such as universal joints and rigid shafts) in the continuum robot, they can be regarded as elastic units to set the pre-tensioning force that adjusts the stiffness of the system (this method is usually used to improve the stiffness of the continuum robot). However, as mentioned earlier, the tension of the drive rope will produce an additional torque on its rear part, resulting in a deterioration in the motion accuracy of the system. The static equation of a single joint is analyzed to establish the stiffness model of a single joint. The static equation of a single joint can then be expressed as

[0136]

[0137] Among them, f j is the driving force of the jth rope; f s is the force of the central axis (the force vector is the same as the upper central axis); F1 is in the robot coordinate system {O i}; M1 robot coordinate system {O i} external torque in; e j is the position vector from the center point of the ball joint to the fixed point of the jth rope.

[0138] It is expressed in matrix form as:

[0139]

[0140] Where W is the torque acting on the 2-DoF joint. f is the driving force matrix of the three cables. J is the Jacobian matrix of the 2-DoF joint. Then, the stiffness of the i-th 2-DoF joint can be obtained by differentiating the torque W with respect to the rotational configuration s.

[0141]

[0142] Among them, W i is the static model of the i-th joint, s i is the rotation pose vector of the i-th joint, which can be expressed as s = [θ i,1 θ i,2 ], K i is the stiffness matrix of the 2-DoF joint, which can be divided into the stiffness of the driving rope K i,1 and structural stiffness K i,2 .

[0143] K i,1 The stiffness matrix generated by the rope elongation is denoted as rope stiffness and can be expressed as:

[0144]

[0145] Among them, k i,1 ,k i,2 and k i,3 is the stiffness of the three drive ropes.

[0146] K i,2 The stiffness matrix generated by the 2-DoF joint is denoted as the structural stiffness and can be expressed as:

[0147]

[0148] in, and They are and A skew-symmetric matrix. is the normal unit vector of the jth driving rope of the i-th joint. From the above formula, we can see that the stiffness component of the 2-DoF joint is closely related to the tension of the driving rope (i.e. ). Therefore, adjusting the tension of the actuation cable can actively adjust the stiffness of the 2-DOF joint, and thus the stiffness of the entire continuous robot with multiple 2-DOF joints can be adjusted.

[0149] To maintain the equilibrium of the 2-DOF joint, the regulated tension of the actuating cable should satisfy the initial static equations of the system. In particular, since each 2-DoF joint has two rigid central axes (connected by universal joints), the net force of the actuating cable should be consistent with the direction of the upper central axis, which can be expressed as:

[0150]

[0151] where Σ Reg is the solution space of the adjusted cable tension. i is the initial force driving the rope. i,s is the net tension change in the drive rope. η is the regulation coefficient that defines the regulation level.

[0152] As the drive rope tension is adjusted (usually increasing the tension to increase stiffness), the additional load (i.e. and ) may increase, resulting in a decrease in kinematic accuracy. In order to study the extent of the impact on kinematic accuracy, the total external load applied to the i-th 2-DoF joint of the n front joints is calculated and expressed as:

[0153]

[0154] The angle change of the 2-DoF joint under all loads (i.e., Δθ i,1 and Δθ i,2 ) can be calculated as:

[0155]

[0156] Using the same principle, the angular changes of all 2-DOF joints under given external loads, gravity loads, and additional loads can be calculated. These calculated angular changes can then be incorporated into the kinematic model of the continuous robot to reveal the true shape of the system. To reduce the deformation of the manipulator arm, simply increase the tension in the ropes to maximize their stiffness, thereby increasing the stiffness of the entire manipulator arm.

[0157] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for stiffness control and compensation of a continuum robot, characterized in that: include: Constructing a kinematic model of the continuum robot, wherein the kinematic model is used to provide a change in the length of a driving rope of the continuum robot; Based on the kinematic model, constructing a static model of the continuum robot; Based on the statics model, a stiffness model of the manipulator arm of the continuum robot is constructed; based on the stiffness model of the manipulator arm, the stiffness model of the rope is obtained; and the tension of the rope is adjusted by the stiffness model of the rope to complete stiffness control and compensation of the continuum robot; The statics model includes: a friction sub-model, a gravity sub-model and an additional force resultant sub-model; The mechanical arm stiffness model is: Among them, W i is the static model of the i-th joint, s i is the rotation pose vector of the i-th joint, K i is the stiffness matrix of the 2-DoF joint, K i,1 is the rope stiffness model, K i,2 is the structural stiffness, f i is the driving force matrix composed of three ropes, is the Jacobian matrix of the i-th joint; The rope stiffness model is: Among them, k i,1 ,k i,2 and k i,3 are the stiffness of the three driving ropes, J i is the Jacobian matrix of the i-th joint rope; The angle change of a 2-DoF joint under all loads is: Using the same principle, the angular changes of all 2-DOF joints under given external loads, gravity loads, and additional loads can be calculated. By bringing the calculated angular changes into the kinematic model of the continuous robot, the true shape of the system is obtained. To reduce the deformation of the robotic arm, it is only necessary to increase the tension of the rope to make the rope as stiff as possible, thereby increasing the stiffness of the entire robotic arm.

2. The stiffness control and compensation method of a continuum robot according to claim 1, characterized in that: Constructing the kinematic model of the continuum robot includes: Obtaining trajectory planning of the continuum robot; Based on the trajectory planning, obtaining the joint angle change driving the joint movement; Based on the changes in the joint angles, a kinematic model of the continuum robot is established.

3. The stiffness control and compensation method of a continuum robot according to claim 1, characterized in that: Constructing the statics model of the continuum robot includes: Based on the kinematic model, obtaining a sub-model of a driving rope length change under different configurations of the continuum robot; Static modeling is performed on the continuum robot based on the driving rope length change sub-model to obtain the static model.

4. The stiffness control and compensation method of a continuum robot according to claim 1, characterized in that: The kinematic model is: in, is the i-th joint coordinate system O i In the i-1th joint coordinate system O i-1 The homogeneous transformation matrix in , i is the i-th joint of the robotic arm, i = 1, 2, ...

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5. The stiffness control and compensation method of a continuum robot according to claim 3, characterized in that: The driving rope length variation sub-model is: Among them, l i,j is the i-th joint, the length of the j-th rope, m is the number of joints, l m,j To drive the rope in the local coordinate system {O i } and {O i+1 } position vector.

6. The stiffness control and compensation method of a continuum robot according to claim 1, characterized in that: The statics model is: in, is the driving force of the jth rope of the i-th joint, is the normal pressure of the jth rope at the i+1th joint, is the force on the central support of each joint i, F i is the force applied to the i-th joint, M i is the torque applied to the i-th joint, is the position vector from the center of the i-th joint universal joint to the fixed point of the j-th rope of the i-th joint, is the position vector from the center of the universal joint of the i-th joint to the fixed point of the j-th cable of the i+1-th joint.

7. The stiffness control and compensation method of a continuum robot according to claim 1, characterized in that: The friction sub-model is: in, The driving force provided to the motor; is the force acting on the rigid disk of the ith joint, is the friction force of the entire driving cable from the driving side to the robotic arm side, and n is the number of joints; The graviton model is: Among them, G i,lower is the gravity vector of the lower part of the i-th 2-DoF joint, G i,upper is the gravity vector on the upper part of the i-th 2-DoF joint, m i,lower and m i,upper are the masses of the lower and upper parts of the i-th 2-DoF joint, respectively, and g is the gravitational constant; The resultant sub-model of the additional force generated by the driving rope is: in, is the resultant force of the rope driving the i-th joint, is the tension of the first driving cable of the i-th joint, is the tension of the second driving cable of the i-th joint, is the tension of the third driving cable of the i-th joint.

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