A Flexible Arm Compensation Control Method

Abstract

The present invention discloses a flexible arm compensation control method, which is applicable to a flexible arm that drives the distal continuum degree of freedom of the flexible arm by driving ropes to drive traction wires, and includes: calculating the joint position increment of the distal continuum of the flexible arm according to the target pose and the current pose of the distal continuum of the flexible arm, and further obtaining the joint position increment of the proximal continuum of the flexible arm; calculating the movement length and bending angle of each traction wire in the proximal continuum of the flexible arm according to the joint position increment of the proximal continuum of the flexible arm, and calculating the corresponding driving rope tension in combination with the relationship between the driving rope tension and the bending angle of the traction wire; calculating the compensation amount of each driving rope according to the force-deformation model of the driving rope, and performing compensation control in combination with the movement length of each corresponding traction wire. This method can compensate for the deformation amount of the flexible driving rope and achieve precise control of the bending and telescopic movements of the distal continuum of the flexible arm.

Description

Technical Field

[0001] The present invention relates to the technical field of surgical robots, and in particular, to a compensation control method for a flexible arm. Background Art

[0002] Surgical robots based on continuum flexible arms are being increasingly widely used in minimally invasive surgery due to their small incisions and flexible movements. Volume and mass, as important factors affecting the convenience of using surgical robots, have also become the direction of design improvement. However, for traditional flexible arm surgical robots driven by nitinol wires, due to the non-bendable characteristics of nitinol wires, a matching lead screw drive proximal continuum needs to be arranged for bending and telescopic movements, which will increase the final volume and weight.

[0003] The drive rope needs to be bendable and easy to arrange. By driving the proximal continuum through the rope for bending and telescopic movements, the volume and weight can be greatly reduced, and the size and mass of the system will be greatly reduced. During the process of winding and unwinding the drive rope, the drive rope will deform, resulting in a difference between the actual required change length of the traction wire and the theoretical change length, which is not conducive to the accurate control of the bending or telescopic movement of the proximal continuum, and also affects the accuracy of the bending or telescopic movement of the distal continuum. Summary of the Invention

[0004] Object of the Invention: In view of the above deficiencies, the present invention proposes a compensation control method for a continuum flexible arm based on proximal drive rope transmission. While selecting a flexible drive rope to drive the proximal continuum, the deformation amount of the flexible drive rope is compensated, so as to improve the accuracy of the bending or telescopic movement of the distal continuum.

[0005] Technical Solution:

[0006] A flexible arm compensation control method, applicable to a flexible arm that drives the degrees of freedom of the distal continuum of the flexible arm by driving a traction wire through a drive rope, includes:

[0007] Calculating the joint position increment of the distal continuum of the flexible arm according to the target pose and the current pose of the distal continuum of the flexible arm, and further obtaining the joint position increment of the proximal continuum of the flexible arm;

[0008] Calculating the movement length and bending angle of each traction wire in the proximal continuum of the flexible arm according to the joint position increment of the proximal continuum of the flexible arm, and calculating the corresponding drive rope tension in combination with the relationship between the drive rope tension and the bending angle of the traction wire;

[0009] Calculating the compensation amount of each drive rope according to the force-deformation model of the drive rope and the tension of the drive rope, and performing compensation control in combination with the movement length of each corresponding traction wire.

[0010] Specifically, calculating the joint position increment of the distal continuum of the flexible arm is:

[0011] The velocity and angular velocity of the workspace that the distal continuum needs to reach are calculated based on the pose error between the target pose and the current pose of the distal continuum of the flexible arm, so as to calculate the velocity and angular velocity of the joint space of the distal continuum, and then calculate the joint position increment of the distal continuum.

[0012] The pose error is calculated based on the target pose and the current pose of the distal continuum of the flexible arm, and it is judged whether it is within the given range;

[0013] If so, update the joint space angle of the distal continuum after movement and start controlling the next target pose;

[0014] If not, calculate the joint position increment of the distal continuum, obtain the joint position increment of the proximal continuum through equi-proportion mapping, and perform compensation control accordingly.

[0015] The relationship between the driving rope tension and the bending angle of the traction wire is obtained through piecewise cubic polynomial interpolation.

[0016] The specific piecewise cubic polynomial interpolation is as follows:

[0017] After connecting the driving rope and the traction wire, 3n - 1 bending angle points are evenly inserted within the angle bending range [0, θ imax of the i-th traction wire, and then adding the two end points to obtain the bending angles at each point: θ1, …, θ j , …, θ 3n+1 , where θ1 = 0, θ 3n+1 = θ imax , The driving rope tensions F1, …, F j , …, F 3n+1 corresponding to the measured bending angles are obtained for these 3n + 1 angle points, resulting in 3n + 1 pairs of data;

[0018] According to the increasing order of the bending angles, four pairs of data are grouped as one set, and the fourth pair of data in each set is the same as the first pair of data in the next set, and a total of n sets of data are divided;

[0019] For the four angles [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1 and the corresponding measured driving rope tensions [F 3m-2 , F 3m-1 , F 3m , F 3m+1 corresponding to the m-th set of data, the tension-bending angle relationship formula between the driving rope tension and the bending angle of this section of the traction wire is calculated through cubic polynomial interpolation as follows:

[0020] f i m f(θ) = aθ 3 + bθ 2 + cθ + d, θ ∈ [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1

[0021] Among them, f i m (θ) represents the tensile force - bending angle relationship corresponding to the m - th group of arrays of the i - th traction wire, i = 1, 2,..., u, where u represents the number of traction wires; a, b, c, and d are calculated according to the following constraints:

[0022]

[0023] Based on this, the aforementioned groups of arrays and their corresponding tensile force - bending angle relational expressions are obtained, and the tensile force - bending angle relationship of the i - th traction wire within its entire angle bending range is obtained:

[0024]

[0025] The specific method for calculating the driving rope compensation amount according to the force - deformation model of the driving rope and the tensile force of the driving rope is as follows:

[0026] Obtain the stiffness coefficient in the force - deformation model of the driving rope, and calculate the driving rope compensation amount in combination with the tensile force of the driving rope.

[0027] The specific method for obtaining the stiffness coefficient in the force - deformation model of the driving rope is as follows:

[0028] The force - deformation model of the driving rope is:

[0029] F = k(L - L0)

[0030] Among them, F is the tensile force borne by the driving rope, L0 is the original length of the driving rope, L is the length of the driving rope after deformation under the action of the tensile force, and k is the stiffness coefficient;

[0031] Taking the strain ε of the driving rope under the action of the tensile force F as the abscissa and its stress σ as the ordinate to obtain the stress - strain curve of the driving rope, then the angle α between its stress - strain curve and the abscissa axis satisfies the following condition:

[0032] σ = tanα * ε

[0033] Among them, ε=(L - L0) / L0, σ = F / A0, and A0 is the cross - sectional area of the driving rope;

[0034] Then the calculated stiffness coefficient k is:

[0035] ​

[0036] The cross-sectional area A0 of the drive rope satisfies the following relationship: where σ P is the proportional limit of the linear region of the stress-strain curve of the drive rope, w is the proportionality coefficient, and F max is the tension of the drive rope at the maximum bending angle of the traction wire.

[0037] The value of w is 0.7.

[0038] Specifically, to obtain the stiffness coefficient in the force-deformation model of the drive rope:

[0039] Several sets of forces and corresponding deformation values of the drive rope are measured, and the least squares method is used to fit and determine the exact value of the stiffness coefficient k in the force-deformation model of the drive rope.

[0040] Beneficial effects: The compensation control method corresponding to the system of the present invention takes into account the framework of the control system and the characteristics of the drive rope, and has a good control effect on this system. The drive rope winds and unwinds under the forward and reverse rotation of the motor, so that the distal continuum can accurately control the bending and telescopic movements under the action of the flexible drive rope. Description of the Drawings

[0041] Figure 1 is the overall control flow chart;

[0042] Figure 2 is the stress-strain schematic diagram of the tungsten wire rope;

[0043] Figure 3 is the schematic diagram of fitting the linear model according to the tensile deformation data of the tungsten wire rope;

[0044] Figure 4 is the schematic diagram of the bending geometric model of the proximal continuum;

[0045] Figure 5 is the schematic diagram of the length change of the tungsten wire rope pulling the nitinol wire;

[0046] Figure 6 is the schematic diagram of the bending of the nitinol wire.

[0047] Among them, 1 is the drive motor, 2 is the drive rope, and 3 is the alloy wire. Specific Embodiments

[0048] The present invention will be further clarified below with reference to the drawings and specific embodiments.

[0049] The present invention is applicable to a flexible arm that drives the degrees of freedom of the distal continuum of the flexible arm by driving a traction wire through a drive rope. Specifically, referring to Figure 5 、 6, the flexible arm includes a proximal continuum for driving at the proximal end and a distal continuum for execution at the distal end. The proximal continuum drives the distal continuum to perform operations through traction wires. In the proximal continuum, there are a motor group and a driving rope for transmission. Specifically, the motor group is fixed on the base plate of the proximal continuum. According to the degrees of freedom of operation of the distal continuum, several driving motors are provided in the motor group. One degree of freedom corresponds to two driving motors. The motor shaft of the driving motor is connected with a winch. One end of two driving ropes is respectively wound around a winch, and the other end is respectively fixedly connected with two traction wires. The two ends of the traction wire are respectively fixedly connected with the distal locking plate of the distal continuum and the proximal locking plate of the proximal continuum. After being fixedly connected with one end of the proximal locking plate, the traction wire extends towards the proximal continuum and is connected with the driving rope without relative sliding at the place passing through the base plate. The driving motor, the driving rope and the traction wire together form a set of driving and transmission components. Two opposite driving and transmission components constitute the motion driving and transmission mechanism of one degree of freedom of the distal continuum. The driving motors of the two opposite driving and transmission components drive the driving ropes to drive the two traction wires to move in the opposite direction, thereby driving the proximal locking plate to swing. Since the proximal locking plate and the distal locking plate are fixedly connected by two alloy wires corresponding to the degrees of freedom, the distal locking plate can be driven to swing correspondingly with the proximal locking plate, and thus the motion of the distal continuum corresponding to the degrees of freedom can be realized.

[0050] Among them, the material of the traction wire is different from that of the driving rope. The driving rope needs to have a certain flexibility and be wound around the winch. The traction wire needs to have a certain rigidity to provide a certain supporting effect for the flexible arm. The flexibility of the driving rope is greater than that of the traction wire, and the rigidity of the traction wire is greater than that of the driving rope.

[0051] In the embodiment of the present invention, the driving rope is made of tungsten wire rope, and the traction wire is made of nickel-titanium alloy wire.

[0052] Figure 1 For the overall control flowchart, as Figure 1 shown, the flexible arm compensation control method of the present invention includes the following steps:

[0053] (1) Calculate the pose error of the current distal continuum working space according to the target pose and its current pose of the distal continuum working space remotely given by the teleoperation master hand, and calculate the joint position increment of the new cycle joint space of the distal continuum accordingly;

[0054] According to the target pose [p t R t of the distal continuum working space remotely given by the teleoperation master hand and its current pose [p R], calculate the pose error λ of the current distal continuum working space:

[0055]

[0056] Among them, p t and Rt The target position and target attitude of the given distal continuum workspace respectively, p and R are the current position and current attitude of the distal continuum workspace, and the pose error λ includes the position error λ p and the attitude error λ R ;

[0057] The purpose of the flexible arm compensation control method is to make the aforementioned pose error reach a given range;

[0058] Judge whether the aforementioned pose error is within the given range;

[0059] If it is, it is considered that the positioning accuracy has been reached, the movement is in place, the joint space angles of the distal continuum after movement are updated, and the control of the next target pose is started;

[0060] If not, judge whether the set number of iterations is reached. If the set number of iterations is reached, exit the flexible arm control and start the control of the next target pose; otherwise, calculate the linear and angular velocities [v w] of the workspace that the distal continuum needs to reach according to the aforementioned pose error, so that the linear and angular velocities of the joint space of the distal continuum can be calculated through the Jacobian matrix and the angular velocity Furthermore, calculate the joint position increment dq of the new cycle joint space of the distal continuum through integration;

[0061] This joint position increment of the joint space is the joint position increment of the distal continuum. In the present invention, it is also the pose change amount of the distal locking disc. The joint position increment of the proximal continuum is obtained through proportional (here 1:1 is taken, but not limited to) mapping. In the present invention, it is also the pose change amount of the proximal locking disc;

[0062] (2) Perform compensation control;

[0063] The joint position increment of the proximal continuum is realized by pulling the nitinol wire to bend through the tungsten wire rope. Because the tungsten wire rope has a certain flexibility and there will be a certain amount of deformation during the stretching process, it is necessary to compensate and control the deformation amount of the tungsten wire rope. After driving the tungsten wire rope, the pose of the updated distal continuum workspace will be calculated by forward kinematics again, and then the pose error will be calculated to enter the next cycle until the set target pose is reached or the number of cycles is exceeded and exit;

[0064] Specifically as follows:

[0065] (21) Establish the relationship between the pulling force of the tungsten wire rope and the bending angle of the corresponding alloy wire, and obtain the pulling force of the tungsten wire rope according to the bending angle of the alloy wire accordingly;

[0066] Since the bending angle of the proximal continuum is obtained by proportional mapping of the distal continuum, and the bending of the proximal continuum is achieved by the bending drive of the alloy wire pulled by the tungsten wire rope, that is, there is a corresponding relationship between the force transmitted to the alloy wire by the tungsten wire rope and the bending angle of the alloy wire. Therefore, the tensile force of the tungsten wire rope can be measured at different bending angles of the alloy wire, that is, the tensile force-bending angle relationship between the tensile force of the tungsten wire rope and the corresponding bending angle of the alloy wire can be obtained.

[0067] The present invention uses the experimental method to establish the tensile force-bending angle relationship between the tensile forces of each tungsten wire rope and the corresponding bending angle of the alloy wire, which is simple and easy for engineering practice. By connecting each tungsten wire rope with the corresponding alloy wire and measuring the tensile force of the tungsten wire rope at the corresponding bending angle of the alloy wire at the actual measurement sampling point when the alloy wire is at different angles, the change in tension caused by the friction between the structures has been included in the measured tensile force, which is more accurate than the force model under ideal conditions. This method uses piecewise cubic polynomial interpolation based on the measured data to determine the relationship formula of the tensile force of each tungsten wire rope changing with the bending angle of the nickel-titanium alloy wire. The steps are as follows:

[0068] 1) Connect the tungsten wire rope with the nickel-titanium alloy wire, and evenly insert 3n - 1 bending angle points within the bending angle range [0, θ imax for the i-th alloy wire. Then, adding the two end points, the bending angles at each point are obtained as θ1,..., θ j ,..., θ 3n+1 , where θ1 = 0, θ 3n+1 = θ imax . Measure the tensile forces F1,..., F j ,..., F 3n+1 of the tungsten wire rope corresponding to the bending angles at these 3n + 1 angle points respectively;

[0069] 2) Form 3n + 1 pairs of data from the 3n + 1 bending angles of the alloy wire and the 3n + 1 corresponding tensile forces of the tungsten wire rope obtained in step 1), and group them in sets of four data according to the increasing order of the bending angle. The fourth data in each group is the same as the first data in the next group, so a total of n groups of data are formed (that is, the i-th alloy wire is divided into n segments). For example, the angles corresponding to the m-th group of data are [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1 , m = 1, 2,..., n;

[0070] 3) For the four angles [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1 corresponding to the m-th group of data and the corresponding measured tensile forces of the tungsten wire rope [F 3m-2 , F 3m-1 , F3m and F 3m+1 , calculate the relationship between the tungsten wire rope tension and the bending angle of the alloy wire corresponding to this section of alloy wire through cubic polynomial interpolation, as follows:

[0071] f i m (θ) = aθ 3 + bθ 2 + cθ + d, θ ∈ [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1

[0072] where f i m (θ) represents the relationship between the tungsten wire rope tension and the bending angle of the alloy wire corresponding to the mth group of arrays of the ith alloy wire, i = 1, 2, 3, 4; a, b, c, and d are calculated according to the following constraints:

[0073]

[0074] In a specific embodiment of the present invention, the degree of freedom of movement of the distal continuum is 2, so there are two pairs of cooperating alloy wires, that is, there are 4 alloy wires. However, in the present invention, the degree of freedom of movement of the distal continuum can be set according to requirements, and the corresponding number of alloy wires is also designed to be twice the degree of freedom;

[0075] 4) According to the arrays in different angle ranges obtained in step 2) and the relationship between the tension and bending angle of each section of alloy wire obtained in step 3), the relationship between the tension and bending angle of each section of the ith alloy wire in its entire angle bending range is as follows:

[0076]

[0077] In the actual control scheme, the tension of the tungsten wire rope corresponding to the bending angle of the alloy wire can be obtained according to the above relationship between the tension and bending angle;

[0078] (22) Obtain the stiffness coefficient k of the force-deformation model of the tungsten wire rope according to the stress-strain curve of the tungsten wire rope, and calculate the compensation amount of the tungsten wire rope accordingly;

[0079] To improve the compensation accuracy and control effect, it should be ensured that the tungsten wire rope works in the linear section of its stress-strain curve (i.e., deformation). Determine the linear model of the force-deformation of the tungsten wire rope through the following steps:

[0080] 1) Determine the maximum tension of the tungsten wire rope corresponding to the ith alloy wire by simulation under the actual working conditions in the actual scenario

[0081] ​2) Obtain the stiffness coefficient k of the tungsten wire rope corresponding to the i-th alloy wire i ;

[0082] According to the material properties of the tungsten wire rope, that is, the stress-strain curve of tungsten. Among them, the strain ε of the tungsten wire rope under the action of the tensile force F is used as the abscissa, and the stress σ of the tungsten wire rope under the action of the tensile force F is used as the ordinate to obtain the stress-strain curve of tungsten. Among them, ε = (L - L0) / L0, L0 is the original length of the tungsten wire rope, L is the length of the tungsten wire rope after deformation under the action of the tensile force, σ = F / A0, as Figure 2 shown;

[0083] Design the cross-sectional area A0 of the tungsten wire rope so that the tungsten wire rope works in the linear region of the stress-strain curve, as Figure 2 in the range [0, σ P , where σ P is the proportional limit of the linear region, σ A is the elastic limit of tungsten, α is the angle between the stress-strain curve of the tungsten wire rope and the abscissa axis ε, and according to the stress-strain curve of tungsten, σ = tanα * ε;

[0084] In the present invention, in order to further ensure the stability of the tungsten wire rope, the design of the cross-sectional area A0 of the tungsten wire rope in the present invention has a set margin (the present invention takes 30%), that is, the cross-sectional area of the tungsten wire rope needs to meet the following design: Furthermore, the cross-sectional area of the tungsten wire rope is designed. In the present invention, w takes 0.7;

[0085] According to the stress-strain curve of the tungsten wire rope, F = σA0, σ = tanα * ε, ε = (L - L0) / L0, then

[0086] As Figure 3 shown, according to Hooke's law, within the elastic limit, the deformation of the tungsten wire rope is proportional to the external force (tensile force of the tungsten wire rope) that causes the deformation, that is, the force-deformation model of the tungsten wire rope F = kx is obtained, where x is the deformation value of the tungsten wire rope caused by the force F, x = L - L0, x ∈ [0, x max , k is the stiffness coefficient of the tungsten wire rope, then according to Hooke's law and the stress-strain curve,

[0087] The present invention also provides another method for obtaining the stiffness coefficient of the tungsten wire rope, which is specifically as follows:

[0088] There may be a slight error between the cross-sectional area A0 of the actually processed tungsten wire rope and the cross-sectional area designed by the above method. In addition, affected by the length of the tungsten wire rope, there will be an error between the theoretical stiffness coefficient and the actual value of the tungsten wire rope. Therefore, by measuring the forces and corresponding deformation values of several processed tungsten wire ropes, in order to obtain an accurate force-deformation model of the tungsten wire rope, the present invention uses the least squares method to fit and obtain the accurate value of the stiffness coefficient k of the tungsten wire rope;

[0089] In this way, by actually measuring several groups of forces and deformation values of the tungsten wire rope and fitting them by the least squares method to obtain the value of k (as Figure 3 shown), the result is more accurate than the first method;

[0090] According to the above, the stiffness coefficients of the tungsten wire ropes corresponding to the four alloy wires are k1, k2, k3, and k4 respectively;

[0091] 3) Combine the length of the movement of the alloy wire caused by the bending of the proximal continuum (that is, the change in the length of the alloy wire between the proximal locking disc and the base disc) and the deformation of the tungsten wire rope at the bending angle of the corresponding alloy wire to obtain the total length that the motor needs to pull the tungsten wire rope, and perform compensation control accordingly;

[0092] In the specific embodiment of the present invention, four tungsten wire ropes are used to drive the movement of the alloy wire, and then drive the change of the proximal continuum. The single-joint geometric model of the proximal continuum is as Figure 4 shown (the hole positions and central axes of the four nickel-titanium alloy wires are drawn in the figure. The four nickel-titanium alloy wires are respectively connected to the proximal locking disc and the base disc (one end of the nickel-titanium alloy wire extends to the distal continuum after passing through the proximal locking disc and is fixedly connected to the distal locking disc of the distal continuum), and the alloy wire is fixedly connected to the tungsten wire rope in the base disc). The origin O1 of the first coordinate system coincides with the center of the base disc, and the origin O2 of the second coordinate system coincides with the center of the proximal locking disc. Among them, the x-axis x1 of the first coordinate system and the x-axis x2 of the second coordinate system both point to the direction of the hole of the first nickel-titanium alloy wire, and the corresponding z-axis z1 and z2 directions are the tangent directions of the central axis; the central axis is bent in an arc shape, and the plane formed by the central axis is the bending plane, as Figure 4 shown, the included angle between the bending plane and the x2-axis is The included angle between the z-axes of the two coordinate systems in the bending plane is θ;

[0093] As Figure 5 shown, the alloy wire is bent into an arc. During the process of winding and unwinding the tungsten wire rope, the length of the alloy wire between the proximal locking disc and the base disc will change under the drive of the tungsten wire rope. Then, the change in the length of the alloy wire between the proximal locking disc and the base disc can be calculated according to the parameters in the joint space:

[0094]

[0095] Among them, dl1, dl2, dl3, and dl4 are the length change amounts of the four alloy wires between the proximal locking disk and the base disk respectively, l is the length of the four alloy wires between the proximal locking disk and the base disk before retracting and releasing, l1, l2, l3, and l4 are the lengths of the four alloy wires between the proximal locking disk and the base disk after retracting and releasing respectively, and R is the distance from the center line of the proximal continuum to the alloy wire, that is, the distance from the center of the proximal continuum end face to the alloy wire hole;

[0096] As Figure 6 described above, the wire rope tensions corresponding to the four alloy wires are calculated according to the bending angles of the alloy wires and the relationship between the tension and the bending angle, and then the deformation amount dx of the corresponding wire rope is calculated according to the stiffness coefficient of the wire rope corresponding to the i-th alloy wire obtained above i = f i (θ) / k i , and it is compensated to the length change amount dl of the corresponding nickel-titanium alloy wire i , then dl i + dx i is used as the total length L that the motor needs to pull the corresponding wire rope Mi = dl i + dx i :

[0097] Therefore, the compensation control for the wire ropes corresponding to the four alloy wires is as follows:

[0098]

[0099] Among them, k i is the stiffness coefficient corresponding to the force-deformation model of the wire rope corresponding to the i-th alloy wire; L M1 , L M2 , L M3 , L M4 are the total lengths that the motor needs to pull the wire ropes corresponding to the 4 alloy wires respectively, that is, the rotation circumferences required for the corresponding motors; f1(θ) / k1, f2(θ) / k2, f3(θ) / k3, and f4(θ) / k4 are the deformation amounts of the wire ropes corresponding to the 4 alloy wires respectively.

[0100] The wire rope has a certain flexibility, and its own length deformation will occur during the retracting and releasing process, which affects the precise control of the driving distance of the proximal continuum. In the present invention, by compensating the force of the wire rope required for the movement of the alloy wire during the actual simulation use process and the deformation amount of the wire rope caused by the force, the bending angle of the proximal continuum is precisely controlled, thereby ensuring the precise control of the distal continuum.

[0101] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention (such as quantity, shape, position, etc.), and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A flexible arm compensation control method, applicable to a flexible arm that drives the distal continuum degrees of freedom of the flexible arm by driving a rope to drive a traction wire, characterized in that: It includes: Calculating the joint position increment of the distal continuum of the flexible arm based on the target pose and the current pose, and then obtaining the joint position increment of the proximal continuum of the flexible arm; Calculating the movement lengths and bending angles of the traction wires in the proximal continuum of the flexible arm according to the joint position increment, and calculating the corresponding driving rope tensions in combination with the relationship between the driving rope tension and the bending angle of the traction wire; Calculating the compensation amounts of the driving ropes according to the force-deformation model of the driving ropes and the tensions of the driving ropes, and performing compensation control in combination with the movement lengths of the corresponding traction wires.

2. The flexible arm compensation control method according to claim 1, wherein: Specifically, calculating the joint position increment of the distal continuum of the flexible arm is as follows: Calculating the linear velocity and angular velocity of the workspace that the distal continuum needs to reach according to the pose error between the target pose and the current pose of the distal continuum of the flexible arm, thereby calculating the linear velocity and angular velocity of the joint space of the distal continuum, and then calculating the joint position increment of the distal continuum.

3. The flexible arm compensation control method according to claim 1 or 2, characterized in that: Calculating the pose error according to the target pose and the current pose of the distal continuum of the flexible arm, and determining whether it is within a given range; If it is, updating the joint space angles of the distal continuum after movement and starting the control of the next target pose; If not, calculating the joint position increment of the distal continuum, obtaining the joint position increment of the proximal continuum through equi-proportion mapping, and performing compensation control accordingly.

4. The flexible arm compensation control method according to claim 1, wherein: The relationship between the driving rope tension and the bending angle of the traction wire is obtained through piecewise cubic polynomial interpolation.

5. The flexible arm compensation control method according to claim 4, characterized in that: Specifically, the piecewise cubic polynomial interpolation is as follows: After connecting the drive rope with the traction wire, for the $i$-th traction wire, uniformly insert $3n - 1$ bending angle points within the angular bending range $[0, \theta imax $, then adding the two end points to obtain the bending angles at each point: $\theta_1, \ldots, \theta j , \ldots, \theta 3n+1 $, where $\theta_1 = 0$, $\theta 3n+1 = \theta imax $, Measure the drive rope tensions $F_1, \ldots, F j , \ldots, F 3n+1 $ corresponding to the respective bending angles at these $3n + 1$ angle points, obtaining $3n + 1$ pairs of data; Taking four pairs of data as a group in the order of increasing bending angle, the fourth pair of data in each group is the same as the first pair of data in the next group, and a total of n groups of data are divided; For the four angles [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1 corresponding to the m-th group of arrays and the corresponding measured driving rope tensions [F 3m-2 , F 3m-1 , F 3m , F 3m+1 , calculate the tension-bending angle relationship between the driving rope tension and the bending angle of the traction wire corresponding to this section of the traction wire through cubic polynomial interpolation as follows: f i m f(θ) = aθ 3 + bθ 2 + cθ + d, θ ∈ [θ 3m-2 , θ 3m-1 , θ 3m , θ 3m+1 ​ where f i m (θ) represents the tensile force-bending angle relationship corresponding to the m-th group of arrays of the i-th traction wire, i = 1, 2, …, u, where u represents the number of traction wires; a, b, c, and d are calculated according to the following constraints: Accordingly, obtaining the above-mentioned groups of data and their corresponding tension-bending angle relationships, and obtaining the tension-bending angle relationship of the i-th traction wire in its entire angle bending range:

6. The flexible arm compensation control method according to claim 1, characterized in that: Specifically, calculating the compensation amount of the driving rope according to the force-deformation model of the driving rope and the tension of the driving rope is as follows: Obtaining the stiffness coefficient in the force-deformation model of the driving rope, and calculating the compensation amount of the driving rope in combination with the tension of the driving rope.

7. The flexible arm compensation control method according to claim 6, characterized in that: Specifically, obtaining the stiffness coefficient in the force-deformation model of the driving rope is as follows: The force-deformation model of the driving rope is: F = k(L - L0) Where, F is the tension borne by the driving rope, L0 is the original length of the driving rope, L is the length of the driving rope after deformation under the action of the tension, and k is the stiffness coefficient; Taking the strain ε of the driving rope under the action of the tension F as the abscissa and its stress σ as the ordinate to obtain the stress-strain curve of the driving rope, then the angle α between the stress-strain curve and the abscissa axis satisfies the following condition: σ = tanα * ε Where, ε = (L - L0) / L0, σ = F / A0, and A0 is the cross-sectional area of the driving rope; Then the calculated stiffness coefficient k is:

8. The flexible arm compensation control method according to claim 7, wherein: The cross-sectional area A0 of the drive rope satisfies the following relationship: where σ P is the proportional limit of the linear region of the stress-strain curve of the drive rope, w is the proportionality coefficient, and F max is the tension of the drive rope at the maximum bending angle of the traction wire.

9. The flexible arm compensation control method according to claim 8, characterized in that: The value of w is 0.

7.

10. The flexible arm compensation control method according to claim 6, characterized in that: Specifically, obtaining the stiffness coefficient in the force-deformation model of the driving rope is as follows: Measuring several groups of forces of the driving rope and the corresponding deformation values, and using the least squares method to fit to determine the exact value of the stiffness coefficient k in the force-deformation model of the driving rope.

Images