A flexible threaded rod torso continuum robot motion accuracy compensation method

Abstract

The present application relates to the field of continuum robot, specifically relates to a kind of flexible screw rod torso continuum robot motion precision compensation method, step 1: the kinematic model of continuum robot is established;Step 2: the torsional compensation model of continuum robot driven by flexible screw rod is established;Step 3: the friction compensation model of continuum robot driven by flexible screw rod is established;Step 4: the length change rate of flexible screw rod is solved;Step 5: the motion of flexible screw rod is compensated, the loss amount of drive in motion process is estimated by the error compensation model of the continuum robot with flexible screw rod torso, and the control precision of continuum robot is improved.

Description

Technical Field

[0001] This invention relates to the field of continuum robots, and more specifically to a method for compensating the motion accuracy of a continuum robot with a flexible threaded rod torso. Background Technology

[0002] Compared to traditional rigid-jointed robots, continuum robots possess high compliance, variable stiffness, and high dexterity, enabling them to exhibit superior performance in adaptive operations within confined spaces. With the current demand for robots with low stiffness and high degrees of freedom, the research and manufacturing of continuum robots have garnered widespread attention.

[0003] Traditional continuous robots are typically driven by either cable-driven or gas-driven systems. Cable-driven continuous robots are limited by the low stiffness of the drive cable and the nonlinear rebound force under varying load conditions, resulting in inconsistent motion accuracy. Gas-driven continuous robots, on the other hand, face challenges in establishing accurate analytical models, kinematic models, and accuracy compensation algorithms. Furthermore, both cable-driven and gas-driven systems struggle to achieve high load capacities.

[0004] Compared to the two drive methods mentioned above for continuum robots, the flexible threaded rod-driven continuum robot achieves high end-effector motion accuracy while incorporating the actuator. Continuum robots with external actuators require larger external devices, limiting their dexterity. In contrast, internal actuators are more conducive to modular and maneuverable robot design. However, traditional internally driven continuum robots suffer from insufficient motion accuracy due to slippage in the motor gears and flexible threaded rods. Currently, there are no relevant accuracy compensation methods for this type of driven continuum robot. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the fact that the motion accuracy of the existing continuous robot with flexible threaded rod body is not accurate enough due to the flexible deformation of the material and the driving friction when the flexible threaded rod moves.

[0006] To address the aforementioned technical problems, this invention provides a method for compensating the motion accuracy of a flexible threaded rod torso continuum robot, comprising the following steps:

[0007] Step 1: Establish the kinematic model of the continuum robot. The kinematic model of the continuum robot mainly includes two parts: first, establishing the mapping relationship between the drive space and the joint space; second, establishing the mapping relationship between the joint space and the operation space. The kinematic model of the robot is derived by superimposing the two. Under the assumption of piecewise constant curvature, the kinematic model of the continuum robot is established using geometric analysis. Then, for a continuum robot with at least two flexible threaded rods, the direction vector of the i-th end effector relative to the (i-1)-th end base is:

[0008] in: Let be the rotation angle of the i-th segment of the continuum robot in the xy plane; Let be the bending angle of the i-th segment of the continuum robot arc; s represents sin; c represents cos.

[0009] Since the two flexible threaded rods are 60° out of phase on the z-axis, the rotation matrix... End effector Relative to the end base The transformation matrix can be represented as Meanwhile, the tubular thread length S of the flexible threaded rod can be expressed as S = , , , .

[0010] in: , and is the length of the three flexible threaded rods; r is the distance from the virtual bone to the tubular actuator; The curvature of the virtual bone;

[0011] The distance r from the center of the i-th flexible threaded rod to the Z0Y0 plane The relationship is

[0012]

[0013]

[0014] in: The length of the central trunk;

[0015] Step 2: Establish a torsional compensation model for the continuum robot driven by the flexible threaded rod. The geometry of the flexible threaded rod will cause its own twisting, affecting accuracy. The length of the flexible threaded rod obtained in Step 1... Its curvature can be calculated. Therefore, for a given unit length of A flexible threaded rod with n threads, the i-th flexible threaded rod needs to rotate by an angle of . Based on this, considering the torsion of the flexible threaded rod, and assuming that the central trunk is virtual and does not bear any internal force, the total force applied to the end base is...

[0016]

[0017] in: The bending stiffness of the rod; For internal force;

[0018] Therefore, the internal forces can be calculated.

[0019]

[0020] Establish for The standard model of torque transmitted by threads

[0021]

[0022] Therefore, the torque that causes each flexible threaded rod i to twist can be calculated.

[0023]

[0024] In addition, due to Caused for,

[0025]

[0026] in: , Shear modulus;

[0027] Step 3: Establish a friction compensation model for the continuum robot driven by the flexible threaded rod. Step 2 only considered the torsional angle of the flexible threaded rod and did not consider the friction between the flexible threaded rod and the sliding pin. Considering both torsion and friction, the total compensation torque is...

[0028]

[0029] Wherein: torque generated by friction for

[0030]

[0031] in: It is a signal function related to the rotational speed of the flexible threaded rod; It is the efficiency of the threaded rod, which is the ratio of the effective work to the input work after taking into account friction when the sliding pins in two adjacent threads rotate one revolution.

[0032]

[0033] in: The effective work done by the sliding pin rotating one revolution; s is the pitch of the sliding pin rising one thread. The input work for one revolution of the sliding pin; when When; hour, ;

[0034] Torque required to rotate one revolution of the thread for

[0035]

[0036] in: This corresponds to the horizontal thrust acting on the thread pitch diameter when tightening the sliding pin;

[0037] Similarly, the standard equation for cylindrical torsion is used to calculate the rod. because The resulting torsion angle, therefore the actual bending angle for

[0038]

[0039] in: It is the rotation angle of the flexible threaded rod;

[0040] Step 4: Solve for the length change rate of the flexible threaded rod. Based on Steps 2 and 3, the length change rate of the i-th flexible threaded rod can be obtained.

[0041] ;

[0042] Step 5: Error compensation for the continuous robot driven by the flexible threaded rod. The rate of change of the flexible threaded rod calculated in Step 4 is superimposed with the theoretical value calculated in Step 1 to compensate for the error in the motion of the flexible threaded rod.

[0043] The technical solution of this invention has the following advantages:

[0044] This invention provides a motion accuracy compensation method for a continuous robot with a flexible threaded rod torso. By estimating the amount of drive loss during motion through an error compensation model of the continuous robot with a flexible threaded rod torso, the control accuracy of the continuous robot is improved. This is especially important for applications requiring high-precision motion. Moreover, compared with traditional accuracy improvement methods, this method does not require additional sensors or auxiliary devices, and is highly economical. Attached Figure Description

[0045] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0046] Figure 1 This is a schematic diagram of a flexible threaded rod torso continuum robot provided in an embodiment of the present invention;

[0047] Figure 2 A perspective view of a tubular actuator provided for an embodiment of the present invention;

[0048] Figure 3 A perspective view of the end base provided for an embodiment of the present invention;

[0049] Figure 4 A perspective view of a tubular actuator provided for an embodiment of the present invention;

[0050] Figure 5 A cross-sectional view of a tubular actuator provided for an embodiment of the present invention;

[0051] Figure 6 To establish the kinematic model of the continuum robot using geometric analysis under the assumption of constant curvature in this invention;

[0052] Figure 7 This is a schematic diagram of the coordinates of a continuum robot established using geometric analysis under the assumption of constant curvature in this invention.

[0053] Figure 8 This is a schematic diagram of the flexible threaded rod of the present invention bending in any direction.

[0054] Explanation of reference numerals in the attached drawings: 1. Torso; 111. Flexible threaded rod; 12. End base; 121. Fixed terminal; 122. Connecting plate I; 13. Tubular actuator; 131. Drive terminal; 132. Connecting plate II; 01. DC motor; 02. Reducer; 03. Drive gear; 04. Driven gear; 05. First sliding pin; 06. Second sliding pin; 07. Third sliding pin; 131a. Front hollow cylinder; 131b. Rear hollow cylinder; 131c. Connecting rib. Detailed Implementation

[0055] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] In the description of this invention, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are used only for the convenience of describing the invention and for 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 invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0057] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0058] Furthermore, the technical features involved in the different embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0059] The motion accuracy compensation method provided by this invention is based on an object-oriented flexible threaded rod torso continuum robot, comprising a torso 11, flexible threaded rods 111, an end cap 12, and a tubular actuator 13. The torso 11 includes three flexible threaded rods 111, each with threads on its surface. The ends of each flexible threaded rod 111 are fixed to the end cap 12. The tip of each flexible threaded rod 111 is driven by the tubular actuator 13 and can move independently axially within the tubular actuator 13. When the three flexible threaded rods 111 move towards the end cap with the same increment, the torso 11 grows as a whole; when the three flexible threaded rods 111 move towards the front end with different increments, the torso 11 bends.

[0060] Specifically, the end base 12 includes several fixed terminals 121 and connecting plates I 122. The number of side lengths of the connecting plates I 122 and the number of fixed terminals 121 correspond to the number of flexible threaded rods 111, which is also three. Each included angle of the connecting plates I 122 is fixed with one fixed terminal 121, and the end of each flexible threaded rod 111 is fixed in the corresponding fixed terminal 121. The end base 12 serves to connect the ends of the three flexible threaded rods 111 and can be used to mount end effectors such as suction cups, cameras, detectors, or robotic grippers.

[0061] The thread profile of the flexible threaded rod 111 is rectangular. The tubular actuator 13 includes a drive terminal 131, a DC motor 01, a reducer 02, a drive gear 03, a driven gear 04, a first sliding pin 05, a second sliding pin 06, and a third sliding pin 07. The drive terminal 131 includes two hollow cylinders 131a and 131b on the same axial direction. There is a gap between the hollow cylinders 131a and 131b, and the hollow cylinders 131a and 131b are connected by two spaced connecting ribs 131c. The front and rear ends of the connecting ribs 131c are fixed on the circumferential surfaces of the hollow cylinders 131a and 131b, respectively. The driven gear 04 is located within the gap between the hollow cylinders 131a and 131b, and the two connecting ribs 131c are located on both sides of the driven gear 04.

[0062] The diameter of the driven gear 04 is larger than the outer diameter of the rear hollow cylinder 131b. The tooth extension distance of the driven gear 04 is the same, and the driven gear 04 and the front hollow cylinder 131a are axially aligned. A reducer 02 and a DC motor 01 are fixed on the front and rear sides of each rear hollow cylinder 131b, respectively. The input end of the reducer 02 is connected to the output end of the DC motor 01. A driving gear 03 is fixed on the output end of the reducer 02. The driving gear 03 and the driven gear 04 mesh with each other. A cavity concentric with the driven gear 04 is provided in the middle of the driven gear 04. The first sliding pin 05, the second sliding pin 06, and the third sliding pin 07 are all fixed on... On the curved inner wall of the cavity, a flexible threaded rod 111 passes into the drive terminal 131. A first sliding pin 05 and a second sliding pin 06 are engaged on both sides of the thread on the outer wall of the flexible threaded rod 111, and the line connecting the first sliding pin 05 and the second sliding pin 06 is parallel to the axis of the flexible threaded rod 111. A third sliding pin 07 is engaged at the lower edge of the thread on the flexible threaded rod 111. The plane containing the third sliding pin 07 and the plane containing the first sliding pin 05 are symmetrical about the central axis of the driven gear 04, and the axial position of the third sliding pin 07 on the driven gear 04 is between the first sliding pin 05 and the second sliding pin 06. Two connecting ribs 131c are located on both sides of the driven gear 04, which can limit the movement of the driven gear 04, effectively ensuring the rotational accuracy of the driven gear 04 and preventing slippage.

[0063] When DC motor 01 starts, its output shaft rotates, driving the output end of reducer 02 to rotate, which in turn causes drive gear 03 to rotate, which in turn drives driven gear 04 to rotate. When driven gear 04 rotates, the three sliding pins slide in the grooves of flexible threaded rods 111, causing the three flexible threaded rods 111 to move relative to the three drive terminals 131 respectively. Of course, the rotation direction of DC motor 01 can be forward or reverse. During operation, the three flexible threaded rods 111 move forward in unison most of the time. When encountering a bend, one or two flexible threaded rods 111 temporarily retract to achieve self-adaptation. After passing the bend, they move forward again.

[0064] This invention provides a motion accuracy compensation method for a torso continuum robot based on the above-mentioned flexible threaded rod, comprising the following steps:

[0065] Step 1: Establish the kinematic model of the continuum robot. The kinematic model of the continuum robot mainly includes two parts: first, establishing the mapping relationship between the drive space and the joint space; second, establishing the mapping relationship between the joint space and the operation space. The kinematic model of the robot is derived by superimposing the two. Under the assumption of piecewise constant curvature, the kinematic model of the continuum robot is established using geometric analysis. Then, for a continuum robot with at least two flexible threaded rods 111, the direction vector of the i-th end effector relative to the (i-1)-th end base 12 is:

[0066]

[0067] in: Let be the rotation angle of the i-th segment of the continuum robot in the xy plane; Let be the bending angle of the i-th segment of the continuum robot arc; s represents sin; c represents cos.

[0068] Since the two flexible threaded rods 111 are 60° apart on the z-axis, the rotation matrix... End effector Relative to end base 12 The transformation matrix can be represented as Meanwhile, the tubular thread length S of the flexible threaded rod 111 can be expressed as S = , , , .

[0069] in: , and is the length of the three flexible threaded rods 111; r is the distance from the virtual bone to the tubular actuator 13; The curvature of the virtual bone.

[0070] The distance between r and the center of the i-th flexible threaded rod 111 to the Z0Y0 plane The relationship is

[0071]

[0072]

[0073] in: The length of the central trunk;

[0074] Step 2: Establish a torsional compensation model for the continuum robot driven by the flexible threaded rod 111. The geometry of the flexible threaded rod 111 will cause its own twisting, affecting accuracy. The length of the flexible threaded rod 111 obtained in Step 1 is... Its curvature can be calculated. Therefore, for a given unit length of A flexible threaded rod 111 with n threads, the i-th flexible threaded rod 111 needs to rotate by the following angle: Based on this, considering the torsion of the flexible threaded rod 111, and assuming that the central trunk is virtual and does not bear any internal force, the total force applied to the end base 12 is...

[0075] in: The bending stiffness of the rod; It is internal force.

[0076] Therefore, the internal forces can be calculated.

[0077]

[0078] Establish for The standard model of torque transmitted by threads

[0079]

[0080] Therefore, the torque that causes each flexible threaded rod i to twist can be calculated.

[0081]

[0082] In addition, due to Caused for,

[0083]

[0084] in: , Shear modulus;

[0085] Step 3: Establish a friction compensation model for the continuum robot driven by the flexible threaded rod 111. Step 2 only considered the torsional angle of the flexible threaded rod 111, without considering the friction between the flexible threaded rod 111 and the sliding pin on the driven gear. Considering both torsion and friction, the total compensation torque is...

[0086]

[0087] Wherein: torque generated by friction for

[0088]

[0089] in: It is a signal function related to the rotational speed of the flexible threaded rod 111; The efficiency of the flexible threaded rod 111 is the ratio of the effective work to the input work after taking into account friction when the sliding pins in two adjacent threads rotate one revolution.

[0090]

[0091] in: The effective work done by the sliding pin rotating one revolution; s is the pitch of the sliding pin rising one thread. The input work for one revolution of the sliding pin; when hour, ;when hour, ;

[0092] Torque required to rotate one revolution of the thread for

[0093]

[0094] in: This corresponds to the horizontal thrust acting on the thread pitch diameter when tightening the sliding pin;

[0095] Similarly, the standard equation for cylindrical torsion is used to calculate the rod. because The resulting torsion angle, therefore the actual bending angle for

[0096]

[0097] in: It is the rotation angle of the flexible threaded rod 111;

[0098] Step 4: Solve for the length change rate of the flexible threaded rod 111. Based on Steps 2 and 3, the length change rate of the i-th flexible threaded rod can be obtained.

[0099] ;

[0100] Step 5: Perform error compensation for the continuum robot. The rate of change of the flexible threaded rod 111 calculated in Step 4 is superimposed with the theoretical value calculated in Step 1. This compensates for the motion error of the flexible threaded rod 111, meaning the actual driving amount equals the value calculated in Step 1. Add the result calculated in step 2

[0101] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A method for compensating the motion accuracy of a flexible threaded rod torso continuum robot, characterized in that, Includes the following steps: Step 1: Establish the kinematic model of the continuum robot. The kinematic model of the continuum robot mainly includes two parts: first, establishing the mapping relationship between the drive space and the joint space; second, establishing the mapping relationship between the joint space and the operation space. The kinematic model of the robot is derived by superimposing the two. Under the assumption of constant curvature in the segments, the kinematic model of the continuum robot is established using geometric analysis. Then, for a continuum robot with at least two flexible threaded rods (111), the i-th end effector relative to the (i-1)-th end effector... The direction vector of the end base (12) is in: Let be the rotation angle of the i-th segment of the continuum robot in the xy plane; Let be the bending angle of the i-th segment of the continuum robot arc; s represents sin; c represents cos; Since the two flexible threaded rods (111) are 60° apart on the z-axis, the rotation matrix... End effector Relative to the end base (12) The transformation matrix can be represented as Meanwhile, the tubular thread length S of the flexible threaded rod (111) can be expressed as... in: , and is the length of the three flexible threaded rods (111); r is the distance from the virtual bone to the tubular actuator (13); The curvature of the virtual bone; The distance from r to the center of the i-th flexible threaded rod (111) to the Z0Y0 plane The relationship is in: The length of the central trunk; Step 2: Establish a torsional compensation model for the continuum robot driven by the flexible threaded rod (111). The geometry of the flexible threaded rod (111) will cause its own twisting, which will affect the accuracy. The length of the flexible threaded rod (111) obtained in Step 1 is used to calculate the torsional compensation model. Its curvature can be calculated. Therefore, for a given unit length of A flexible threaded rod (111) with n threads, the angle required for the i-th flexible threaded rod (111) to rotate is Based on this, the torsion of the flexible threaded rod (111) is considered, and it is assumed that the central trunk is virtual and does not bear any internal force. The total force applied to the end base (12) is ; in: The bending stiffness of the rod; For internal force; Therefore, the internal forces can be calculated. Establish for The standard model of torque transmitted by threads; ； Therefore, the torque that causes each flexible threaded rod i to twist can be calculated. ； In addition, due to the cause for, ； in: , Shear modulus; Step 3: Establish a friction compensation model for the continuum robot driven by the flexible threaded rod (111). Step 2 only considered the torsional angle of the flexible threaded rod (111) and did not consider the friction between the flexible threaded rod (111) and the sliding pin on the driven gear. Considering both torsion and friction, the total compensation torque is... Wherein: torque generated by friction for ； in: It is a signal function related to the rotational speed of the flexible threaded rod (111); It is the efficiency of the flexible threaded rod (111), which is the ratio of the effective work after friction to the input work when the sliding pins in two adjacent threads rotate one revolution. ； in: The effective work done by the sliding pin rotating one revolution; s is the pitch of the sliding pin rising one thread. The input work for one revolution of the sliding pin; when hour, ;when hour, ; Torque required to rotate one revolution of the thread for ； in: This corresponds to the horizontal thrust acting on the thread pitch diameter when tightening the sliding pin; Similarly, the standard equation for cylindrical torsion is used to calculate the rod. because The resulting torsion angle, therefore the actual bending angle for: ； in: It is the rotation angle of the flexible threaded rod (111); Step 4: Solve for the length change rate of the flexible threaded rod (111). Based on Steps 2 and 3, the length change rate of the i-th flexible threaded rod can be obtained. ; Step 5: Error compensation for the continuous robot driven by the flexible threaded rod (111). The rate of change of the flexible threaded rod (111) calculated in step 4 is superimposed with the theoretical value calculated in step 1, thereby compensating for the motion error of the flexible threaded rod (111).

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