Coupling flexible cable kinematics solving method

Abstract

The application discloses a kind of coupling cable kinematics solving method, including obtaining the coordinates of each key point at the jth joint;According to the coordinates of each key point at the jth joint, the theoretical length of two sections of cable driving the ith joint at the jth joint is obtained;Without considering the coupling phenomenon of cable, according to the theoretical length of two sections of cable driving the ith joint at the jth joint, the theoretical total length of cable driving the ith joint is obtained;Considering the coupling phenomenon of cable, according to the theoretical total length of cable driving the ith joint, the actual length of two sections of cable driving the ith joint is obtained;According to the actual length of two sections of cable driving the ith joint, the change of two sections of cable driving the ith joint is obtained;According to the change of two sections of cable driving the ith joint, the required rotation angle of driving motor is determined.The application can realize kinematics conversion and solving in coupling cable system, and has guiding significance for accurate control of cable driven object.

Description

Technical Field

[0001] This invention belongs to the field of surgical robot technology, and relates to a kinematics solution method, particularly a coupled flexible cable kinematics solution method. Background Technology

[0002] Flexible cables can drive the movement of rotary joints via a cross-axis or rotary axis. A joint can be driven by one, two, or three flexible cables. The length of the flexible cable changes with the joint deflection angle. A drive motor alters the position and length of the flexible cable, thereby controlling the joint deflection angle. Existing kinematic solutions related to cable-driven systems generally analyze the conversion relationship between cable length and joint deflection angle from a spatial geometry perspective. They derive formulas to analyze the change in cable length under theoretical conditions, treating the flexible cables driving a joint as independent cables without coupling. However, in minimally invasive surgical robot systems, where a joint is driven by the two ends of a single driving cable, it is necessary to analyze the coupling effect existing between the two ends of this driving cable.

[0003] Minimally invasive surgical robot systems are a current hot research area, involving the intersection and integration of multiple disciplines, with a very broad application prospect. The human heart has a complex environment. On the one hand, the heart chambers are narrow and filled with various tissue fluids, and the surface of the myocardium is covered with a layer of slippery fatty tissue, making it difficult for surgical robots to be fixed in the heart chambers using suction cup-like auxiliary tools. On the other hand, the heart beats rhythmically, and the environment of the heart chambers is constantly changing. This dynamic environment brings great difficulties to the positioning and precise operation of the surgical robot. Currently, many routine cardiac surgeries still require cardiac arrest to ensure the accuracy of the surgeon's precise operations, placing a heavy burden on the patient. To ensure safety and navigation accuracy, existing cardiac surgical robots have low motion efficiency, slow movement speed, and cumbersome operation, greatly limiting their application in actual clinical practice. Therefore, how to improve motion capability while ensuring safety and operability has become a problem that cardiac surgical robots must face. Due to the complex environment and high safety requirements of minimally invasive surgical robots, the kinematic model construction and kinematic solution methods are particularly important for improving control accuracy for cable-driven surgical robot systems.

[0004] Based on the motor's position information, the changes in the two flexible cables can be calculated, and thus the deflection angle of the driven joint can be determined. In traditional solutions, a joint is driven by two independent flexible cables, which are independent of each other and have no coupling. However, in minimally invasive robot structures, a joint is driven by the two ends of a single flexible cable, and these two ends of the cable are coupled.

[0005] In a cable-driven surgical robot system, the middle segment of the cable driving the i-th joint is connected to the motor-driven transmission system, and this connection point is defined as O.i Point, the two ends of the driving flexible cable are connected to the rotary joint, and the two ends are defined as A and B respectively. ii2 Point and B ii2 Point, will O i Point and A ii2 The length of the driving cable between points is defined as l ia , will O i Point and B ii2 The length of the driving cable between points is defined as l ib It is generally believed that the total length of the same driving cable remains unchanged, i.e., l ia +l ib It is a constant value. However, in reality, as the joint deflection angle changes, it can be analyzed through spatial geometry that its theoretical total length will change, i.e., l ja +l jb It will change with the deflection angle. But l ia With l ib There is no relevant proof or research result regarding the magnitude of their respective changes. Summary of the Invention

[0006] The purpose of this invention is to overcome the above-mentioned defects and provide a method for solving the kinematics of coupled flexible cables. This method solves the technical problem that traditional solution methods are not applicable to coupled flexible cables, thus leading to the inability to effectively control the motion of coupled flexible cables. This invention can realize the kinematic transformation and solution of coupled flexible cable systems and has guiding significance for the precise control of flexible cable driven objects.

[0007] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0008] A method for solving coupled flexible cable kinematics includes:

[0009] S1 obtains the coordinates of each key point at the j-th joint;

[0010] S2 obtains the theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint based on the coordinates of each key point at the j-th joint.

[0011] S3 does not consider the coupling phenomenon of the flexible cable. Based on the theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint, the total theoretical length of the flexible cable driving the i-th joint is obtained.

[0012] S4 considers the coupling phenomenon of the flexible cable. Based on the theoretical total length of the flexible cable driving the i-th joint, the actual lengths of the two flexible cables driving the i-th joint are obtained.

[0013] S5 obtains the change in the two flexible cables driving the i-th joint based on the actual lengths of the two flexible cables driving the i-th joint.

[0014] S6 determines the required rotation angle of the drive motor based on the change in the two flexible cables driving the i-th joint.

[0015] i>j≥1.

[0016] Furthermore, the two flexible cables driving the i-th joint are defined as rope A and rope B, respectively. When the two flexible cables driving the i-th joint pass through the j-th joint, rope A passes from point A. ij1 Pass through the (j-1)th arm, starting from point A ij2 Insert the j-th arm rod, and rope B starts from point B. ij1 Pass through the (j-1)th arm, starting from point B ij2 Insert the j-th arm, the point A ij1 Point A ij2 Point B ij1 and point B ij2 These are the key points at the j-th joint;

[0017] Step S1, which obtains the coordinates of each key point at the j-th joint, includes: determining point A based on the basic kinematic model of the cable-driven robotic arm. ij1 Point A ij2 Point B ij1 and point B ij2 The coordinates of the j-th joint in the body coordinate system.

[0018] Furthermore, the method for obtaining the coordinates of each key point at the j-th joint in step S1 includes:

[0019] Determine the midpoint A of the body coordinate system of the j-th joint. ij1 and point B ij1 coordinates S ija1_j and S ijb1_j And point A in the body coordinate system of the (j+1)th joint. ij2 and point B ij2 coordinates S ija2_j+1 and S ijb2_j+1 :

[0020]

[0021] Where, r ij d is the distance between the axis of the drive hole corresponding to the drive cable that drives the i-th joint at the j-th joint and the axis of the arm center where the drive hole is located; pj d represents the distance from the center point of the j-th joint to the front end, where the front end is the drive cable inlet; qj ψ is the distance from the center point of the j-th joint to the rear end, where the rear end is the output end of the drive cable; ija ψ ijb The phase angle between two corresponding drive holes on the same arm when the drive cable for driving the i-th joint passes through the j-th joint;

[0022] Based on the transformation matrix between the body coordinate system of the j-th joint and the body coordinate system of the (j+1)-th joint. Point A in the body coordinate system of the (j+1)th joint ij2 and point B ij2 The coordinates are converted to the midpoint A of the body coordinate system of the j-th joint. ij2 and point B ij2 Coordinates:

[0023]

[0024]

[0025] Where, q j Let be the degree of freedom corresponding to the j-th joint.

[0026] Furthermore, step S2 is based on the coordinates S of each key point at the j-th joint. ija1_j S ija2_j S ijb_1 and S ijb_2 The theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint are obtained through the following methods:

[0027]

[0028]

[0029] Where, ζ ija * For S ija1_j and S ija2_j The distance between them, ζ ijb * For S ijb_1 and S ijb_2 The distance between them.

[0030] Furthermore, step S3 does not consider the coupling phenomenon of the flexible cable. The method for obtaining the theoretical total length of the flexible cable driving the i-th joint based on the theoretical lengths of the two flexible cable segments driving the i-th joint at the j-th joint includes:

[0031] Based on the theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint, the theoretical total length ζ of the flexible cable driving the i-th joint at the j-th joint is obtained. ij * :

[0032] ζ ij * =ζ ija * +ζ ijb * ;

[0033] Based on the theoretical total length of the flexible cable driving the i-th joint at each joint, the theoretical total length l of the flexible cable used to drive the i-th joint is obtained. i * :

[0034]

[0035] Among them, κ j Let be the length of the j-th arm.

[0036] Furthermore, step S4 considers the coupling phenomenon of the flexible cable, based on the theoretical total length l of the flexible cable driving the i-th joint. i * The actual length l of the two flexible cables driving the i-th joint is obtained. ia and l ib The methods include:

[0037]

[0038] dζ ij ==ζ ij * -2(d pj +d qj ),

[0039] Furthermore, step S6 is based on the change Δl between the two flexible cables driving the i-th joint. ia and △l ib Methods for determining the required rotation angle of the drive motor include:

[0040] Δn i =Δl ia / θ=-Δl ib / θ

[0041] Where θ is the transmission coefficient of the drive motor.

[0042] Furthermore, it also includes determining the coupling cable layout that minimizes the cumulative change in the length of the two flexible cables driving the i-th joint at the j-th joint, based on the theoretical lengths of the two flexible cables at the j-th joint. Under this layout, steps S3 to S6 are executed.

[0043] Furthermore, the coupling cable layout that minimizes the cumulative change in the lengths of the two flexible cables driving the i-th joint at the j-th joint is as follows:

[0044] |ψ ija -ψ ijb |=180°;

[0045] ψ ija=0° and ψ ijb =180°, or ψ ija =180° and ψ ijb =0°.

[0046] Furthermore, the method for determining the coupling cable layout that minimizes the cumulative change in the lengths of the two flexible cables driving the i-th joint at the j-th joint, based on the theoretical lengths of the two flexible cables at the j-th joint, includes:

[0047] Construct a model of the cumulative change in length of the two flexible cables driving the i-th joint at the j-th joint:

[0048] dζ ij =ζ ija * +ζ ijb * -2(d pj +d qj )

[0049] The ζ obtained in step S2 ija * and ζ ijb * Substituting into the above model, we obtain dζ ij Follow q j and ψ ija -ψ ijb Based on the changing simulation data, determine |ψ ija -ψ ijb |=180°;

[0050] In |ψ ija -ψ ijb Given that | = 180°, let ψ ija and ψ ijb One of them is ψ, and the other is ψ+π. The above model can be transformed into the following form:

[0051] dζ=ζ * (ψ)+ζ * (ψ+π)-2(d pj +d qj )≤4r|cos(ψ)sin(q j / 2)|;

[0052] Where, ζ * (ψ) and ζ * (ψ+π) represents ζ ija * and ζ ijb * ;

[0053] The value of ψ is determined by the transformed form, which is either 0° or 180°.

[0054] Compared with the prior art, the present invention has at least one of the following advantages:

[0055] (1) This invention creatively proposes a method for solving the kinematics of coupled flexible cables. By comprehensively considering the relationship between the length of the flexible cable and the deflection angle, the kinematic transformation and solution of the coupled flexible cable system are realized. This invention is applied to systems such as minimally invasive surgical robots, flexible cable driven robotic arms, and flexible cable driven deformation mechanisms, and has guiding significance for the precise control of flexible cable driven objects.

[0056] (2) This invention designs the driving cable with a 180° phase difference, minimizing the cumulative change in length of the two coupled cables at the same joint, thus enabling more precise motion control. Furthermore, this invention theoretically derives the range of variation in the total theoretical length of the single-joint driving cable, allowing analysis of the upper limit of the change in the total theoretical length dζ of the single-joint driving cable when the phase angle ψ takes different values, thereby enabling better selection of the phase angle ψ value. All of these methods contribute to further improving the solution accuracy.

[0057] (3) This invention takes into account the coupling phenomenon of the flexible cable and constructs the relationship between the length of the two flexible cables and the joint deflection angle, which can be used to solve the kinematics of the coupled flexible cable, thereby improving the motion control effect. Attached Figure Description

[0058] Figure 1 This is a flowchart of the coupled flexible cable kinematics solution method of the present invention;

[0059] Figure 2 Simplified diagram of independent cable drive;

[0060] Figure 3 A simplified diagram of the flexible cable coupling drive;

[0061] Figure 4 This is a diagram showing the distribution of the drive holes in the flexible cable.

[0062] Figure 5 For ψ ija A schematic diagram of the theoretical total length change of a single-joint driven flexible cable at 0°, where (a), (b), (c), and (d) are the front view, left view, contour map, and oblique view, respectively;

[0063] Figure 6 For ψ ija A schematic diagram of the theoretical total length change of a single-joint driven flexible cable at 45°, where (a), (b), (c), and (d) are the front view, left view, contour map, and oblique view, respectively;

[0064] Figure 7 For ψ ija =0°、ψ ijbThe variation of the sum of the lengths of the flexible rope at 180° with the deflection angle;

[0065] Figure 8 For ψ ija =45°, ψ ijb The variation of the sum of the lengths of the flexible rope at 225° with the deflection angle;

[0066] Figure 9 For ψ ija =90°, ψ ijb The variation of the sum of the lengths of the flexible rope at 270° with the deflection angle;

[0067] Figure 10 This is a simplified diagram of an application object of the present invention;

[0068] Figure 11 The curve showing the change in rope length over time in the flexible rope theory;

[0069] Figure 12 The curve showing the change in the difference between the expected total length of the driving cable and the initial length of the driving cable;

[0070] Figure 13 The curve showing the change in length of the driving flexible cable considering coupling. Detailed Implementation

[0071] The features and advantages of the present invention will become clearer and more apparent from the following detailed description.

[0072] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0073] This invention solves the problem that the theoretical total length of the same driving cable is not constant under different deflection angles, and derives a layout where the phase difference between the two segments of the driving cable is 180°, minimizing the cumulative change in the length of the two coupled cables at the same joint. This invention also constructs a more complete kinematic solution method for the coupling problem in coupled cable systems, which can be used for solving the kinematics of coupled cables, thereby improving motion control performance.

[0074] This invention provides a method for solving coupled flexible cable kinematics, comprising:

[0075] Step 1: Construct the basic kinematic model of the cable-driven robotic arm;

[0076] Step 2: Based on the constructed kinematic model, solve for the coordinates of each key point at each joint;

[0077] Step 3: Based on the coordinates of each key point, calculate the theoretical value of the flexible cable length at each joint;

[0078] Step 4: Design a layout with a 180° phase difference between the driving cables and two driving cable segments with phases of 180° and 0° respectively, based on theoretical values;

[0079] Step 5: Ignoring the coupling phenomenon of the flexible cable, solve for the theoretical total length of the coupled flexible cable;

[0080] Step 6: Considering the coupling phenomenon of the flexible cable, solve for the lengths of the two segments driving the flexible cable;

[0081] Step 7: Calculate the rotation angle of the drive motor based on the two lengths of the drive cable.

[0082] Step 2: Solve for the coordinates of each key point at each joint, including:

[0083] The two drive cables at the j-th joint drive the i-th joint. Each drive cable segment is divided into an inlet and an outlet at the j-th joint. These four key points are represented by point A. ij1 Point A ij2 Point B ij1 Point B ij2 In the body coordinate system of the j-th joint, that is, in the j-th coordinate system, point A... ij1 and point B ij1 The corresponding coordinates are represented as: S ija1_j (x ija1_j ,y ija1_j ,z ija1_j ), S ijb1_j (x ijb1_j ,y ijb1_j ,z ijb1_j The parameters are related to the structural dimensions of the robotic arm and are fixed quantities. In the (j+1)th coordinate system, point A... ij2 and point B ij2 The corresponding coordinates are represented as: S ija2_j+1 (x ija2_j+1 ,y ija2_j+1 ,z ija2_j+1 ), S ijb2_j+1 (x ijb2_j+1 ,y ijb2_j+1 ,z ijb2_j+1 The parameters are related to the dimensions of the robotic arm and are fixed. Based on the mechanical structure of the robotic arm, the body coordinates of four key points can be obtained, as shown below:

[0084]

[0085] The coordinates of key points in different coordinate systems can be obtained through the transformation matrix T. Point A can be obtained ij2 and point B ij2 The coordinate value of the j-th joint in the body coordinate system (i.e., the j-th coordinate system): S ija2_j S ijb2_j As shown below:

[0086]

[0087] The degree of freedom corresponding to the j-th joint is the yaw degree of freedom q. j When, the corresponding transformation matrix As shown below:

[0088]

[0089] r in the formula ij The distance between the axis of the drive hole corresponding to the drive cable of the i-th joint at the j-th joint and the axis of the boom center; d pj It is the distance from the center point of the j-th joint to the front end, i.e., the distance from the inlet end of the drive cable; d qj ψ is the distance from the center point of the j-th joint to the rear end, i.e., the distance from the exit end of the drive cable; ija ψ ijb It is the phase angle between the two corresponding drive holes on the same arm when the drive cable driving the i-th joint passes through the j-th joint.

[0090] The specific process of solving the theoretical value of the flexible cable length at each joint in step S3 is as follows: Based on the key points related to the flexible cable length, at each joint, the theoretical value of the flexible cable length is analyzed by the distance between two key points.

[0091] The theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint are:

[0092]

[0093] In the formula, the dis function represents the distance between two points, and S can be obtained through step 3. ija1_j S ijb1_j S ija2_j S ijb2_j The value.

[0094] Substituting the values ​​and rearranging them, we can obtain a general formula for calculating the theoretical length of a flexible rope:

[0095]

[0096] With point A ij1 and point A ij2 For example, in the above formula, ζ* d p d q , q, r, ψ are respectively ζ ija * d pj d qj q j r ij ψ ija .

[0097] The theoretical length ζ of a single-joint flexible cable can be seen from the formula. * The distance d between the joint center point and the anterior end of the joint p d, the distance between the center point of the joint and the posterior end of the joint q The distance r between the axis of the drive hole and the central axis of the boom, as well as the phase angle ψ and the degree of freedom q, are related parameters.

[0098] In step 4, the theoretical basis for designing a layout with a 180° phase difference between the driving cables based on theoretical values ​​includes: the driving cable driving the i-th joint starts from point A. ij1 and point B ij1 When passing through and entering the j-th joint, the phase angles of the two corresponding drive holes are respectively ψ ija ψ ijb Point A ij1 and point B ij1 The distance between the circle and the center is r. ij The theoretical lengths of these two flexible cables at this joint are ζ, respectively. ija * and ζ ijb * The relationship between the theoretical length of the flexible cable and the phase angle can be obtained. Since these two sections of the flexible cable are the same driving cable, when the joint deflection angle changes, it is necessary to minimize ζ while satisfying the basic constraints. ija * +ζ ijb * The change in is characterized by dζ, as shown in the following formula, which represents the change in the total theoretical length of the single-joint driven flexible cable.

[0099] dζ ij =ζ ija * +ζ ijb * -2(d pj +d qj )

[0100] When the phase angle ψ of the aperture ija ψ ijb Satisfy |ψ ija -ψ ijbWhen the relationship is |=180°, the corresponding dζ is approximately zero, meaning that the sum of the lengths of the two coupled flexible cables is less affected by the change in joint deflection angle; when the phase difference between the two flexible cables corresponding to the same joint is 180°, the cumulative change in the length of the two coupled flexible cables at the same joint is minimal.

[0101] The theoretical basis for designing the two driving cable segments with phases of 180° and 0° respectively in step 4 is as follows:

[0102] Substituting the condition that the two flexible cable segments are 180° out of phase, we can obtain the following equation for the theoretical total length change dζ of the single-joint driven flexible cable:

[0103] dζ=ζ * (ψ)+ζ * (ψ+π)-2(d p +d q )≤4r|cos(ψ)sin(q / 2)|

[0104] That is, the total change in the theoretical length of the single-joint driven flexible cable is less than or equal to 4r|cos(ψ)sin(q / 2)|;

[0105] When the phase angle ψ is 0° or 180°, i.e. cos(ψ)=1, the upper limit of the total change in the theoretical length of the single-joint driven flexible cable dζ is relatively large, and dζ can be positive or negative;

[0106] When the phase angle ψ is 90° or -90°, i.e., cos(ψ) = 0, the upper limit of the total change in the theoretical length dζ of the single joint driven flexible cable is zero. As the absolute value of the joint deflection angle increases, dζ will decrease accordingly.

[0107] Ignoring the coupling phenomenon of the flexible cable, solve for the total theoretical length of the coupled flexible cable, including:

[0108] The driving cable that drives the i-th joint is divided into two segments, A and B, at the j-th joint, with lengths ζ and ζ respectively. ija * ζ ijb * The corresponding theoretical length ζ of the flexible cable ij * The following equations must be satisfied:

[0109] ζ ij * =ζ ija * +ζ ijb *

[0110] Then, the theoretical total length of the driving rope is obtained.

[0111] κ in the formula j Let be the length of the j-th arm.

[0112] Considering the coupling phenomenon of the flexible cable, solve for the lengths of the two segments driving the flexible cable, including:

[0113] The driving cable that drives the i-th joint is split into two segments at the j-th joint, with a corresponding cable length ζ. ij The following equations must be satisfied:

[0114] ζ ij =ζ ija +ζ ijb

[0115] Since the material of each segment of the coupling cable is the same, a parameter ζ at a joint is obtained. ija ζ ijb The formula for the numerical value:

[0116]

[0117] The difference dζ between the expected total length of the driving cable at a joint in the formula and the initial length of the driving cable. ij as follows:

[0118] dζ ij ==ζ ij * -2(d p +d q )

[0119] The expected total length ζ of the driving cable at a joint ij * The calculation formula is as follows:

[0120] ζ ij * =ζ ija * +ζ ijb *

[0121] As can be seen from the above, the parameter ζ at a joint... ija With ζ ijb The sum is always a constant:

[0122] ζ ija +ζ ijb =2(d p +d q )

[0123] That is, the change dζ of segment A of the flexible cord driving the i-th joint. ija The length of segment B of the flexible cord driving the i-th joint changes by dζ ijb The sum of their lengths is zero:

[0124] dζ ija +dζ ijb =0

[0125] By summing up the changes in the flexible cable at each joint, the expected total length l of the driving flexible cable can be obtained. i * With the initial length l of the driving flexible cable i The difference △l i * The calculation formula is as follows:

[0126]

[0127] Finally, the lengths l of the two segments of the flexible cable driving the i-th joint can be solved using the following formula. ia l ib :

[0128]

[0129] In the formula

[0130] Example:

[0131] This embodiment is combined with the appendix Figure 1-13 The present invention will be described.

[0132] This invention provides a method for solving coupled cable kinematics, which can be applied to systems such as minimally invasive surgical robots, cable-driven robotic arms, and cable-driven deformation mechanisms. This method enables kinematic transformation and solving in coupled cable systems, laying the foundation for precise control of cable-driven objects.

[0133] The symbols used in this invention are explained as follows: the number of joints and degrees of freedom of the robotic arm are both N; a 4×4 transformation matrix is ​​represented by T; a 3×3 transformation matrix is ​​represented by R; the j-th coordinate system is the body coordinate system of the j-th joint, the origin of the j-th coordinate system is the center point of the j-th joint, and the x-axis direction is the same as the axis direction of the j-th arm; the transformation matrix between the (j-1)-th coordinate system and the j-th coordinate system is... The rotation transformation matrix between the (j-1)th coordinate system and the j-th coordinate system is: The degree of freedom of the j-th joint is denoted by q. j The two flexible cables driving the same joint are defined as rope A and rope B, and the lengths of the two flexible cables driving the i-th joint are l and l respectively. ia and l ib ;l i The total length of the driving cable for the i-th joint; when the two segments of the cable driving the i-th joint pass through the j-th joint, rope A starts from point A. ij1 Pass through the (j-1)th arm, starting from point A ij2 Insert the j-th arm rod, and rope B starts from point B.ij1 Pass through the (j-1)th arm, starting from point B ij2 Insert the j-th arm; the coordinates of key points in the robotic arm are denoted by S, for example, the coordinates of the center point of the j-th joint are Sj. j (x j ,y j ,z j Point A) ij1 The coordinates are S ija1 (x ija1 ,y ija1 ,z ija1 The lengths of the two driving cables driving the i-th joint at the j-th joint are ζ respectively. ija and ζ ijb The corresponding change is dζ ija and dζ ijb The total length of the two driving cables driving the i-th joint at the j-th joint is ζ. ij ;r ij The distance between the axis of the drive hole corresponding to the drive cable of the i-th joint at the j-th joint and the axis of the boom center; d pj d is the distance from the center point of the j-th joint to the front end face; qj It is the distance from the center point of the j-th joint to the rear end face; the center point of the j-th joint is point O. j x in the j-th coordinate system j axis and y j All axes pass through point O j x j The axial direction is the same as the axial direction of the j-th arm, y j The axis is perpendicular to x j Axis; When the drive cable driving the i-th joint passes through the j-th joint, the two segments of the drive cable respectively start from point A. ij1 and point B ij1 Exit, point A ij1 The line connecting the center of the front face and x j The angle between the axes is the phase angle ψ ija Point B ij1 The line connecting the center of the front face and x j The angle between the axes is the phase angle ψ ijb ;κ j Let be the length of the j-th arm. In this invention, the length of the arm refers to the sleeve length, which is the distance between the front end face and the rear end face.

[0134] In this invention, the symbols with an asterisk (*) in the upper right corner represent ideal variable values ​​without considering the effects of flexible cable coupling, while the symbols without an asterisk represent variable values ​​considering the effects of flexible cable coupling.

[0135] The specific implementation steps of this invention are as follows: Figure 1 As shown.

[0136] Existing research related to this invention includes a kinematic model of a cable-driven independent drive system. This model constructs a kinematic model where each joint drives two independent cables (without considering cable deformation) via two motors. The transformation relationships between various parameters in the robotic arm model are derived. These two driving cables are independent and uncoupled. The construction of the DH coordinate system and the acquisition of the transformation matrix T between the joints are fundamental kinematic modeling steps and will not be described in detail here.

[0137] like Figure 2 As shown, in a traditional cable-driven independent actuation system, each joint is driven by two independent cables. The two cables driving the i-th joint pass through the j-th joint, and the ideal lengths of these two cables at that joint are ζ and ζ, respectively. ija * and ζ ijb * The mapping relationship between the length of the flexible cable and the joint deflection angle can be solved by using the transformation matrix.

[0138] The length of each flexible cable is related to the rotation angle of the drive motor, as shown in the following formula:

[0139] Δl i =θ·Δn i

[0140] In the formula, △l i Let be the change in the i-th driving cable; θ is the transmission coefficient, equal to the distance the driving cable moves for one revolution of the motor; Δn i This represents the number of revolutions of the motor, which can be taken as a decimal.

[0141] Research on traditional cable-driven independent actuation systems is quite mature. However, if a joint is driven not by an independent cable, but by the two ends of a single cable, as described in the paper "A survey on actuators-driven surgical robots" published in the journal "Sensors and Actuators A: Physical," then the lengths of the actuation cables at the joint exhibit a coupling relationship. No research has been conducted on the kinematic relationship of this coupling. Therefore, research is needed on systems like... Figure 3 The invention presents a flexible cable coupled drive system. It analyzes the mapping relationship between joint deflection angles and the driving flexible cable under flexible cable coupled drive, and proposes a method for solving the kinematics of the coupled flexible cable. The specific implementation steps are as follows:

[0142] Step 1: Build the model.

[0143] Analyzing a cable-driven robotic arm requires constructing a corresponding DH coordinate system and transformation matrix to lay the groundwork for kinematic analysis. The method used in this step is an existing one and will not be described in detail here.

[0144] Step 2: Solve for the coordinates of the key points.

[0145] The two drive cables at the j-th joint drive the i-th joint. Each drive cable segment is divided into an inlet and an outlet at the j-th joint. These four key points are represented by point A. ij1 Point A ij2 Point B ij1 Point B ij2 In the body coordinate system of the j-th joint, that is, in the j-th coordinate system, point A... ij1 and point B ij1 The corresponding coordinates are represented as: S ija1_j (x ija1_j ,y ija1_j ,z ija1_j ), S ijb1_j (x ijb1_j ,y ijb1_j ,z ijb1_j The parameters are related to the structural dimensions of the robotic arm and are fixed quantities. In the (j+1)th coordinate system, point A... ij2 and point B ij2 The corresponding coordinates are represented as: S ija2_j+1 (x ija2_j+1 ,y ija2_j+1 ,z ija2_j+1 ), S ijb2_j+1 (x ijb2_j+1 ,y ijb2_j+1 ,z ijb2_j+1 The parameters are related to the dimensions of the robotic arm and are fixed. Based on the mechanical structure of the robotic arm, the body coordinates of four key points can be obtained, as shown below:

[0146]

[0147] The coordinates of key points in different coordinate systems can be obtained through the transformation matrix T. Point A can be obtained ij2 and point B ij2 The coordinate value of the j-th joint in the body coordinate system (i.e., the j-th coordinate system): S ija2_j S ijb2_j As shown below:

[0148]

[0149] The degree of freedom corresponding to the j-th joint is the yaw degree of freedom q. j When, the corresponding transformation matrix As shown below:

[0150]

[0151] Step 3: Solve for the theoretical length of the single-joint flexible cable.

[0152] Based on the coordinates of the key points of the flexible cable in each coordinate system, the theoretical value of the cable length can be obtained by measuring the distance between two key points within the same coordinate system. For example, based on point A... ij1 and point A ij2 The distance between them, solve for ζ ija * .

[0153] The theoretical lengths of the two flexible cables driving the i-th joint at the j-th joint are:

[0154]

[0155] In the formula, the dis function represents the distance between two points, and S can be obtained through step 3. ija1_j S ijb1_j S ija2_j S ijb2_j The value.

[0156] Substituting the values ​​and rearranging them, we can obtain a general formula for calculating the theoretical length of a flexible rope:

[0157]

[0158] With point A ij1 and point A ij2 For example, in formula (1), ζ * d p d q , q, r, ψ are respectively ζ ija * d pj d qj q j r ij ψ ija .

[0159] The theoretical length ζ of a single-joint flexible cable can be seen from the formula. * The distance d between the joint center point and the anterior end of the joint p d, the distance between the center point of the joint and the posterior end of the joint q The distance r between the axis of the drive hole and the central axis of the boom, as well as the phase angle ψ and the degree of freedom q, are related parameters.

[0160] Step 4: Design the flexible cable layout.

[0161] The driving cable for the i-th joint starts from point A. ij1and point B ij1 When passing through and entering the j-th joint, the phase angles of the two corresponding drive holes are respectively ψ ija ψ ijb Point A ij1 and point B ij1 The distance between the circle and the center is r. ij That is, the distance between the axis of the drive hole corresponding to the drive cable that drives the i-th joint at the j-th joint and the axis of the arm center where the drive hole is located, such as Figure 4 As shown. The center point of the j-th joint is point O. j x in the j-th coordinate system j axis and y j All axes pass through point O j x j The axial direction is the same as the axial direction of the j-th arm, y j The axis is perpendicular to x j The theoretical lengths of these two flexible cables at this joint are ζ. ija * and ζ ijb * According to formula (1), the relationship between the theoretical length of the flexible cable and parameters such as the phase angle can be obtained. Since these two sections of the flexible cable are the same driving cable, when the joint deflection angle changes, ζ should be minimized as much as possible. ija * +ζ ijb * The change in length is represented by dζ, as shown in the following formula, which characterizes the change in the total theoretical length of the single-joint driven flexible cable.

[0162] dζ ij =ζ ija * +ζ ijb * -2(d pj +d qj )

[0163] Substituting formula (1) into the above equation, we can obtain dζ as a function of the degree of freedom parameter q. j With phase difference ψ ija -ψ ijb Changing surfaces, such as Figure 5 and Figure 6 As shown. In Figure 5 Select ψ ija =0°, at Figure 6 Select ψ ija =45°, if ψ is chosen ija For other values, the pattern of change is similar, and the conclusions are the same.

[0164] As can be seen from the figure, when the phase angle ψ of the aperture... ija ψ ijbSatisfy |ψ ija -ψ ijb When the angle is |=180°, the corresponding dζ is approximately zero, meaning the sum of the lengths of the two coupled flexible cables is less affected by changes in the joint deflection angle. Let ψ ija =0°、ψ ijb =180°, resulting in the following Figure 7 The change in the sum of the lengths of the flexible ropes, dζ, varies with the deflection angle q. j The changing pattern of ψ. ija =45°, ψ ijb =45° + 180° = 225°, resulting in: Figure 8 The variation of the sum of the lengths of the flexible ropes, dζ, with respect to the degree of freedom parameter q is shown. j The changing pattern of ψ. ija =90°, ψ ijb =90° + 180° = 270°, resulting in: Figure 9 The change in the sum of the lengths of the flexible ropes, dζ, varies with the deflection angle q. j The changing pattern. From... Figures 5-9 It can be seen that when the phase difference between the two segments of the flexible cable controlling the same joint is 180°, the cumulative change in the length of the two coupled flexible cables at the same joint is the smallest.

[0165] Step 5: Calculate the theoretical total length variation range of the single-joint drive cable, and then determine the phase angle of the hole.

[0166] In step 4, simulations demonstrated that the cumulative change is minimized when the phase angle difference between the two coupled flexible cables is 180° (i.e., π). The following analysis examines the range of variation in the theoretical total length of the two flexible cables at a single joint.

[0167] By substituting the phase angle difference into formula (1) in step 3, the length of the flexible cord at the joint can be obtained:

[0168]

[0169] For ease of derivation, the length of the flexible rope is expressed in the following form:

[0170]

[0171] The formulas for calculating variables C and D are shown below:

[0172]

[0173] Therefore, we can conclude that:

[0174]

[0175] Therefore, we can conclude that:

[0176]

[0177] After sorting, we can obtain:

[0178]

[0179]

[0180] Finally, the total change in the theoretical length dζ of the single-joint driven flexible cable can be obtained by satisfying the following formula:

[0181] dζ=ζ * (ψ)+ζ * (ψ+π)-2(d p +d q )≤4r|cos(ψ)sin(q / 2)|

[0182] When the phase angle ψ of the aperture is 0° or 180°, i.e., cos(ψ) = 1, as follows: Figure 7 As shown, the upper limit of the theoretical total length change dζ of the single-joint driven flexible cable is relatively large; through the simulation results in step 4 and the conclusion in step 5, it can be seen that dζ can be positive or negative, and its absolute value has a small range of variation.

[0183] When the phase angle ψ of the aperture is 90° or -90°, i.e., cos(ψ) = 0, as follows: Figure 9 As shown, the upper limit of the theoretical total length change dζ of the single-joint driven flexible cable is zero. According to the simulation results in step 4 and the conclusion in step 5, as the absolute value of the joint deflection angle increases, dζ will decrease accordingly, and its absolute value has a large range of variation.

[0184] In summary, when the phase angle ψ of the aperture is taken as 0° or 180°, its absolute value varies within a small range. Therefore, it is preferable to take the phase angle ψ of the aperture as 0° or 180°.

[0185] It should be noted that the method of the present invention is not applicable to the solution of coupled flexible cables of general structures. The derivation of steps 4 and 5 is not a necessary step in the kinematic solution method of coupled flexible cables of the present invention. For existing conventional coupled flexible cables, when the phase angle ψ is 0° or 180° and the phase difference is 180°, the method of the present invention can achieve higher solution accuracy.

[0186] Step 6: Solve for the total theoretical length of the coupled flexible cable.

[0187] If we disregard the coupling phenomenon of the flexible cable and only analyze the positions of the key nodes related to the flexible cable, we can obtain the theoretical total length l of the driving flexible cable that drives the i-th joint. i * Based on steps 3, 4, and 5, the value of ζ at a single joint can be determined.ija * ζ ijb * The numerical values ​​of the theoretical length parameter of the isoflexible cable. i * The solution formula is as follows:

[0188]

[0189] κ in the formula j Let be the length of the j-th arm.

[0190] The driving cable that drives the i-th joint is divided into two segments, A and B, at the j-th joint, with lengths ζ and ζ respectively. ija * ζ ijb * The corresponding theoretical length ζ of the flexible cable ij * The following equations must be satisfied:

[0191] ζ ij * =ζ ija * +ζ ijb *

[0192] By substituting the relevant values ​​into this step, the theoretical total length l of the driving cable can be obtained. i * .

[0193] Step 7: Determine the lengths of the two segments of the driving cable.

[0194] Analyzing the total length of the driving cable theory from a spatial geometry perspective i * The relationship between this variable and parameters such as joint deflection angle can be obtained according to step 6.

[0195] Although the driving cable for the i-th joint is divided into two parts, these two parts are integrated. If the coupling phenomenon of the cable is not considered, its actual total length l i It is a constant value. However, in real-world environments, due to the coupling phenomenon of the flexible cable, its actual total length l is... i The theoretical total length l of the rope, obtained using formula (2) i * Related to parameters, the specific values ​​are obtained by "normalization" in this invention.

[0196] The total length l of the driving cable driving the i-th joint i The solution can be obtained using the following formula:

[0197]

[0198] κ in the formula j Let be the length of the j-th arm.

[0199] The driving cable that drives the i-th joint is split into two segments at the j-th joint, with a corresponding cable length ζ. ij The following equations must be satisfied:

[0200] ζ ij =ζ ija +ζ ijb

[0201] The local length value ζ of the flexible cable ija ζ ijb The exact value of this parameter is currently unknown, and there is no research on solving it. Therefore, this invention analyzes the total length of the flexible cable, taking into account coupling phenomena, using the theoretical length of the flexible cable.

[0202] The expected total length ζ of the driving cable at a joint ij * as follows:

[0203] ζ ij * =ζ ija * +ζ ijb *

[0204] The difference dζ between the expected total length of the drive cable at a joint and the initial length of the drive cable. ij as follows:

[0205] dζ ij ==ζ ij * -2(d p +d q )

[0206] Because the material of each segment of the coupling cable is the same, a parameter ζ at the joint is obtained. ija ζ ijb The formula for the numerical value:

[0207]

[0208] Adding the two parameters in the above formula, we get:

[0209]

[0210] From the above formula, we can see that ζ ija With ζ ijb The sum is always a constant, that is:

[0211] dζ ija +dζ ijb =0

[0212] The above equation illustrates the change dζ of segment A of the flexible cord driving the i-th joint. ija If the length of segment B is dζ, then the change in segment B is dζ. ijb =-dζ ija The length satisfies the coupling condition between drive cable segment A and drive cable segment B.

[0213] And so on, the expected total length of the driving cable is l i * With the initial length l of the driving flexible cable i The difference △l i * The calculation formula is as follows:

[0214]

[0215] Finally, the lengths l of the two segments of the flexible cable driving the i-th joint can be solved using the following formula. ia l ib :

[0216]

[0217] Step 8: Determine the rotation angle of the drive motor.

[0218] The lengths l of the two segments of the flexible cable driving the i-th joint are obtained. ia l ib Then, the change in length Δl between the two segments can be calculated. ia , △l ib The angle that the drive motor should rotate can be calculated using the following formula:

[0219] Δn i =Δl ia / θ=-Δl ib / θ

[0220] The angle of the drive motor obtained using the method of this invention is beneficial for improving the control accuracy of the flexible cable. Applying this method to flexible cable-driven structures such as surgical robots can improve end-effector positioning accuracy.

[0221] Example 1:

[0222] by Figure 10 The robotic arm shown is the application example, with three degrees of freedom: yaw (q1), pitch (q2), and torsion (q3). The variation of these three degrees of freedom with time t is shown below:

[0223]

[0224]

[0225]

[0226] Based on existing methods, simulation results can be obtained as follows: Figure 11 The curves showing the change in the theoretical length of the flexible cable over time, and the curves showing the change in the difference between the expected total length of the driving flexible cable and the initial length of the driving flexible cable are shown in the figure. Figure 12 As shown in the figure. The simulation results show that the difference between the expected total length of the driving cable and its initial length, Δl... i * It is not always equal to zero, so it cannot satisfy the coupling phenomenon of flexible cables and cannot be applied to the solution of coupled flexible cable kinematics.

[0227] The curve of the flexible rope length considering coupling versus time was obtained by simulation according to the method in this invention. This figure is consistent with... Figure 11 Similarly, considering the length Δl of the coupled driving flexible cable. i The change curve is as follows Figure 13 As shown in the simulation results, l ia +l ib The value remains constant, satisfying the coupling phenomenon of the flexible cable. That is, the method proposed in this invention can be used to solve the kinematics of the coupled flexible cable, thereby improving the motion control effect.

[0228] The present invention has been described in detail above with reference to specific embodiments and exemplary examples; however, these descriptions should not be construed as limiting the present invention. Those skilled in the art will understand that various equivalent substitutions, modifications, or improvements can be made to the technical solutions and embodiments of the present invention without departing from the spirit and scope of the invention, and all such modifications and improvements fall within the scope of the present invention. The scope of protection of the present invention is defined by the appended claims.

[0229] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for solving coupled flexible cable kinematics, characterized in that, including: S1 obtains the first j Coordinates of key points at each joint; S2 according to the j The coordinates of each key point at the joint are obtained to get the first... j The first joint drives the first i The theoretical length of the two flexible cables at each joint; S3 does not consider the coupling phenomenon of the flexible cable, according to the first j The first joint drives the first i The theoretical lengths of the two flexible cables at the joint are used to drive the first joint. i The theoretical total length of the flexible cable at each joint; S4 considers the coupling phenomenon of the flexible cable, according to the driving... i The theoretical total length of the flexible cable at the nth joint is obtained to drive the nth joint. i The actual length of the two flexible ropes at each joint; S5 according to the driver i The actual length of the two flexible cables at each joint is driven by the first... i The amount of change in the two flexible cords of each joint; S6 according to the driver i The change in the two flexible cables of each joint determines the required rotation angle of the drive motor. i ＞ j ≥1； Step S2 according to the first j Coordinates of key points at each joint S ija1_j , S ija2_j , S ijb_1 and S ijb_2 Get the first j The drive at the joint i The theoretical length of the two flexible ropes at each joint, and the specific methods include: in, for S ija1_j and S ija2_j The distance between them for S ijb_1 and S ijb_2 The distance between them; r ij In the first j The first joint drives the first i The distance between the axis of the drive hole corresponding to the drive cable of each joint and the axis of the center of the arm where the drive hole is located. d pj For the first j The distance from the center point of each joint to the front end, wherein the front end is the drive cable inlet; d qj For the first j The distance from the center point of each joint to the rear end, wherein the rear end is the drive cable outlet; ψ ija , ψ ijb To drive the first i The drive cable of the first joint is from the first j When a joint passes through, the phase angle of the two corresponding drive holes on the same arm; in, q j For the first j The degrees of freedom corresponding to each joint; Step S3 does not consider the coupling phenomenon of the flexible cable, according to the first j The first joint drives the first i The theoretical lengths of the two flexible cables at the joint are used to drive the first joint. i Methods for determining the total theoretical length of the flexible cable at each joint include: According to the j The first joint drives the first i The theoretical lengths of the two flexible rope segments at the nth joint are obtained. j The first joint drives the first i The theoretical total length of the flexible cable at each joint : ； According to the drive at each joint i The theoretical total length of the flexible cable of the nth joint is obtained to drive the nth joint. i Total theoretical length of the flexure at each joint : ； in, k j For the first j The length of each boom; Step S4 considers the coupling phenomenon of the flexible cable, according to the driving... i Total theoretical length of the flexure at each joint , get the driving first i The actual length of the two flexible ropes at each joint l ia and l ib The methods include: ， ， ， 。 2. The method for solving coupled flexible cable kinematics according to claim 1, characterized in that, Will drive the first i The two flexible sections of each joint are defined as follows: A rope and B Rope, driving the first i The two sections of flexible rope from the first joint j When the joint passes through A rope from point A ij1 Wear out of the j -1 boom, from point A ij2 Entering the j One boom, B rope from point B ij1 Wear out of the j -1 boom, from point B ij2 Entering the j One arm, the point A ij1 ,point A ij2 ,point B ij1 and points B ij2 For the first j Key points at each joint; Step S1 obtains the first j The method for determining the coordinates of each key point at each joint includes: determining the points based on the basic kinematic model of the cable-driven robotic arm. A ij1 ,point A ij2 ,point B ij1 and points B ij2 In the j The coordinates of each joint in the body coordinate system.

3. The method for solving coupled flexible cable kinematics according to claim 2, characterized in that, Step S1 obtains the first j The methods for determining the coordinates of key points at each joint include: Determine the first j Midpoint of the body coordinate system of each joint A ij1 and points B ij1 coordinates S ija1_j and S ijb1_j and the j +1 joint midpoint of the body coordinate system A ij2 and points B ij2 coordinates S ija2_j+1 and S ijb2_j+1 : According to the j The body coordinate system of the first joint and the first joint j Transformation matrix between the body coordinate systems of +1 joint , will the j +1 joint midpoint of the body coordinate system A ij2 and points B ij2 The coordinates are converted to the first j Midpoint of the body coordinate system of each joint A ij2 and points B ij2 Coordinates: 。 4. The method for solving the kinematics of coupled flexible cables according to claim 1, characterized in that, Step S6 according to the driver i The change in the two flexible sections of the joint △ l ia and △ l ib Methods for determining the required rotation angle of the drive motor include: in, This is the transmission coefficient of the drive motor.

5. The method for solving the kinematics of a coupled flexible cable according to claim 1, characterized in that, It also includes, according to the first j The first joint drives the first i The theoretical lengths of the two flexible cables at the first joint are determined to make the first joint... j The first joint drives the first i The coupled flexible cable layout with the smallest cumulative change in the length of the two flexible cables at each joint is executed in steps S3 to S6.

6. The method for solving coupled flexible cable kinematics according to claim 5, characterized in that, Make the first j The first joint drives the first i The coupling cable layout with the smallest cumulative change in the lengths of the two flexible cables at each joint is: ； and ,or and .

7. The method for solving the kinematics of coupled flexible cables according to claim 6, characterized in that, It also includes, according to the first j The first joint drives the first i The theoretical lengths of the two flexible cables at the first joint are determined to make the first joint... j The first joint drives the first i Methods for optimizing the coupled cable layout that minimize the cumulative change in the lengths of the two cable segments at a given joint include: Construct the first j The first joint drives the first i Model of cumulative change in the length of the two flexible cables at each joint: The result obtained in step S2 and Substituting into the above model, we get Follow q j and ψ ija - ψ ijb The changing simulation data, based on the simulation data, determine ; exist Under the premise of, set ψ ija and ψ ijb One of them is The other is The above model can be converted into the following form: ； in, and represent and ; Determined by the transformed form ψ Set it to 0° or 180°.

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