A redundant cable parallel robot cable force optimization method

Abstract

The application provides a redundant cable parallel robot cable force optimization method, first, according to the structural parameters and the terminal position of the cable parallel robot, a Jacobian matrix of the redundant cable parallel robot is constructed; second, the null space vector of the Jacobian matrix of the redundant cable parallel robot is solved, and the augmented Jacobian matrix and the augmented terminal force screw space are constructed by using the null space vector and the Jacobian matrix; third, the augmented force screw convex hull is constructed in the augmented force screw space by using the augmented Jacobian matrix, and the optimization target is constructed by using the force screw convex hull, which is used as the selection principle of the cable force optimization; finally, the redundant cable force null space coefficient is optimized, the cable force solution that maximizes the optimization target is solved, and the cable force solution with good force screw output and anti-disturbance performance is obtained, so that the performance of the redundant cable parallel robot is effectively exerted.

Description

Technical Field

[0001] The present invention relates to the field of cable parallel robots, and particularly to a method for optimizing the cable forces of a redundant cable parallel robot, so as to make full use of the performance of the redundant cable parallel robot and effectively improve the performance of the redundant cable parallel robot in resisting and outputting forces and torques. Background Art

[0002] Cable parallel robots use cables instead of rigid links, inheriting the advantages of rigid parallel robots such as modularity and easy reconfiguration, and achieving a further significant reduction in inertia. They have a simple structure and a large load-to-self-weight ratio, and have been applied in some typical scenarios. However, since cables can only transmit tensile forces, situations such as virtual cable traction may occur during the use of cable parallel robots, resulting in end-point out-of-control, and their performance in resisting and outputting external forces and external torques is weaker than that of rigid parallel robots.

[0003] According to the number of cables m and the number of end-point degrees of freedom n of the CDPR, cable parallel robots can be classified into under-constrained mechanisms (m < n), incompletely constrained mechanisms (m = n), fully constrained mechanisms (m = n + 1), and redundant constrained mechanisms (m > n + 1). Reasonably adding redundant drives can effectively enhance the load capacity and dynamic characteristics of the robot, expand the working space volume, and reduce the singular configurations of the mechanism.

[0004] However, more drives also bring difficulties to control, and cable force distribution becomes a difficult problem in the control process of redundant drive cable parallel robots. Since the number of cables is more than the number of force balance equations, there can be an infinite number of solutions for the cable forces that keep the end-point balanced. Usually, various optimization methods are used to obtain a corresponding set of cable force solutions, so as to meet the corresponding performance requirements. Common optimization objectives include the sum of cable forces, the two-norm of cable forces, stiffness performance, maximum cable force, etc. Existing methods can meet the requirements of end-point force balance, but pay more attention to characteristics such as cable force distribution and stiffness of the robot, and consider less the external disturbances suffered during the operation of the cable parallel robot. Although these methods can indirectly improve the performance of the robot in resisting and outputting external forces and external torques to a certain extent, their optimization objectives are not directly aimed at such performance, nor can they clearly reflect the performance of the robot in resisting and outputting external forces and external torques. Summary of the Invention

[0005] The present invention provides a method for optimizing the cable forces of a redundant cable parallel robot for a redundant cable parallel robot with the number of cables more than the number of end-point degrees of freedom. This method can effectively improve the performance of the redundant cable parallel robot in outputting forces and torques, as well as in resisting external forces and external torque disturbances.

[0006] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for optimizing cable force in a redundant cable parallel robot, characterized by the following steps:

[0008] Step 1: For a redundant cable parallel robot with m cables, n terminal degrees of freedom, and m > n; determine the equilibrium equations and Jacobian matrix of the redundant cable parallel robot based on its structural parameters and terminal pose:

[0009] J T t = q e

[0010] in For the Jacobian matrix of the parallel robot, This represents the cable force on each rope of the cable-connected robot. This represents the net external force and net external torque acting on the moving platform, where f e τ represents the net external force acting on the corresponding moving platform. e This represents the net external torque acting on the corresponding moving platform;

[0011] Step 2: Solve for all null space vectors c1, c2, ..., c of the Jacobian matrix J. s Where s = mn is the redundancy of the robot; any null space vector satisfy:

[0012]

[0013] Therefore, the equilibrium equation of the redundant cable parallel robot is expressed as:

[0014] J(t0+λ1c1+λ2c2+...+λ s c s )=q e

[0015] Where t0=J(J T J) -1 q e To provide a set of cable force special solutions that satisfy the terminal force equilibrium equations, λ1,λ2,...,λ s These are called the null space coefficients corresponding to each null space vector;

[0016] Define matrix The null space matrix of the redundant cable parallel robot is given by [formula missing]. Furthermore, the augmented Jacobian matrix of the redundant cable parallel robot is constructed as follows: A new dimension, λ1, λ2, ..., λ3, is added to the end-effector force screw space of the redundant cable parallel robot as a new dimension. Based on this, an augmented end-effector force screw space containing redundant information dimensions is constructed. This space not only includes the force and torque dimensions of the original end-effector force screw space to represent the effects of external forces and torques on the end-effector of the redundant cable parallel robot, but also adds λ1, λ2, ..., λ3. s The axis also corresponds to the cable force distribution information of the cable parallel robot;

[0017] Step 3: Based on the augmented Jacobian matrix and the augmented terminal force spinor space, construct the augmented force spinor convex hull of the redundant cable parallel robot; specifically, the augmented force spinor convex hull is represented by a set of inequalities, as follows:

[0018]

[0019] The i-th line of the system of inequalities is: It corresponds to a half-space that forms a convex hull in the augmented force spinor space. Let be the normal vector of the separating hyperplane of this half-space. Let be the intercept of the separating hyperplane of this half-space; Let m×2m be an m-matrix containing the normal vectors of all separating hyperplanes, called the normal vector matrix, and let its i-th column be... Right now The 2m×1 matrix containing all the intercepts of the separating hyperplanes is called the intercept matrix, and its i-th element is... Right now The specific steps to solve this system of inequalities are as follows:

[0020] Step 3.1: Solve for the normal vector

[0021] normal vector H is defined using the adjoint matrix and algebraic cofactor of the augmented Jacobian matrix H. * Let H be the adjoint matrix of matrix H. For matrix H * The i-th column, for The j-th element in H corresponds to the first-order algebraic cofactor in the j-th row and i-th column of matrix H. * Each column corresponds to a set of parallel normal vectors of the hyperplane, namely... and Therefore, the normal vector is solved. The expression is:

[0022]

[0023] in, The matrix H is obtained by removing the j-th row and ith column respectively;

[0024] Step 3.2: Solve for the intercept

[0025] intercept The solution is obtained using the augmented Jacobian matrix H and the constructed matrix A, as shown in the following equation:

[0026]

[0027] in, t i , Let A represent the minimum and maximum cable force constraints of the i-th rope, respectively. Let A be the construction matrix, which is an m-row 2x2 matrix. m The matrix consists of columns, where all elements are either 0 or 1. Each column represents a possible combination of m 0s and 1s, corresponding to a situation where all ropes of the redundant cable parallel robot trigger the maximum or minimum cable force constraint. Elements of 0 represent the minimum cable force constraint, and elements of 1 represent the maximum cable force constraint. When m = 3, the resulting constructed matrix A is:

[0028]

[0029] Step 3.3: Construct the augmented force spinor convex hull:

[0030] Based on the normal vector and intercept obtained in steps 3.1 and 3.2, construct a system of inequalities. Finally, the augmented force spinor convex hull is obtained, with the normal vector matrix and intercept as follows:

[0031]

[0032] The terminal force spinor state of the redundant cable parallel robot in the augmented force spinor space contains information on the external forces and torques acting on the terminal of the redundant cable parallel robot, as well as null space coefficient information. For a cable parallel robot with n=6, x=[f x f y f z τ x τ y τ z λ1…λ m-n ] T

[0033] Step 3.4: Construct performance evaluation indicators:

[0034] normal vector matrix The problem is divided into a force-space component, a torque-space component, and a null-space component, allowing us to focus on solving for its resistance to external forces and torques.

[0035]

[0036] Among them, W F Normal vector matrix The part related to force space, W M Normal vector matrix The part related to torque space, W λ Normal vector matrix The part related to null space, Normal vector matrix The part related to force space and torque space.

[0037] For a given terminal force screw state x of a redundant cable parallel robot in the augmented force screw space, its ability to resist external forces in any direction or output forces in any direction is called its force margin, and its calculation expression is:

[0038] FMI = min(d f,1 ,d f,2 ,...d f,2m )

[0039]

[0040] in, Normal vector matrix The i-th column, w F,i Representation matrix W F The i-th column;

[0041] Its ability to resist external torque in any direction or to output torque in any direction is called its torque margin, and its calculation expression is:

[0042] MMI = min(d m,1 ,d m,2 ,...d m,2m )

[0043]

[0044] Among them, w M,i Representation matrix W M The i-th column;

[0045] Step 4: Select the force margin or torque margin optimization objective, and calculate the null space coefficients λ1, λ2, ..., λ for each null space vector. sOptimization is performed to obtain the cable force solution that maximizes the optimization objective, thus achieving the strongest target performance for the redundant cable parallel robot.

[0046] The redundant cable parallel robot cable force optimization method proposed in this invention can be used to analyze redundant cable parallel robots with terminal degrees of freedom n of 1 to 6 and number of cables m ≥ 2. The number of cables and degrees of freedom of the analyzed redundant cable parallel robot satisfy the relationship m > n.

[0047] When optimizing cable forces, in addition to directly using force margin or torque margin as the optimization objective, the weighted values ​​of the obtained force margin and torque margin can be constructed to obtain cable force optimization results that take into account both force and torque performance. When the focus is on the performance of the redundant cable parallel robot in resisting external forces and outputting driving force to the outside world, the optimization objective is to take the force margin; when the focus is on the performance of the redundant cable parallel robot in resisting external torque and outputting driving torque to the outside world, the optimization objective is to take the torque margin; when it is necessary to take into account both force and torque output performance, the optimization objective is to take the weighted average of the two, and the specific weights are selected according to the specific requirements for force and torque output performance.

[0048] Specifically, the optimization objective based on force margin (FMI) and torque margin (MMI) is defined as WMI, where WMI is the weighted average of the force margin and torque margin, i.e.:

[0049] WMI = α1 × FMI + α2 × MMI

[0050] The coefficients α1 and α2 are selected according to the actual task requirements. When only the robot's performance against external force disturbances is considered, α1 is 1 and α2 is 0. When only the robot's performance against external torque disturbances is considered, α1 is 0 and α2 is 1. When both the robot's performance against external forces and its performance against external torque are considered, and it is desired that the weights of the two are the same, α1 is 0.5 and α2 is 0.5.

[0051] When finding the optimal cable force solution, the null space coefficients λ1, λ2, ..., λ can be used. s Discretize the values ​​into a series of discrete values, then iterate through the discrete points for optimization, or use an intelligent optimization algorithm for optimization. By setting the force margin, torque margin, or a weighted sum of the two as the optimization objective, the optimal cable force solution is obtained through optimization, thereby reducing the amount of computation compared to the traversal method.

[0052] Specifically, the optimization problem can be expressed as:

[0053]

[0054] Among them, F e and M e These are the external forces and torques acting on the moving platform, respectively. Fe M e ,C,t0, All of these are known quantities. Depending on the specific optimization objective, radius(λ) can be either FMI or MMI. As the boundary condition for cable forces, the optimized cable forces are restricted between the maximum and minimum cable force constraints; These are the feasibility boundary conditions to ensure the optimization results are feasible.

[0055] When using intelligent optimization algorithms for cable force optimization, algorithms such as SQP, genetic algorithm, particle swarm optimization, ant colony optimization, annealing algorithm, or neural network algorithm can be adopted.

[0056] The cable force optimization method proposed in this invention can be used for both off-line and on-line cable force optimization.

[0057] When using off-line force optimization, the external forces and torques experienced by the redundant cable parallel robot during operation are estimated in advance. Based on this, the cable forces at each position on the trajectory are optimized and stored in the controller. During operation, the redundant cable parallel robot implements force servoing with the pre-optimized cable forces as the target, thereby adjusting the cable forces to distribute them according to the optimized cable force distribution.

[0058] In the process of optimizing cable force, the cable force optimization method is deployed into the controller, and cable force sensors are installed on each cable. When the redundant cable parallel robot is running, the controller calculates and estimates the external force and torque state of the terminal based on the cable force measurement results on each cable. On this basis, cable force optimization is performed in each control cycle, and the redundant cable parallel force servo is implemented with the optimized cable force solution as the target.

[0059] When performing redundant cable parallel force servo control, a mode of partial cable position control and partial cable force control, or a mode of force-position hybrid control using all cables, can be adopted. When using the partial cable position control and partial cable force control mode, the zero-space vectors c1, c2, ..., c are selected. s The s-cable with the smallest corresponding component is used as the tension adjustment cable and adopts the force control mode; the other cables adopt the position control mode.

[0060] Compared with the prior art, the beneficial effects that can be achieved by implementing the present invention are:

[0061] 1. The cable force optimization method proposed in this invention directly optimizes and improves the output, resistance, and torque performance of redundant cable parallel robots. Compared with traditional cable force optimization methods that indirectly improve performance by optimizing cable force distribution and stiffness, the effect is more significant.

[0062] 2. When optimizing cable force based on the augmented Jacobi matrix and augmented terminal force spinter space proposed in this invention, the augmented Jacobi matrix is ​​supplemented with null space vector components, making the matrix full rank. During the mapping process, redundant cable force information is mapped using the supplemented null space vector components. Therefore, the problem of loss of redundant cable force information caused by the non-full rank of the Jacobi matrix in existing analysis methods based on the Jacobi matrix is ​​avoided. Attached Figure Description

[0063] Figure 1 This is a flowchart of the process for optimizing the cable force of a redundant cable parallel robot according to the present invention.

[0064] Figure 2 This is a schematic diagram of a planar three-cable two-degree-of-freedom redundant cable parallel robot according to the present invention.

[0065] Figure 3 This is a schematic diagram of the terminal augmented force spinor space and the augmented force spinor convex hull proposed in this invention.

[0066] Figure 4 This invention compares the force margin distribution before and after force optimization for a planar three-cable, two-degree-of-freedom redundant cable parallel robot. Detailed Implementation

[0067] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. It should be noted that the terms "upper," "lower," "left," "right," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention.

[0068] Figure 1 This is a flowchart illustrating the cable force optimization process for a redundant cable parallel robot. First, based on the structural parameters and terminal positions of the redundant cable parallel robot, a Jacobian matrix is ​​constructed. Second, the null space vector of the Jacobian matrix is ​​solved, and an augmented Jacobian matrix and an augmented terminal force screw space are constructed using the null space vector and the Jacobian matrix. Third, an augmented force screw convex hull is constructed in the augmented force screw space using the augmented Jacobian matrix, and a force margin or torque margin is constructed using the augmented force screw convex hull as the optimization objective, serving as the selection principle for cable force optimization. Finally, the null space coefficients of the redundant cable force are optimized to obtain the cable force solution that maximizes the optimization objective, thus obtaining the cable force solution with the strongest force screw output and anti-interference performance, effectively maximizing the performance of the redundant robot.

[0069] Figure 2This is a schematic diagram of a planar three-cable, two-DOF redundant cable parallel robot. Based on this robot, an implementation example of the cable force optimization proposed in this invention is given. In this embodiment, the robot can perform translational motion along the X and Y directions in the XOY plane, totaling two degrees of freedom. The cable exit points B1 to B3 of the robot's static platform are distributed on an equilateral triangle with a side length of 1m, and their coordinates are... P is a point-shaped moving platform with a weight of m. The moving platform is subjected to gravity along the negative Y-axis, q. e =[0-mg] T .

[0070] Order No. i The unit direction vector of the rope is e i =[e ix e iy ] T Then the Jacobian matrix J of the robot is written as:

[0071]

[0072] The robot has a redundancy of 1, and its Jacobian matrix J has a null space vector of c1 = null(J). Therefore, the augmented Jacobian matrix H = [JC] = [J c1] can be constructed.

[0073] Using the adjoint matrix and algebraic cofactors of the augmented Jacobian matrix H, the normal vectors of the corresponding hyperplanes of each half-space constituting the augmented force spinor convex hull can be solved. and intercept Then, the normal vector matrix is ​​obtained. and intercept matrix Right now:

[0074]

[0075] The items are as follows:

[0076] The matrix H is the matrix obtained by removing the j-th row and i-th column.

[0077] A is the construction matrix. For the cable parallel robot in this embodiment, it is a 3x8 matrix, with the following structure:

[0078]

[0079] Based on the normal vector matrix and intercept matrix Finally, a system of inequalities can be constructed.

[0080] Figure 3This diagram illustrates the augmented force spinor space and its augmented force spinor convex hull of the redundant cable parallel robot terminal in this embodiment. The augmented force spinor space of the redundant cable parallel robot terminal in this embodiment comprises two force dimensions (Fx and Fz dimensions) and one null space dimension (λ dimension). Its augmented force spinor convex hull is a convex polyhedron enclosed by six hyperplanes, wherein… These correspond to the maximum cable force constraints of ropes 1 through 3, and their normal vectors are... α 1~ α 3 corresponds to the minimum cable force constraints of ropes 1 through 3, and their normal vectors are... The force state of the redundant cable parallel robot terminal and the distribution of redundant cable forces correspond to points in the augmented force spinor space. The relative positional relationship between this point and the augmented force spinor convex hull indicates whether the force state corresponding to this point can be balanced by the cable forces. For example, if Q1 falls inside the augmented force spinor convex hull, it means that there exists a set of cable forces that balances the external force corresponding to Q1 and ensures that all cables satisfy the maximum and minimum cable force constraints; if Q2 falls outside the augmented force spinor convex hull, it means that there is no cable force solution that balances the external force corresponding to Q2 and ensures that all cables satisfy the maximum and minimum cable force constraints.

[0081] Will It is separated into a part related to force space and a part related to null space, that is:

[0082]

[0083] The redundant cable parallel robot in this embodiment has an augmented force spinor vector. The formula for calculating its force margin (FMI) is:

[0084] FMI = min(d f,1 ,d f,2 ,...d f,6 )

[0085]

[0086] in, Normal vector matrix The i-th column, w F,i Representation matrix W F The i-th column;

[0087] In this embodiment, the force margin (FMI) is used as the optimization objective to optimize the cable force in the robot's workspace, and the optimization method is compared with the existing optimization method that aims to minimize the second norm of the cable force.

[0088] When the force margin (FMI) is taken as the optimization objective, the optimization problem can be expressed as:

[0089]

[0090] When the optimization objective is to minimize the Soleil L2 norm, the optimization problem can be expressed as:

[0091]

[0092] Figure 4 The distribution of cable force optimized with the objective of maximizing the force margin and the force margin FMI optimized with the objective of minimizing the cable force L2 norm are shown in the workspace. The upper surface corresponds to the FMI optimized with the objective of minimizing the force margin FMI, and the lower surface corresponds to the FMI optimized with the objective of minimizing the cable force L2 norm.

[0093] As can be seen, traditional optimization methods that aim to minimize the L2 norm of cable force only consider minimizing the cable force, without taking into account the problem of poor resistance to external disturbances due to insufficient cable force on redundant cables. In this case, when the moving platform is subjected to external forces, cable tension can easily become slack, leading to loss of control of the terminal. By using the cable force optimization method proposed in this invention, the force margin of the redundant cable parallel robot in the workspace is effectively improved, enabling the redundant cable parallel robot to achieve good force output performance and resistance to external forces throughout the workspace, thereby fully leveraging the performance advantages of the redundant cable parallel robot.

[0094] It is worth noting that although the technical solutions and preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, the present invention is not limited to the specific embodiments described above. The embodiments described above are merely illustrative. Those skilled in the art can make many other forms based on the inspiration of the present invention without departing from the spirit and scope of the claims, and these all fall within the scope of protection of the present invention.

Claims

1. A redundant cable parallel robot cable force optimization method, characterized by, The method comprises the following steps: Step 1: for a redundant cable parallel robot with m ropes, n terminal degrees of freedom, and m>n; according to the structural parameters of the redundant cable parallel robot and the terminal pose, the balance equation and the Jacobian matrix of the redundant cable parallel robot are determined: J T t = q e wherein is the Jacobian matrix of the cable parallel robot, denotes the cable forces on each cable of the cable parallel robot, denotes the resultant external force and the resultant external moment on the moving platform, wherein f e denotes the resultant external force on the moving platform, e denotes the resultant external moment on the moving platform; Step two: Solve for all null-space vectors cl, c2,..., cn of Jacobian matrix J s where s = m - n is the redundancy of the robot; any null-space vector satisfies: Therefore, the balance equation of the redundant cable parallel robot is expressed as: J(t0+λ1c1+λ2c2+...+λ s c s )=q e where t0= J(J T J) -1 q e For a set of cable force particular solutions satisfying the terminal force equilibrium equation, λ1, λ2,..., λ s are called the null space coefficients corresponding to each null space vector. Definition matrix is the null space matrix of the redundant cable parallel robot; and the augmented Jacobian matrix of the redundant cable parallel robot is constructed as The null space coefficient dimension is added as a new dimension to the terminal force wrench space of the redundant cable parallel robot, and an augmented terminal force wrench space containing the redundant information dimension is constructed based on the terminal force wrench space. This space not only contains the force and torque dimensions in the original terminal force wrench space, which are used to represent the action of external force and external torque on the terminal of the redundant cable parallel robot, but also contains the added λ1, λ2,..., λ s The axis also corresponds to the cable force distribution information of the cable parallel robot; Step 3: based on the augmented Jacobian matrix and the augmented terminal force wrench space, the augmented force wrench convex hull of the redundant cable parallel robot is constructed; specifically, the augmented force wrench convex hull is represented by a set of inequalities, and is specifically expressed as: where the i-th row of the inequality system is: It corresponds to a half-space in the augmented force-couple space that encloses a convex hull, is the normal vector of the separating hyperplane of this half-space, is the intercept of the separating hyperplane of this half-space; is an mx2m matrix containing the normal vectors of all separating hyperplanes, called normal matrix, whose i-th column is i.e. is a 2mxl matrix containing the intercepts of all separating hyperplanes, called intercept matrix, whose i-th element is i.e. The specific steps to solve this inequality system are as follows: Step 3.1: Solving the normal vector Normal vector The normal vector of the hyperplane corresponding to the i-th column of matrix H is defined as the i-th column of the adjugate matrix of the augmented Jacobian matrix H * is the adjugate matrix of the matrix H, is the i-th column of the matrix H * is the i-th column of the matrix H is the j-th element of the matrix H is the j-th element of the matrix H * Each column of the matrix H corresponds to a set of mutually parallel hyperplanes, and the normal vectors are respectively and The expression of the normal vector is wherein Hj represents the matrix H with the jth row removed; Step 3.2: Solving for the intercept Intercept Solving with the augmented Jacobian matrix H and the construction matrix A is done as follows: Where t and Let A represent the minimum and maximum cable force constraints, respectively, and let A be the construction matrix, which is an m-row 2x2 matrix. m The matrix consists of columns, where all elements are either 0 or 1. Each column represents a possible combination of m 0s and 1s, corresponding to a situation where all ropes of the redundant cable parallel robot trigger the maximum or minimum cable force constraint. Elements of 0 represent the minimum cable force constraint, and elements of 1 represent the maximum cable force constraint. When m = 3, the resulting constructed matrix A is: Step 3.3: the augmented force wrench convex hull is constructed: Based on the normal vector and intercept obtained from step 3.1 and 3.2, construct inequality system Finally, the augmented force wrench convex hull, normal vector matrix and intercept are obtained as follows: The terminal force wrench space of the redundant cable-driven parallel robot corresponds to the terminal force wrench state of the redundant cable-driven parallel robot, which contains the information of the external force and external torque suffered by the terminal of the redundant cable-driven parallel robot and the information of the null space coefficient. For the cable-driven parallel robot with n = 6, x = [f x f y f z τ x τ y τ z λ1…λ m-n ] T Step 3.4: the performance evaluation index is constructed: The normal vector matrix is split into a part related to the force space, and a part related to the moment space, and a part related to the null space, so that the performance against external forces and external moments is focused on, i.e.: where W F is the normal vector matrix is the part of the normal vector matrix W M is the part of the normal vector matrix W λ is the normal vector matrix is the part of the normal vector matrix is the normal vector matrix is the part of the normal vector matrix For a given terminal force wrench state x of the redundant cable parallel robot in the augmented force wrench space of the redundant cable parallel robot, the performance of resisting external force in any direction or outputting force in any direction is called the force margin of the redundant cable parallel robot, and the calculation expression is: FMI = min(d f,1 ,d f,2 ,...d f,2m ) wherein is the i-th column of the matrix w F,i denotes the i-th column of the matrix F W The performance of resisting external torque in any direction or outputting torque in any direction is called the torque margin of the redundant cable parallel robot, and the calculation expression is: MMI = min(d m,1 ,d m,2 ,...d m,2m ) where w M,i denotes the i-th column of the matrix W M ; Step four: select the force margin or torque margin optimization target, and optimize the null space coefficients λ1, λ2,..., λ s The optimization is performed to obtain the cable force solution that maximizes the optimization target, and the strongest target performance of the redundant cable parallel robot is obtained.

2. The redundant cable parallel robot cable force optimization method of claim 1, wherein, The method can be used to analyze the redundant cable parallel robot with n=1-6 terminal degrees of freedom and m≥2 ropes, and the number of ropes and the number of redundant degrees of freedom satisfy the relationship m>n.

3. The redundant cable parallel robot cable force optimization method of claim 1, wherein, In addition to directly using the force margin or torque margin, the weighted value of the force margin and torque margin obtained by solving can also be constructed, so as to obtain the cable force optimization result considering the force and torque performance; When focusing on the performance of the redundant cable parallel robot resisting external force and outputting driving force to the outside world, the optimization target takes the force margin; when focusing on the performance of the redundant cable parallel robot resisting external torque and outputting driving torque to the outside world, the optimization target takes the torque margin; when the force and torque output performance need to be considered, the optimization target takes the weighted average value of the two, and the specific weight value is selected according to the specific demand of the force output and torque output performance; Specifically, the optimization target based on the force margin FMI and the torque margin MMI is defined as WMI, which is the weighted average value of the force margin and the torque margin, that is: WMI=α1×FMI+α2×MMI The coefficients α1 and α2 are selected according to the actual task requirement; when only the performance of the robot resisting external force disturbance is concerned, α1 takes 1 and α2 takes 0; When only the performance of the robot resisting external torque disturbance is concerned, α1 takes 0 and α2 takes 1; when both the performance of the robot resisting external force and the performance of the robot resisting external torque are concerned, and the weight values of the two are expected to be the same, α1 takes 0.5 and α2 takes 0.

5.

4. The redundant cable parallel robot cable force optimization method of claim 1, wherein, When the optimal cable force solution is sought, the null space coefficients λ1, λ2,..., λ s The discrete values are discretized into a series of discrete values, and then the discrete points are traversed for optimization, or an intelligent optimization algorithm is used for optimization, and the optimal cable force solution is obtained by setting the force margin, the torque margin, or the weighted sum of the two as the optimization target, thereby reducing the amount of calculation compared to the traversal method.

5. The redundant cable parallel robot cable force optimization method of claim 4, wherein, Specifically, the optimization problem is expressed as: where F e and M e are the external force and external moment on the moving platform, respectively; F e , M e , C, t0, are known quantities; according to the specific optimization objective value, radius(λ) takes FMI or MMI; is the cable force boundary condition, limiting the optimized cable force between the maximum and minimum cable force constraints; is the feasibility boundary condition, ensuring the feasibility of the optimization result.

6. The redundant cable parallel robot cable force optimization method of claim 4, wherein, The intelligent optimization algorithm is an SQP algorithm, a genetic algorithm, a particle swarm algorithm, an ant colony algorithm, an annealing algorithm or a neural network algorithm.

7. The redundant cable parallel robot cable force optimization method of claim 1, wherein, The method can adopt offline cable force optimization or online cable force optimization; When offline cable force optimization is adopted, the external force and external torque state of the redundant cable parallel robot during operation are estimated in advance, and the cable force at each position on the trajectory is optimized and stored in the controller; The redundant cable parallel robot runs to implement force servo with the pre-optimized cable force as the target, so as to adjust the cable force to be distributed according to the optimized cable force distribution state. When the online cable force optimization is adopted, the cable force optimization method is deployed to the controller, and cable force sensors are installed on each cable; when the redundant cable parallel robot is running, the controller calculates and estimates the external force and external torque state on the terminal according to the cable force measurement results on each cable, and implements cable force optimization in each control cycle, and implements force servo of the redundant cable parallel robot with the optimized cable force solution as the target.

8. The redundant cable parallel robot cable force optimization method of claim 7, wherein, The redundant cable parallel robot force servo process adopts a mode of partial cable position control and partial cable force control, or a mode of all cable force-position hybrid control; when the mode of partial cable position control and partial cable force control is selected, the s roots of the cable corresponding to the minimum components of the zero space vectors c1, c2,..., c s In the mode, the s roots of the cable corresponding to the minimum components of the zero space vectors c1, c2,..., c s In the mode, the s roots of the cable corresponding to the minimum components of the zero space vectors c1, c2,..., c The remaining cables adopt a position control mode.

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