A cable parallel robot posture optimization method

Abstract

This invention proposes a posture optimization method for a cable-parallel robot. First, the area to be reached within the region enclosed by the exit point of the cable-parallel robot is selected and defined as its workspace. This workspace is then discretized into a series of points, which represent the entire workspace. Next, based on the task requirements of the cable-parallel robot at each point in the workspace, the posture angle range at each point is defined and discretized. An optimization objective based on force margin and torque margin is constructed as the selection principle for the optimal posture angle. The force margin and torque margin of the cable-parallel robot at each discrete posture angle at each point in the workspace are calculated. Finally, the optimization objective value at each discrete point is calculated based on the values ​​of the force margin and torque margin. The optimal posture angle that maximizes the optimization objective is selected, resulting in a continuously distributed posture distribution map in the workspace, effectively improving the robot's performance.

Description

Technical Field

[0001] This invention relates to the field of cable parallel robots, and specifically designs a posture optimization method for cable parallel robots, thereby effectively improving the performance of cable parallel robots in resisting and outputting external forces and torques. Background Technology

[0002] Cable-connected robots, which use ropes instead of rigid chains, offer advantages such as simple structure, low cost, low inertia, and large workspace, leading to their widespread application in fields like ship painting and large equipment hoisting. However, because ropes can only transmit tension, cable-connected robots may experience situations like rope slippage during operation, resulting in end-effector loss of control. Their resistance to and output of external forces and torques is weaker compared to rigid parallel robots. For cable-connected robots with a single-point moving platform, their resistance to and output of external forces is primarily related to the platform's position within the workspace, and they lack the ability to output and resist external torques. For cable-connected robots with a non-point-shaped moving platform, they possess a certain ability to output and resist external torques, and this ability depends not only on the platform's position within the workspace but also on its orientation. By appropriately selecting the robot's orientation at various positions within the workspace, its resistance to and output of external forces and torques can be effectively improved.

[0003] Traditional optimization focuses more on the robot's cable force distribution and stiffness characteristics. Although it can indirectly improve the robot's ability to resist and output external forces and torques to some extent, its optimization goal is not directly aimed at these performance characteristics, nor can it clearly reflect the robot's ability to resist and output external forces and torques. Summary of the Invention

[0004] This invention addresses the attitude optimization of cable-parallel robots with non-point-shaped motion platforms, providing a method for attitude optimization that obtains continuously distributed attitude angles in the workspace of the cable-parallel robot. This effectively improves the robot's resistance to external disturbances at corresponding positions in the workspace, thereby enhancing its output, resistance, and torque performance.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for posture optimization of a cable-connected robot, comprising the following steps:

[0007] Step 1: Select the area to be reached within the area enclosed by the cable exit point of the cable parallel robot, define these areas as the workspace of the cable parallel robot, and discretize the workspace into a series of points at preset intervals. Use these scattered points to represent the entire workspace.

[0008] Step 2: Based on the task requirements of the cable-parallel robot at various scattered locations in the workspace, define the attitude angle range of the cable-parallel robot at each scattered location, and discretize the attitude angle range according to a preset interval. Construct an optimization objective based on force margin and torque margin as the principle for selecting the optimal attitude angle subsequently;

[0009] Step 3: Solve for the force margin and torque margin of the cable-parallel robot at various discrete attitude angles at various scattered points in the workspace;

[0010] Step 4: Solve for the optimization objective value of the parallel robot at each discrete point position when it is at each discrete attitude angle, select the optimal attitude angle at each discrete point position in the workspace that maximizes the optimization objective value, and then obtain the attitude distribution map that is continuously distributed in the workspace.

[0011] In step three, the force margin and torque margin represent the robot's ability to output force and torque to the outside world, respectively, and also represent the robot's ability to resist external forces and torques. For a cable-parallel robot with m cables and n degrees of freedom, the specific calculation process is as follows:

[0012] Step 3.1: Construct the equilibrium equations for the cable parallel robot based on the force and torque equilibrium conditions:

[0013] JT+q e =0

[0014] Where J is the Jacobian matrix of the cable-parallel robot, and T represents the cable force on each cable of the cable-parallel robot. This represents the net external force and net external torque acting on the moving platform, where f e The net external force τ acting on the corresponding moving platform e The corresponding external torque acting on the moving platform;

[0015] Step 3.2: Construct the coefficient matrix N, which is an n x 2m matrix, where:

[0016]

[0017] For N in the coefficient matrix + The i-th column have:

[0018]

[0019] Θ(H {i} ) = [...(-1) k+1 |H {i}[k] |...] T k = 1, 2, 3

[0020] H {i}H represents the matrix formed by removing the i-th column from matrix H. {i}[k] The matrix H is formed by removing the i-th column and k-th row from the matrix H. Matrix H is derived from the Jacobian matrix J of the cable parallel robot and the maximum and minimum cable force constraints f. max and f min structure:

[0021] H=(f max -f min )J T

[0022] Step 3.3: Construct the intercept column matrix d, where d is a 2m x 1 matrix, and:

[0023]

[0024]

[0025]

[0026] A is the construction matrix, which is an m-row 2-dimensional matrix. m A matrix of columns, where all elements are either 0 or 1. Each column of the matrix corresponds to one possible combination using a total of m 0s or 1s. For example, when m = 3, the resulting constructed matrix A is:

[0027]

[0028] Δd is a constant, and the i-th row of the Jacobian matrix J is denoted as Ji. i Then Δd can be calculated using the following formula:

[0029]

[0030] Step 3.4: Construct a system of inequalities N based on the coefficient matrix N and the intercept column matrix d. T xd≤0

[0031] Each row of the system of inequalities corresponds to one inequality. Where n i d represents the i-th column of the coefficient matrix N. i Let represent the i-th element of the intercept matrix d, and the system of inequalities has 2m rows;

[0032] Step 3.5: Based on the constructed system of inequalities N T xd≤0 and the net external force and net external torque acting on the moving platform Construct a system of force space inequalities and a system of moment space inequalities;

[0033] The elements in x can be divided into xF Let x be the term corresponding to the external force. M The term in x corresponds to the external torque; the elements in N can be divided into Where NF is the term in N corresponding to the force component, N F These are the terms in N corresponding to the torque components;

[0034] Use the current external torque state as the equality constraint x M =τ e Substituting these terms into the system of inequalities, the torque-related terms are now fixed by the system of inequalities, thus constructing a system of force-space inequalities. The system of inequalities consists of 2m lines. The current external force state is used as the equality constraint x. F =f e Substituting these terms into the system of inequalities, the force-related terms are now fixed by the system of inequalities, thus constructing a system of inequalities in the moment space. The system of inequalities consists of 2m lines;

[0035] Step 3.6: Set the current external force state x F =f e and the current external torque state x M =τ e Substitute the values ​​into the force space inequalities and the moment space inequalities respectively to solve for the force margin and the moment margin;

[0036] Among them, the force margin FMI is solved according to the system of force space inequalities, and its value is equal to the current external force state x. F =f e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities:

[0037] FMI = min(d f,1 ,d f,2 ,...d f,2m )

[0038]

[0039] Where, n Fi Represents matrix N F The i-th column, n Mi Represents matrix N M The i-th column;

[0040] The torque margin (MMI) is solved using a system of torque space inequalities, and its value is equal to the current external torque state (x). M =τ e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities:

[0041] MMI = min(d τ,1 ,d τ,2,...d τ,2m )

[0042]

[0043] Using the cable parallel robot posture optimization method proposed in this invention, cable parallel robots with a non-point-shaped motion platform and a number of degrees of freedom of 3 to 6, a number of cables greater than or equal to 3, and a number of cables greater than or equal to the number of degrees of freedom can be analyzed. Specifically, this includes planar cable parallel robots with a workspace in a two-dimensional plane (3 degrees of freedom) and spatial cable parallel robots with a workspace in three-dimensional space (4 to 6 degrees of freedom).

[0044] For a planar cable parallel robot, its attitude angle can be described by a single independent angle, which is discretized into a series of discrete values ​​between two extreme positions. For a spatial cable parallel robot, its attitude angle can be described by 1 to 3 independent angles. When the number of attitude angles is 1, the attitude angle is discretized into a series of discrete values ​​between two extreme positions; when the number of attitude angles is greater than 1, the attitude angle is discretized into a series of scattered points in a two-dimensional or three-dimensional angle space that satisfy the extreme position constraints of the attitude angle.

[0045] When optimizing the posture of a cable-parallel robot using the optimization method proposed in this invention, the optimization objective is constructed based on the force margin and torque margin proposed in this invention. When the focus is on the performance of the cable-parallel robot in resisting external forces and outputting driving force to the outside world, the optimization objective is taken as the force margin; when the focus is on the performance of the cable-parallel robot in resisting external torque and outputting driving torque to the outside world, the optimization objective is taken as the torque margin; when it is necessary to consider both force and torque output performance, the optimization objective is taken as the weighted average of the two, and the specific weight is selected according to the specific requirements for force output and torque output performance.

[0046] Let R be the optimization objective based on force margin (FMI) and torque margin (MMI), where R is the weighted average of the force margin and torque margin, i.e.:

[0047] R = λ1 × FMI + λ2 × MMI

[0048] The coefficients λ1 and λ2 are selected according to the actual task requirements. For example, when only the performance of the cable-parallel robot in resisting external force disturbances is considered, λ1 is set to 1 and λ2 is set to 0; when only the performance of the cable-parallel robot in resisting external torque disturbances is considered, λ1 is set to 0 and λ2 is set to 1; when both the performance of the cable-parallel robot in resisting external forces and resisting external torques are considered, and it is desired that the weights of the two are equal, λ1 is set to 0.5 and λ2 is set to 0.5. At each discrete point in the workspace, the optimization objective value of the cable-parallel robot at that position and corresponding to the discrete attitude angles at that point is solved. The attitude angle with the maximum optimization objective value is taken as the optimal attitude angle at that point in the workspace. By traversing all discrete points in the entire workspace, the optimal attitude angles at all discrete point positions in the workspace are obtained, and finally, the distribution image of the attitude angles with the best anti-external disturbance performance in the workspace is obtained.

[0049] When determining the optimal attitude angle of a robot at a certain pose in the workspace, in addition to traversing all discrete attitude angles, intelligent optimization algorithms such as SQP and genetic algorithms can also be used for optimization. By setting the attitude angle range as the optimization constraint and setting the force margin, torque margin, or a weighted sum of the two as the optimization objective, the optimal attitude angle at each discrete position in the workspace can be obtained through optimization, thereby reducing the amount of computation compared to the method of traversing discrete attitude angles.

[0050] Compared with the prior art, the beneficial effects that can be achieved by implementing the present invention are:

[0051] 1. The method proposed in this invention optimizes the posture of a cable-parallel robot. By constructing force margin and torque margin indices, it analyzes and optimizes the force and torque output and resistance capabilities of the cable-parallel robot, thereby selecting the optimal posture of the cable-parallel robot at various positions in the workspace. This effectively improves the performance of the cable-parallel robot in outputting force and torque to the outside world and resisting external force and torque interference, thus effectively improving the performance of the cable-parallel robot and reducing the loss of control caused by cable traction.

[0052] 2. The analysis and optimization method proposed in this invention directly optimizes and improves the performance of output, resistance, and torque of the cable parallel robot. Compared with the traditional attitude optimization method that indirectly improves the performance by optimizing cable force distribution and stiffness, the effect is more significant. Attached Figure Description

[0053] Figure 1 This is a flowchart of the process of optimizing the posture of the cable-connected robot according to the present invention.

[0054] Figure 2 This is a schematic diagram of a planar three-cable, three-degree-of-freedom cable parallel robot according to the present invention.

[0055] Figure 3 This invention relates to the robot attitude angle distribution when optimizing a planar three-cable, three-degree-of-freedom parallel robot with the goal of maximizing the force margin.

[0056] Figure 4 This invention compares the force margin distribution before and after attitude optimization for a planar three-cable, three-degree-of-freedom parallel robot. Detailed Implementation

[0057] 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.

[0058] Figure 1 This is a flowchart of the attitude optimization method for a cable-parallel robot. First, the areas to be reached within the region enclosed by the exit point of the cable-parallel robot are selected, defining these areas as the robot's workspace. The workspace is then discretized into a series of points at preset intervals, representing the entire workspace. Next, based on the task requirements of the cable-parallel robot at each of the workspace's points, the attitude angle range for each point is defined and discretized at preset intervals. Simultaneously, optimization objectives based on force and torque margins are constructed as the selection principle for the optimal attitude angle. Based on this, the force and torque margins of the cable-parallel robot at each discrete attitude angle at each point in the workspace are calculated. Finally, the optimization objective values ​​at each discrete point are calculated based on the force and torque margin values, and the optimal attitude angle that maximizes the optimization objective is selected, resulting in a continuously distributed attitude distribution map within the workspace.

[0059] Specifically, such as Figure 1 As shown, firstly, the area to be reached within the region enclosed by the exit point of the cable-parallel robot is selected and defined as the workspace. This area is then discretized into 'a' discrete points at preset intervals (where 'a' is the number of discrete points). These discrete points represent the entire workspace. Next, based on the task requirements at each discrete point, the range of the cable-parallel robot's attitude angles at each point is defined. The attitude angle range corresponding to each discrete point is then discretized into 'b' discrete attitude angle values ​​at preset intervals (where 'b' is the number of discrete attitude angles at each discrete point).

[0060] Based on the mission requirements, an optimization objective R is constructed based on the force margin (FMI) and torque margin (MMI) as the principle for selecting the optimal attitude angle. R is the weighted average of the force margin and torque margin, i.e.:

[0061] R = λ1 × FMI + λ2 × MMI

[0062] The coefficients λ1 and λ2 are selected according to the actual task requirements. For example, when only the performance of the cable parallel robot in resisting external force disturbances is considered, λ1 is 1 and λ2 is 0; when only the performance of the cable parallel robot in resisting external torque disturbances is considered, λ1 is 0 and λ2 is 1; when both the performance of the cable parallel robot in resisting external forces and the performance of the cable parallel robot in resisting external torques are considered, and it is desired that the weights of the two are the same, λ1 is 0.5 and λ2 is 0.5.

[0063] During optimization, all discrete attitudes at all discrete points in the workspace are solved.

[0064] Specifically, when analyzing the i-th discrete point, the initial value R of the optimization objective R for the i-th discrete point is first set. i Set it to 0, and then solve for the force margin FMI and torque margin MMI for all b discrete attitude angles at the i-th discrete point one by one.

[0065] Specifically, based on the force margin FMI and torque margin MMI at the j-th discrete attitude angle at the i-th discrete point, the optimization objective value R can be solved. ij If R ij Greater than the R already stored at that point i The value of R will then be... ij Assigned to R i The optimal attitude angle for the i-th discrete point is recorded, otherwise no value is assigned or recorded. When all b discrete attitude angles at the i-th discrete point have been solved using the above steps, i.e., when j = b, the obtained R is considered optimal. i It is the optimal objective value at the i-th discrete point, and the recorded corresponding optimal objective value R is considered to be... i The attitude angle is the optimal attitude angle at the i-th discrete point.

[0066] After all a discrete points have been solved using the above steps, i.e., when i = a, the optimal attitude angles and optimization target values ​​for the coordinates corresponding to all a discrete points will be obtained. The surface determined by the optimal attitude angles corresponding to these discrete points is the optimal attitude distribution in the workspace, and the optimal optimization target values ​​corresponding to these discrete points are the anti-disturbance performance distribution of the cable-parallel robot in the workspace when it is in the optimal attitude.

[0067] Figure 2This is a schematic diagram of a planar three-cable, three-DOF parallel robot, and an implementation example of the posture optimization proposed in this invention is given based on this robot. In this embodiment, the robot can perform translation along the X and Z directions and rotation around the Y axis in the XOZ plane, for a total of three degrees of freedom. The robot's static platform width B1B3 = 1m, and the moving platform width A1A3 = 0.1m. B1 to B3 are the cable exit points, with coordinates [1m, 1m], [0.9m, 1m], and [0, 1m], respectively. A1 to A3 are the cable connection points on the moving platform, and P is the midpoint of the moving platform. The area the robot needs to reach (i.e., the workspace) is a square area with a side length of 0.5m, and the coordinates of its four vertices are [0.25m, 0], [0.75m, 0], [0.25m, 0.5m], and [0.75m, 0.5m].

[0068] Angle between the moving platform and the X-axis The magnitude of is the attitude angle of the moving platform, and the range of the attitude angle is [-80°, 80°]. The weight of the moving platform is m. Let the first... i The unit direction vector of the rope is If the distance from the midpoint of the moving platform to the three rope connection points A1 to A3 is r, then the Jacobian matrix of the robot is written as:

[0069]

[0070] The only net external force and net external torque acting on the moving platform is gravity.

[0071] Matrix H is derived from the Jacobian matrix J of the cable-parallel robot and the maximum and minimum cable force constraints f. max and f min Construct, here f max Take 2mg, f min Taking 0.05mg, matrix H is constructed as follows:

[0072] H=(f max -f min )J T =1.95mgJ T

[0073] For the cable-parallel robot in this embodiment, the coefficient matrix N can be constructed as a 3x6 matrix, where:

[0074]

[0075] For N in the coefficient matrix + The i-th column have:

[0076]

[0077] Θ(H {i} ) = [...(-1) k+1 |H {i}[k] |...] T k = 1, 2, 3

[0078] H {i} H represents the matrix formed by removing the i-th column from matrix H. {i}[k] This represents the matrix H formed by removing the i-th column and k-th row.

[0079] The intercept matrix d can be constructed as a 6x1 matrix, where:

[0080]

[0081]

[0082]

[0083] A is the construction matrix. For the cable parallel robot in this embodiment, it is a 3x8 matrix, with the following structure:

[0084]

[0085] Δd is a constant, and the i-th row of the Jacobian matrix J is denoted as Ji. i Then Δd can be calculated using the following formula:

[0086]

[0087] Based on the coefficient matrix N and the intercept column matrix d, a system of inequalities N can be constructed. T xd≤0

[0088] Each row of the system of inequalities corresponds to one inequality. Where n i d represents the i-th column of the coefficient matrix N. i Let represent the i-th element of the intercept matrix d. The system of inequalities consists of 6 rows.

[0089] Based on the constructed system of inequalities N T Given xd≤0 and the net external force and net external torque qe acting on the moving platform, we can construct a system of force-space inequalities and a system of torque-space inequalities. The elements in x can be divided into... x F Let x be the term corresponding to the external force. M Let x be the term corresponding to the external torque. The elements in N can be divided into... Where N F N is the term in N corresponding to the force component. FThis is the term in N corresponding to the torque component.

[0090] Use the current external torque state as the equality constraint x M =τ e Substituting these terms into the system of inequalities, the torque-related terms are now fixed by the system of inequalities, thus constructing a system of force-space inequalities. The system of inequalities consists of 6 lines. The current external force state is used as the equality constraint x. F =f e Substituting these terms into the system of inequalities, the force-related terms are now fixed by the system of inequalities, thus constructing a system of inequalities in the moment space. The system of inequalities consists of 6 lines.

[0091] Let the current external force state be x F =f e and the current external torque state x M =τ e By substituting these values ​​into the force space inequalities and the moment space inequalities respectively, the force margin and moment margin can be obtained.

[0092] Among them, the force margin FMI is solved according to the system of force space inequalities, and its value is equal to the current external force state x. F =f e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities:

[0093] FMI = min(d f,1 ,d f,2 ,...d f,6 )

[0094]

[0095] Where, n Fi Represents matrix N F The i-th column, n Mi Represents matrix N M The i-th column.

[0096] The torque margin (MMI) is solved using a system of torque space inequalities, and its value is equal to the current external torque state (x). M =τ e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities:

[0097] MMI = min(d τ,1 ,d τ,2 ,...d τ,6 )

[0098]

[0099] In this embodiment, the force margin (FMI) is used as the optimization objective, i.e., R = FMI. The entire workspace is traversed to solve for the optimal attitude angle of the robot at each discrete point in the workspace, as well as the FMI values ​​when the attitude angle is 0° and the optimal attitude angle at these positions. The optimal attitude angle distribution surface of the cable force in the workspace, as well as the FMI distribution surface before and after attitude angle optimization, are obtained.

[0100] The optimal attitude angle of the cable parallel robot obtained by solving the problem Distribution in the workspace as follows Figure 3 As shown, the force margin (FMI) distribution before and after optimization is as follows: Figure 4 As shown, the upper curved surface corresponds to the FMI after attitude optimization, and the lower curved surface corresponds to the attitude angle of the moving platform before attitude optimization. Take the FMI at 0°.

[0101] As can be seen, by optimizing the attitude, the force margin of the cable-parallel robot in the workspace was effectively improved. When the moving platform's attitude angle... When the angle is always 0°, there are large unreachable areas in the workspace (areas with an FMI of 0). By carrying out attitude optimization, the reachability of all positions in the workspace is achieved, and strong force output performance and resistance to external forces are obtained.

[0102] 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 method for posture optimization of a cable-connected parallel robot, characterized in that, Includes the following steps: Step 1: Select the area to be reached within the area enclosed by the cable exit point of the cable parallel robot, define these areas as the workspace of the cable parallel robot, and discretize the workspace into a series of points at preset intervals. Use these scattered points to represent the entire workspace. Step 2: Based on the task requirements of the cable-parallel robot at various scattered locations in the workspace, define the attitude angle range of the cable-parallel robot at each scattered location, and discretize the attitude angle range according to a preset interval; construct an optimization objective based on force margin and torque margin as the principle for selecting the optimal attitude angle in the future. Step 3: Solve for the force margin and torque margin of the cable-parallel robot at various discrete attitude angles at various scattered points in the workspace; Step 4: Solve for the optimization objective value of the parallel robot at each discrete point position when it is at each discrete attitude angle, select the optimal attitude angle at each discrete point position in the workspace that maximizes the optimization objective value, and then obtain the attitude distribution map that is continuously distributed in the workspace. In step three, the force margin and torque margin represent the robot's ability to output force and torque to the outside world, respectively, and also represent the robot's ability to resist external forces and torques. For a cable-parallel robot with m cables and n degrees of freedom, the specific calculation process is as follows: Step 3.1: Construct the equilibrium equations for the cable parallel robot based on the force and torque equilibrium conditions: JT+q e =0 Where J is the Jacobian matrix of the cable-parallel robot, and T represents the cable force on each cable of the cable-parallel robot. This represents the net external force and net external torque acting on the moving platform, where f e The net external force τ acting on the corresponding moving platform e The corresponding external torque acting on the moving platform; Step 3.2: Construct the coefficient matrix N, which is an n x 2m matrix, where: For N in the coefficient matrix + The i-th column have: This represents the matrix H formed by removing the i-th column. The matrix H is formed by removing the i-th column and k-th row from the matrix H. Matrix H is derived from the Jacobian matrix J of the cable parallel robot and the maximum and minimum cable force constraints f. max and f min structure: H=(f max -f min )J T Step 3.3: Construct the intercept column matrix d, where d is a 2m x 1 matrix, and: A is the construction matrix, which is an m-row 2-dimensional matrix. m The matrix consists of columns, where all elements are either 0 or 1. Each column corresponds to one possible combination of m 0s or 1s. When m = 3, the resulting constructed matrix A is: Δd is a constant, and the i-th row of the Jacobian matrix J is denoted as Ji. i Then Δd can be calculated using the following formula: Step 3.4: Construct a system of inequalities N based on the coefficient matrix N and the intercept column matrix d. T xd≤0 Each row of the system of inequalities corresponds to one inequality. Where n i d represents the i-th column of the coefficient matrix N. i Let represent the i-th element of the intercept matrix d, and the system of inequalities has 2m rows; Step 3.5: Based on the constructed system of inequalities N T xd≤0 and the net external force and net external torque acting on the moving platform Construct a system of force space inequalities and a system of moment space inequalities; The elements in x are divided into x F Let x be the term corresponding to the external force. M The term in x corresponds to the external torque; the elements in N are divided into... Where N F N is the term in N corresponding to the force component. M These are the terms in N corresponding to the torque components; Use the current external torque state as the equality constraint x M =τ e Substituting these terms into the system of inequalities, the torque-related terms are now fixed by the system of inequalities, thus constructing a system of force-space inequalities. The system of inequalities consists of 2m lines; the current external force state is used as the equality constraint x. F =f e Substituting these terms into the system of inequalities, the force-related terms are now fixed by the system of inequalities, thus constructing a system of inequalities in the moment space. The system of inequalities consists of 2m lines; Step 3.6: Set the current external force state x F =f e and the current external torque state x M =τ e Substitute the values ​​into the force space inequalities and the moment space inequalities respectively to solve for the force margin and the moment margin; Among them, the force margin FMI is solved according to the system of force space inequalities, and its value is equal to the current external force state x. F =f e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities: FMI=min(d f,1 ,d f,2 ,...d f,2m ) Where, n Fi Represents matrix N F The i-th column, n Mi Represents matrix N M The i-th column; The torque margin (MMI) is solved using a system of torque space inequalities, and its value is equal to the current external torque state (x). M =τ e The minimum distance among the distances to the hyperplane determined by each row of inequalities in the system of force-space inequalities: MMI=min(d τ,1 ,d τ,2 ,...d τ,2m ) 2. The method for optimizing the posture of a cable-connected robot according to claim 1, characterized in that, This method can be used to analyze cable-parallel robots with 3 to 6 degrees of freedom (n) and 3 or more ropes (m ≥ 3). The moving platform of the analyzed cable-parallel robot is not a point-like moving platform, and the number of ropes and degrees of freedom satisfy the relationship m ≥ n. The cable-parallel robot is either a planar cable-parallel robot with a workspace in a two-dimensional plane (i.e., 3 degrees of freedom) or a spatial cable-parallel robot with a workspace in three-dimensional space (i.e., 4 to 6 degrees of freedom).

3. The method for optimizing the posture of a cable-connected robot according to claim 1, characterized in that, For a planar cable parallel robot, its attitude angle is described by a single independent angle, which is discretized into a series of discrete values ​​between two extreme positions. For a spatial cable parallel robot, its attitude angle is described by 1 to 3 independent angles. When the number of attitude angles is 1, the attitude angle is discretized into a series of discrete values ​​between two extreme positions. When the number of attitude angles is greater than 1, the attitude angle is discretized into a series of scattered points in a two-dimensional or three-dimensional angle space that satisfy the extreme position constraints of the attitude angle.

4. The method for optimizing the posture of a cable-connected robot according to claim 1, characterized in that, The optimization objective is constructed based on the force margin and torque margin obtained from the solution; when the focus is on the performance of the cable parallel robot in resisting external forces and outputting driving force to the outside world, the optimization objective is taken as the force margin; When focusing on the performance of the 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. Specifically, the optimization objective based on force margin (FMI) and torque margin (MMI) is defined as R, where R is the weighted average of the force margin and torque margin, i.e.: R = λ1 × FMI + λ2 × MMI The coefficients λ1 and λ2 are selected according to the actual task requirements. When only the performance of the cable parallel robot against external force disturbances is considered, λ1 is 1 and λ2 is 0; when only the performance of the cable parallel robot against external torque disturbances is considered, λ1 is 0 and λ2 is 1. When considering both the performance of the cable parallel robot in resisting external forces and its performance in resisting external torques, and desiring that the weights of the two are equal, λ1 is set to 0.5 and λ2 is set to 0.

5. At each discrete point in the workspace, the optimal objective value of the parallel robot at that position is calculated, corresponding to the discrete attitude angles at that point. The attitude angle with the maximum optimal objective value is taken as the optimal attitude angle at that point in the workspace. By traversing all discrete points in the entire workspace, the optimal attitude angles at all discrete point positions in the workspace are obtained, and finally, the distribution image of the attitude angle with the best anti-interference performance in the workspace is obtained.

5. The method for optimizing the posture of a cable-connected robot according to claim 1, characterized in that, When determining the optimal attitude angle, the method of traversing all discrete attitude angles can be adopted, or an intelligent optimization algorithm can be used for optimization. By setting the attitude angle range as the optimization constraint, and setting the force margin, torque margin, or a weighted sum of the two as the optimization objective, the optimal attitude angle at each discrete position in the workspace can be obtained through optimization, thereby reducing the amount of computation compared to the method of traversing discrete attitude angles.

6. The method for optimizing the posture of a cable-connected robot according to claim 5, characterized in that, The intelligent optimization algorithm is SQP algorithm, genetic algorithm, particle swarm optimization algorithm, ant colony optimization algorithm, annealing algorithm or neural network algorithm.

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