A series mechanical arm configuration optimization method

Abstract

The serial mechanical arm configuration optimization method provided by the present application realizes configuration optimization of a serial mechanical arm, and comprises the following steps: a configuration code model is derived according to a serial mechanical arm configuration expression mode, a structure tree without repeated configurations is constructed, a mathematical expression of a typical performance index of the mechanical arm is obtained, the typical performance index comprises a flexibility index, an operability, a condition number, a minimum singular value, a workspace index and end precision, a forward normalization process is performed according to the monotonicity, an expert scoring system comprehensive index evaluation system is established, a configuration screening is performed in the configuration structure tree growth process by using a hierarchical pruning method, and an optimal solution set is obtained. According to the technical scheme provided by the present application, the evaluation and rapid configuration optimization of multiple performance indexes of an indefinite degree of freedom serial mechanical arm can be realized.

Description

TECHNICAL FIELD

[0001] The application relates to a preferred method for a serial mechanical arm configuration and belongs to the field of mechanical arm configuration optimization. BACKGROUND

[0002] With the deepening of human space exploration, the complexity of space missions increases, and the difficulty also increases. From the aspects of safety, efficiency and cost, it is not enough to complete the space exploration task only by astronauts. Space robots have gradually become the main force of future space exploration due to the diversity of application scenarios, and therefore, it is inevitable to use space robots to replace astronauts to complete on-orbit tasks. The space robot mainly takes a serial mechanical arm as the core, has multiple degrees of freedom and certain flexibility, and can perform accurate operations in a small and complex environment. Therefore, the design of a space robot mainly taking a serial mechanical arm as the main body has become a main trend.

[0003] For the configuration design of a serial mechanical arm, existing methods are an experience method and an exhaustive method.

[0004] The experience method is based on the existing mechanical arm configuration design experience to form a mechanical arm configuration database, and searches for a configuration close to a design target during design. However, the experience method only considers typical mechanical arm configurations and has certain limitations. The exhaustive method is to calculate all possible configurations and then screen according to performance indicators, but the degrees of freedom are usually given, and the calculation amount is large and the efficiency is low. Therefore, it is of great significance to establish a comprehensive and efficient configuration optimization method for a serial mechanical arm for the mechanical arm selection problem. SUMMARY

[0005] Therefore, the application provides a serial mechanical arm configuration optimization method, which can quickly classify serial mechanical arms with indefinite degrees of freedom when facing multiple performance index design requirements, and then obtain an optimal configuration solution set.

[0006] The application provides a serial mechanical arm configuration optimization method, which comprises the following steps:

[0007] According to the types and connection relationships of joint kinematic pairs, a coded configuration model of the serial mechanical arm is constructed, and a non-repeated configuration structure tree is created;

[0008] Typical mechanical arm performance evaluation index expressions are sorted, including flexibility indexes, operability, condition numbers, minimum singular values, workspace indexes and end accuracy, and the expressions are positively normalized according to their monotonicity;

[0009] An expert scoring system is established, classification standards of each index in the configuration optimization process are designed according to the scores of experts on the importance of each index, and the configuration optimization process is completed.

[0010] A serial manipulator configuration optimization method based on hierarchical pruning method is designed, and the manipulator configuration is classified according to different design requirements to obtain the optimal solution set.

[0011] In the above method, the serial manipulator coded configuration model is constructed according to the type of joint motion pair and the connection relationship, and a non-repeating configuration structure tree is created, including:

[0012] (1) Joint motion pair type

[0013] The joint is the basic unit of the manipulator configuration. In actual design, the axes of adjacent joints are generally parallel or orthogonal. Taking the base coordinate system as the reference, the rotation around the X-axis direction is the deflection, the rotation around the Y-axis direction is the pitch, and the rotation around the Z-axis direction is the roll.

[0014] (2) Coded configuration model

[0015] In order to describe the relative position relationship between adjacent joints, the coded configuration model e i is defined

[0016] e i =(Rx i Ry i Rz i ux i uy i uz i )|(i=1,…,n)

[0017] In the formula:

[0018] Rx i , Ry i , Rz i - The rotation direction of the i-th joint. If Rx i =1, Ry i =0, Rz i =0, it means that the i-th joint rotates around the X-axis direction. If Rx i =0, Ry i =1, Rz i =0, it means that the i-th joint rotates around the Y-axis direction. If Rx i =1, Ry i =0, Rz i =1, it means that the i-th joint rotates around the Z-axis direction.

[0019] ux i , uy i , uz i— super parameters, respectively representing whether there is a distance between the positions of the i-1 joint and the i joint in the X, Y, Z directions of the base coordinate system, when the value is 0, it represents that there is no distance between the i-1 joint and the i joint in the direction; when the value is 1, it represents that there is a distance between the i-1 joint and the i joint in the direction;

[0020] (3) Configuration structure tree

[0021] The tree diagram is a graphical tool for representing data or information in a hierarchical structure, which is composed of nodes and edges, and the nodes represent data or information, and the edges represent the relationship between the nodes.

[0022] Use Config n to represent the configuration information of the n-degree-of-freedom serial branch joint:

[0023] Config n = (e1; e2; …; e n )|i = (1, …, n)

[0024] In the formula, e i represents the configuration of joint i;

[0025] In the n-degree-of-freedom serial robot arm Config n , a joint e n+1 is added at the end joint to obtain an n+1-degree-of-freedom serial robot arm Config n+1 , and the configuration generation expression is as follows:

[0026]

[0027] Define the connection matrix T i i+1 to represent the connection relationship between the configuration Config n and the joint e n+1 :

[0028]

[0029] In the formula, t1, t2, t3 respectively represent the rotation of the joint around the X, Y, Z axes, represents whether the t j type joint can be connected with the t k type joint, when , it represents that if the end joint of Config n is t j , then t k cannot be used as a subsequent joint; if , it represents that if the end joint of Config n is t j , then t k can be used as a subsequent joint;

[0030] Configuration repetition and failure cases are:

[0031] (1) When the adjacent joint axis is perpendicular, all the rotation pairs orthogonal to it are equivalent for the rotation pair after it;

[0032] (2) When the axes of the adjacent two rotation pairs are collinear, the adjacent two degrees of freedom degenerate into one degree of freedom; considering the joint connection constraint condition, the connection matrix under the constraint condition is established:

[0033]

[0034] Among them:

[0035]

[0036] V is or, XOR is exclusive or.

[0037] In the above method, the typical mechanical arm performance evaluation index expression includes flexibility index, operability, condition number, minimum singular value, workspace index, end precision, and according to the monotonicity, the positive normalization processing is carried out, including:

[0038] (1) Flexibility index

[0039] The flexibility matrix is used to describe the displacement response characteristics of the mechanical arm end under the force condition, and is an important tool for analyzing the deformation of the mechanical arm under external force. The generalized force required to cause the end to produce a small change amount ΔX e is:

[0040] F=K x ΔX e

[0041] Wherein, K x is the Cartesian stiffness matrix

[0042] The Cartesian stiffness matrix K x and the joint stiffness matrix K θ have the following transformation:

[0043] K x =J -T K θ J -1

[0044] Wherein, J represents the Jacobian matrix of the mechanical arm

[0045] Therefore,

[0046] F=K x ΔX e =J -T K θ J-1 ΔX e

[0047] K x The inverse matrix can obtain the flexibility matrix E flex :

[0048]

[0049] When the robot is in the boundary singularity, its stiffness is often poor, and the maximum eigenvalue f of the flexibility matrix is selected as the performance evaluation index;

[0050] (2) Operability

[0051] The operability is used to represent the flexibility of the robot motion:

[0052]

[0053] Where, det represents calculating the determinant of the matrix

[0054] (3) Condition number

[0055] The singular value decomposition is performed on the Jacobian matrix:

[0056] J = U∑V

[0057] Where, U, V are orthogonal matrices, and ∑ has the following form:

[0058]

[0059] Where, σ1, σ2, …, σ m are the singular values of J, and σ1> σ2> …> σ m , σ1is the maximum singular value, and σ m is the minimum singular value;

[0060] The condition number is the ratio of the maximum singular value to the minimum singular value:

[0061]

[0062] (4) Minimum singular value

[0063] The minimum singular value represents the motion ability in the worst direction of the robot. At the configuration singularity, the minimum singular value of the robot is zero, and the expression is:

[0064] s = σ m

[0065] (5) Workspace index

[0066] The workspace index Q is defined as the ratio of the sum of the lengths of the robot links to the cube root of the volume of the reachable workspace at the end, and the calculation formula is:

[0067]

[0068] In the formula:

[0069] L - the sum of the lengths of the links;

[0070] V - the volume of the reachable workspace;

[0071] a - the length of the link;

[0072] d - the offset of the link;

[0073] (6) End error index

[0074] To calculate the pose accuracy of the robot arm, the joint repeatability accuracy is simulated by setting the joint angle error to +0.001°; in addition, errors are generated during the manufacturing process and assembly process, which will cause errors in the structural parameters of the links of the robot, and the size accuracy of the robot arm is set to ±0.01% of the actual value; therefore, the link parameter (a, d) error is set to ±0.01%;

[0075] According to the forward kinematics equation, the pose of the end relative to the reference coordinate system can be obtained, and the actual position is P N = (x N , y N , z N ), the theoretical position is P A = (x A , y A , z A ), and the end position deviation index is:

[0076]

[0077] wherein, aver represents the calculation of the average number

[0078] (7) Forward normalization

[0079] The six performance indicators of the serial robot arm are: flexibility index f, operability ω, condition number c, minimum singular value s, workspace index Q, and end accuracy E P ; all performance indicators can be divided into two categories: forward indicators and reverse indicators, the greater the value of the forward indicators, the better the performance; the greater the reverse indicators, the worse the performance, when performing configuration evaluation, it must be first trended, generally the reverse indicators are converted into forward indicators, the formula is:

[0080] h' = 1 / h

[0081] After the positive direction of all evaluation indexes, in order to eliminate the incommensurability caused by the different dimensions of each index, the indexes should be dimensionless through normalization, the formula is:

[0082]

[0083] After the normalization of the six performance indexes (f, ω, c, s, Q, E P ), (h1, h2, h3, h4, h5, h6) are obtained respectively.

[0084] In the above method, the establishment of the expert scoring system, according to the expert's score of the importance of each index, the classification standard of each index in the configuration optimization process is designed, including:

[0085] Assuming that the task requirement a is faced, n experts use the scale of 0-10 to score the importance of each performance index according to their experience, and then the scale sequence of each evaluation index can be obtained: Taking the average value of each expert's score as the final score of each index, the final score of index h i is:

[0086]

[0087] According to the value range of the score, the classification threshold of each performance index is determined The classification standard of configuration screening is established:

[0088]

[0089] When the final score of index i is in , the index evaluation level is "poor", and the index classification threshold Q1 is the lower quartile; when the final score of index i is in , the index evaluation level is "good", and the index classification threshold Q2 is the second quartile; when the final score of index i is in , the index evaluation level is "excellent", and the index classification threshold Q3 is the upper quartile.

[0090] In the above method, the design of series mechanical arm configuration optimization method based on hierarchical pruning method, according to different design requirements, the mechanical arm configuration is classified, and the configuration optimization solution set is obtained, including:

[0091] For the multi-indexed optimal problem of serial manipulator synthesis configuration, the performance indexes should be classified first: for the optimization indexes with monotonicity, pruning method is adopted in the tree growth process to effectively exclude configurations that do not meet the requirements; for the optimization indexes without monotonicity, structure tree traversal layering is performed afterwards to ensure that all possible configurations are considered, and finally a configuration set that meets all performance requirements is obtained. The specific optimization process is as follows:

[0092] ① Degree of freedom n, performance index set ψ, performance index threshold set χ;

[0093] ② Divide the six performance indexes into two categories: set ψ1={κ1, κ2, …, κ i} with monotonicity, and set ψ2={λ1, λ2, …, λ i} without monotonicity;

[0094] ③ Input the minimum degree of freedom n min , and establish the configuration structure tree Tree min of the serial manipulator;

[0095] ④ Get all leaf nodes e i under the structure tree, and calculate the performance index value with monotonicity of each tree branch

[0096] ⑤ Compare the performance index value with monotonicity with the corresponding threshold value If , the current node branch is pruned, and no new child node is generated. If , the current node branch is not pruned, and a new child node is generated.

[0097] ⑥ Calculate the node growth factor

[0098] ⑦ Design the new connection matrix as When the node growth factor E1=0, it indicates that the current node branch is pruned, and no new child node is generated.

[0099] ⑧ Increase the depth of the tree by one, i.e. depth=depth+1.

[0100] ⑨ Judge whether the depth depth reaches n. If yes, stop the calculation, get the structure tree Tree_Mid n at this time, and if not, return to step ④.

[0101] ⑩ Get all configurations Config_Mid n under the current structure tree Tree_Mid n by recursive traversal method, and calculate the performance index value without monotonicity

[0102] Computing classification factor To configuration Config_Mid n It is layered, all configurations satisfying E2=1 are retained, all E2=0 configurations are removed, and finally the configuration set Config_Dis satisfying all optimization objectives is obtained n . BRIEF DESCRIPTION OF DRAWINGS

[0103] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creativity and labor on the premise of not paying.

[0104] Figure 1 is a flowchart of the series mechanical arm configuration optimization method provided by the embodiments of the present application;

[0105] Figure 2 is a comparison diagram of the calculation efficiency of the first traversal method and the mixed hierarchical pruning method in the expert scoring case three in the embodiments of the present application;

[0106] Figure 3 is a comparison diagram of the calculation efficiency of the second traversal method and the mixed hierarchical pruning method in the expert scoring case four in the embodiments of the present application;

[0107] Figure 4 is a comparison diagram of the calculation efficiency of the second traversal method and the mixed hierarchical pruning method in the expert scoring case four in the embodiments of the present application;

[0108] Figure 5 is a comparison diagram of the calculation efficiency of the second traversal method and the mixed hierarchical pruning method in the expert scoring case four in the embodiments of the present application;

[0109] Figure 6 is a comparison diagram of the average calculation efficiency in the case of 100 expert scoring in the embodiments of the present application; DETAILED DESCRIPTION

[0110] Five experts are invited to score the performance design of the series mechanical arm facing 4-7 degrees of freedom, and the comprehensive score is calculated to design the threshold of each performance index. Since each scoring result is divided into three levels, the six performance indexes will produce three 6 classification results. Let H=[q1, q2, q3, q4, q5, q6] represent the classification level of each index, q i can be divided into three levels: {excellent, good, poor}. 100 groups of scoring results are randomly generated for configuration optimization. Figures 2 to 5The configuration number required by the hierarchical pruning method in four groups of scoring conditions is given. The abscissa represents the corresponding degree of freedom, the ordinate represents the configuration number required to calculate the performance, the left column in the figure represents the calculation number of the traversal method, the right column represents the calculation number of the hierarchical pruning method, the curve in the figure represents the ratio of the right column to the left column, when the ratio is greater than 1, it means that the calculation number of the traversal method is less than that of the hierarchical pruning method, and the efficiency is higher, when the ratio is less than 1, it means that the calculation number of the hierarchical pruning method is less than that of the traversal method, and the efficiency is higher.

[0111] Figure 2 Corresponding scoring result H=[excellent good poor good poor], Figure 3 Corresponding scoring result H=[excellent good poor good poor], Figure 4 Corresponding scoring result H=[excellent good poor good poor], Figure 5 Corresponding scoring result H=[poor poor good poor good, good]. The flexibility index h1 and the operability index h2 have monotonicity, and the condition number h3, the minimum singular value h4, the end error h5 and the workspace index h6 do not have monotonicity. From Figure 2 It can be seen that the calculation efficiency of the hierarchical pruning method is always higher than that of the traditional traversal method as the degree of freedom changes. From Figure 5 It can be seen that when the flexibility index h1 and the operability index h2 have low classification levels, the calculation amount of the hierarchical pruning method is greater than that of the traversal method, which is caused by the large number of configurations of the upper degree of freedom used to calculate h1 and h2. In addition, only low degree of freedom configurations may have this situation, and when the degree of freedom is 6 or 7, the efficiency of the hierarchical pruning method is significantly higher than that of the traditional traversal method.

[0112] In addition, 100 groups of scoring results H are randomly generated for configuration optimization, Figure 6 The average calculation number of the traversal method and the hierarchical pruning method is given.

[0113] According to Figure 6 As a result, regardless of the H evaluation, the calculation amount of the two methods shows an upward trend as the degree of freedom increases, but the calculation efficiency of the hierarchical pruning method is significantly higher than that of the traditional traversal method, and the advantage is more obvious as the degree of freedom increases, and the calculation efficiency is increased by 36.8% when the degree of freedom is 7R.

[0114] The technical scheme of the embodiment of the application has the following beneficial effects:

[0115] Based on the type and connection relationship of the joint motion pair, a serial robot coding configuration model is constructed, a configuration structure tree without failure and repeated configuration is designed, a plurality of robot operation performance evaluation indexes are sorted out, normalized, and a multi-expert scoring system is combined with the hierarchical pruning method, and a serial robot configuration optimization is designed for multiple indexes. The optimization scheme can select the configuration of the serial robot according to different needs, and has high efficiency and feasibility.

[0116] The above description is only the preferred embodiment of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

[0117] The contents not described in detail in the present application specification are the known technology of the person skilled in the art.

Claims

1. A method for optimizing a configuration of a series mechanical arm, characterized in that, The method comprises: According to the type of joint movement pair and the connection relationship, a coded configuration model of the serial mechanical arm is constructed, and a non-repeated configuration structure tree is created; The performance evaluation index expression of the typical mechanical arm is sorted out, including the flexibility index, the operability, the condition number, the minimum singular value, the workspace index, and the end precision, and the forward normalization processing is performed according to the monotonicity thereof; An expert scoring system is established, the classification standards of the indexes in the configuration optimization process are designed according to the scores of the experts on the importance of the indexes, and A serial mechanical arm configuration optimization method based on the hierarchical pruning method is designed, the mechanical arm configurations are classified according to different design requirements, and the configuration optimization solution set is obtained, including: for the multi-index serial mechanical arm comprehensive configuration optimization problem, the performance indexes are classified first: for the optimization indexes with monotonicity, the pruning method is used for screening in the tree growth process, so as to effectively exclude the configurations that do not meet the requirements; and for the optimization indexes without monotonicity, the hierarchical structure tree traversal is performed later, so as to ensure that all possible configurations are considered, and finally a configuration set that meets all performance requirements is obtained.

2. The method of claim 1, wherein, According to the type of joint movement pair and the connection relationship, the coded configuration model of the serial mechanical arm is constructed, and the non-repeated configuration structure tree is created, including: (1) the type of joint movement pair Joints are the basic units of a robotic arm's configuration. In practical design, the axes of adjacent joints are parallel or orthogonal, with the base coordinate system as a reference, and revolving around... Rotation along the axis is deflection, around... Rotation along the axis is pitch, and rotation around the axis is rotation. Rotation along the axis is called rolling; (2) the coded configuration model To describe the relative positional relationship between adjacent joints, a coded configuration model is defined : In the formula: - the first joint is rotated in the direction of the first axis if - the second joint is rotated in the direction of the second axis if - the third joint is rotated in the direction of the third axis if - the fourth joint is rotated in the direction of the fourth axis if - the fifth joint is rotated in the direction of the fifth axis if - the sixth joint is rotated in the direction of the sixth axis if - the seventh joint is rotated in the direction of the seventh axis if - the eighth joint is rotated in the direction of the eighth axis if - the ninth joint is rotated in the direction of the ninth axis if - the tenth joint is rotated in the direction of the tenth axis if - the eleventh joint is rotated in the direction of the eleventh axis if — hyperparameters, respectively representing joint and the position of the joint in the base frame , , whether there is a distance in the direction, when the value is 0, it means that there is no distance in the direction joint and no distance between the joints; when the value is 1, it means that there is a distance in the direction joint and distance between the joints (3) the configuration structure tree The tree diagram is a graphical tool for representing data or information in a hierarchical structure, which is composed of nodes and edges, the nodes represent data or information, and the edges represent the relationship between the nodes; With Indicates Degrees of freedom series branch joint configuration information: In serial manipulator with degrees of freedom adding a joint at the end joint , resulting in serial manipulator with degrees of freedom , the configuration generation expression is as follows: Definition of connection matrix Representation of configuration Connection relationship with joint ​ In the formula, These represent the joint rotation. Axis rotation, express Can type joints be related to Type of joint connection, when When, it means if The distal joint is ,but Cannot be used as a subsequent joint; if When, it means if The distal joint is ,but It can be used as a subsequent joint; The configuration repetition and failure conditions are: (1) when the adjacent joint axes are perpendicular, all the rotation pairs that are orthogonal to the rotation pair are equivalent; (2) when the axes of the adjacent two rotation pairs are collinear, the adjacent two degrees of freedom degenerate into one degree of freedom; Considering the joint connection constraint conditions, the connection matrix under the constraint conditions is established: In the formula: is or, is exclusive or.

3. The method of claim 1, wherein, The performance evaluation index expression of the typical mechanical arm includes the flexibility index, the operability, the condition number, the minimum singular value, the workspace index, and the end precision, and the forward normalization processing is performed according to the monotonicity thereof, including: (1) the flexibility index The flexibility matrix is used to describe the displacement response characteristics of the end of the robot arm under force, and is an important tool for analyzing the deformation of the robot arm under external force, causing a small change in the end The generalized force required to cause a small change in the end is: wherein is the Cartesian stiffness matrix cartesian stiffness matrix with joint stiffness matrix there exists a transformation: wherein, denotes the Jacobian matrix of the robot arm Therefore, :​​ When the robot is in the boundary singularities, its stiffness is often poor, and the maximum eigenvalue of the flexibility matrix is selected As a performance evaluation index; (2) the operability The operability is used to represent the flexibility of the movement of the mechanical arm: wherein denotes the determinant of the calculation matrix (3) the condition number The singular value decomposition is performed on the Jacobian matrix: wherein are orthogonal matrices, has the form: wherein is the singular value of , is the largest singular value, is the smallest singular value; The condition number is the ratio of the maximum singular value to the minimum singular value: (4) the minimum singular value The minimum singular value represents the movement ability in the worst direction of the mechanical arm, and at the configuration singularity, the minimum singular value of the mechanical arm is zero, and the expression is: (5) the workspace index Workspace metrics The workspace metric is defined as the ratio of the sum of the lengths of the links of the robot arm to the cube root of the volume of the reachable workspace at the end of the robot arm. The formula is: In the formula: - the sum of the lengths of the connecting rods; - the volume of the reachable workspace; - length of the connecting rod; - link biasing; (6) the end error index To calculate the pose accuracy of the robot arm, the joint repeatability accuracy is simulated by setting the joint angle error to ±0.001°. In addition, errors are generated during the manufacturing process and assembly process, which can cause errors in the link structure parameters of the robot. The size accuracy of the robot arm is set to ±0.01% of the actual value. Therefore, the link parameters error is set to ±0.01%. According to the forward kinematics equation, the pose of the end relative to the reference coordinate system can be obtained, and the actual position is , the theoretical position is , and the end position deviation index is wherein represents calculating the average (7) the forward normalization The six performance indexes of the serial manipulator are: flexibility index , operability index , condition number , minimum singular value , workspace index , end accuracy ; all the performance indexes can be divided into two categories: forward index and reverse index, the greater the value of the forward index, the better the performance; the greater the reverse index, the worse the performance. When evaluating the configuration, it is necessary to first trend it and convert the reverse index into a forward index, the formula is: After the forward normalization of all the evaluation indexes, in order to eliminate the incommensurability caused by the different dimensions of the indexes, the indexes should be dimensionless through normalization, and the formula is: The six performance indicators After normalization, the six performance indicators correspond to .

4. The method of claim 1, wherein, The expert scoring system is established, the classification standards of the indexes in the configuration optimization process are designed according to the scores of the experts on the importance of the indexes, and Assume task-oriented requirements Please Bit experts use 0-10 scale according to their own experience on the importance of each performance index, and then the scale sequence of each evaluation index can be obtained: The average value of each expert's score is taken as the final score of each index, and the final score of the index is: According to the value range of the score result, determine the classification threshold of each performance index , establish the classification standard of configuration screening: When the indicator The final score was in When the indicator evaluation level is "poor", the indicator classification threshold is... The lower quartile; when the index The final score was in At that time, the indicator evaluation level is "good", and the indicator classification threshold is... It is a quartile; when the index The final score was in At that time, the indicator evaluation level is "excellent", and the indicator classification threshold is... It is the upper quartile.

5. The method of claim 1, wherein, The multi-index-oriented serial manipulator comprehensive configuration optimization problem is preferably classified according to the performance index: for the optimization index with monotonicity, the pruning method is used in the tree growth process to effectively exclude the configurations that do not meet the requirements; and for the optimization index without monotonicity, the structure tree is traversed and layered, so that all possible configurations are considered, and finally a configuration set satisfying all performance requirements is obtained, and the specific optimization process is as follows: ① degree of freedom , set of performance indicators , set of performance indicator thresholds ; ii. 6 performance indexes are divided into two categories, one with monotonic change set , and one without monotonic change set ; iii. input minimum degrees of freedom , establishing a configuration structure tree of the serial manipulator ; (4) Acquire all leaf nodes under the structure tree and calculate the performance index value of each branch with monotonicity ; ⑤ comparing the monotonicity performance index value with the corresponding threshold value , if , , if , ; • Compute node growth factor ; ⑦ Design new connection matrix as When the node growth factor is 0, it indicates that the current node branch is pruned and no new child node is generated.

8. Increase the depth of a tree ; Depth of judgment Whether to reach If yes, stop calculation, and obtain the structure tree at this time If no, return to step 4; ⑩ Obtain the current tree structure using recursive traversal. All configurations And calculate the performance index values ​​that do not have monotonicity. ; © Calculate the classification factor On the configuration Layering, keep all configurations that meet All configurations are rejected The final configuration set that meets all optimization objectives is obtained .

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