CN109623814B - Mechanical arm control method - Google Patents
Mechanical arm control method Download PDFInfo
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- CN109623814B CN109623814B CN201811530472.2A CN201811530472A CN109623814B CN 109623814 B CN109623814 B CN 109623814B CN 201811530472 A CN201811530472 A CN 201811530472A CN 109623814 B CN109623814 B CN 109623814B
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1602—Programme controls characterised by the control system, structure, architecture
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The application discloses a control method of a mechanical arm, which comprises the following steps: 1) Establishing a forward kinematic model of the mechanical arm as a system input, and giving control parameters of a self-adaptive variation differential evolution algorithm; 2) Randomly initializing a population in a parameter space; 3) Randomly selecting individuals from the population to perform mutation operation to generate a mutation vector; 4) Performing cross operation on the variation vector and the target vector to generate a test vector; 5) Comparing the test vector with the target vector, and selecting a better individual as a new target vector; 6) Judging whether a preset stopping criterion is met, if yes, ending and outputting an optimal individual as a joint variation matrix of the mechanical arm, otherwise, returning to the step 3). The method can obtain the shortest stroke solution while ensuring the pose accuracy of the mechanical arm, improves the flexibility of the joint and improves the operation efficiency.
Description
Technical Field
The application relates to the field of mechanical arm kinematics, in particular to a mechanical arm control method
Background
The mechanical arm is a complex system with multiple inputs and multiple outputs, high nonlinearity and strong coupling. Because of its unique operational flexibility, it has been widely used in the fields of industrial assembly, safety explosion protection, etc. The redundancy freedom degree of the mechanical arm can ensure the flexibility, obstacle avoidance performance and operation performance of the operation, but brings the problem of multiple solutions of inverse kinematics and the problem of selecting an optimal solution from infinite multiple groups of inverse solutions.
The mechanical arm kinematics inverse solution refers to knowing the position and the gesture of the end effector relative to a basic coordinate system and solving a joint angle sequence meeting the gesture precision requirement. The mechanical arm kinematics equation is a nonlinear transcendental equation, the solution of which is relatively complex, and may be multi-solution or non-solution. Whether a solution exists depends on the working space of the robotic arm. If the target point is located within the workspace, then a solution exists. If the target point is outside the workspace, then there is no solution. For the multi-solution situation, the solution method of the mechanical arm kinematic inverse solution can be divided into two main categories: a closed solution and a numerical solution. The closed solution is limited to the robotic arm configuration. The mechanical arm with the adjacent three joint axes intersecting at one point only has a closed solution. Among numerical solutions, the iterative method based on jacobian matrix is most widely used. However, a part of the mechanical arm configuration may have a singularity problem, and the stability of iterative convergence cannot be ensured. Only pose accuracy requirements are considered above. In order to find the optimal inverse solution, additional control criteria must be added.
The existing method for solving the inverse solution with the minimum joint variation mainly comprises a weighted sum method, a storage feasible solution method and a punishment function method. And the weighted sum method and the penalty function method solve the values of the superior and inferior dependency weight coefficients of the results. The save feasible solution method needs to provide an initial feasible solution and is easily trapped in a locally optimal solution. The penalty function method converts constraint problems to unconstrained problems, but it is difficult to set an appropriate penalty factor.
Disclosure of Invention
The application aims to provide a mechanical arm control method, which can ensure pose accuracy and obtain the shortest stroke solution, improve joint flexibility and improve operation efficiency.
In order to achieve the above object, the present application provides a control method for a mechanical arm, comprising the steps of:
1) Establishing a forward kinematic model of the mechanical arm as a system input, and giving control parameters of a self-adaptive variation differential evolution algorithm;
2) Randomly initializing a population in a parameter space;
3) Randomly selecting individuals from the population to perform mutation operation to generate a mutation vector;
4) Performing cross operation on the variation vector and the target vector to generate a test vector;
5) Comparing the test vector with the target vector, and selecting a better individual as a new target vector;
6) Judging whether a preset stopping criterion is met, if yes, ending and outputting an optimal individual (the individual represents the joint variable of the mechanical arm and is the input of a matrix model), taking the optimal individual as a joint variable matrix of the mechanical arm and controlling the joint action of the mechanical arm, otherwise, returning to the step 3).
Further, in step 1), the control parameters include a mutation constant F, a crossover probability CR, a population size N, an algebraic evolutionary counter T, and a maximum algebraic evolutionary T.
Further, in step 2), the population is p= { X 1 ，…，X N "and individuals of the population are X i ＝{x i1 ，…，x iD I= … N, N representing population size, D representing the number of joints of the robotic arm.
Further, the specific implementation process of the step 3) includes: randomly generating a random number rand1 between 0 and1, comparing the sizes of rand1 and 1-T/T, and if rand1 < -T/T, selecting a variation mode DE/rand/1/bin to generate a variation vector, namelyIf rand1 is more than or equal to 1-T/T, a variation pattern DE/best/1/bin is selected to generate a variation vector, namely +.>Wherein r is 1 、r 2 、r 3 Is a random integer, and represents the serial number of an individual in a population, X b For the best individuals in the current generation population, +.>Three individuals randomly drawn from the contemporary population.
Further, the specific implementation process of the step 4) includes: randomly generating a random number rand2 between 0 and1, comparing the magnitudes of rand2 and the crossover probability CR, and if rand2 < CR, u ij ＝v ij Namely, a variation vector is selected as a test vector; if rand2 is equal to or greater than CR, u ij ＝x ij I.e. selecting the target vector as the test vector, where u ij Representing test vectors, v ij Representing the variation vector, x ij Representing the target vector.
Further, the specific implementation process of the step 5) includes:
1) Setting the fitness function of the shortest travelWherein x is i (k)-x i (k-1) represents the variation of the pose joint angle of the kth target task of the joint i relative to the kth-1 target task; omega i Weight coefficients representing the relative importance of balancing the joints;
2) Setting constraint conditions of the expected target pose: a. position constraint conditions: g 1 (X)＝E p -T p Less than or equal to 0; b. attitude constraint conditions: g 2 (X)＝E o -T o Less than or equal to 0; wherein E is p Representing position error, T p Representing a position error threshold, E o Representing attitude error, T o Representing a posing error threshold;
3) Setting constraint violation degree G (X): g (X) =p 1 G 1 (X)+p 2 G 2 (X); wherein G is 1 (X)＝max{0，g 1 (X)}，G 2 (X)＝max{0，g 2 (X)}，p 1 、p 2 Weight coefficients respectively representing the position constraint condition and the attitude constraint condition;
4) Setting the allowable relaxation degree epsilon (t) of population constraint:where θ represents the proportion of each evolutionary generation of population that allows a reduction in the degree of relaxation; when the population evolves to the t generation, if 0< G (X)). Ltoreq.ε (t), then individual X is an acceptable solution; when the population evolves to the t-th generation, if G (X) > ε (t), then individual X is an unacceptable solution;
5) Calculation of test vector X i And the target vector U i Is set to be 0, i.e., G (X) i )＝G(U i ) =0, then select the individual with smaller objective function as the new objective vector; if the violation constraints of both the trial vector and the target vector are greater than 0, i.e., G (X i ) > 0 and G (U) i ) If the value is more than 0, selecting an individual with smaller violating constraint as a new target vector; if one of the trial vector and the target vector is a violation constraint of 0 and the other violation constraint is greater than 0, i.e., one is a feasible solution and the other is an infeasible solution, then: 1) If the infeasible solution is an acceptable solution, it is relatively infeasibleSelecting an individual with smaller objective function as a new objective vector according to the objective functions of the row solution and the feasible solution; 2) If the infeasible solution is an unacceptable solution, then the feasible solution is selected as the new target vector.
Further, the preset stopping criterion refers to whether the maximum evolution algebra is reached or whether the convergence accuracy requirement is satisfied.
The application has the following beneficial effects:
according to the application, the self-adaptive variation differential evolution constraint optimization algorithm is used for carrying out inversion, the objective function and the constraint violation degree are reasonably balanced on the selection mechanism, the excellent infeasible solution information in the population is fully utilized, the balance of the feasible solution and the infeasible solution in the population is realized, and the searching process is guided to approach to the global optimal solution from the feasible domain and the infeasible domain simultaneously. The method can ensure the pose accuracy and obtain the shortest stroke solution, improves the flexibility of the joint and improves the operation efficiency.
The application will be described in further detail with reference to the accompanying drawings.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. In the drawings:
fig. 1 is a flowchart of a robot arm control method according to a preferred embodiment of the present application.
Detailed Description
Embodiments of the application are described in detail below with reference to the attached drawings, but the application can be implemented in a number of different ways, which are defined and covered by the claims.
Unless defined otherwise, all technical and scientific terms used hereinafter have the same meaning as commonly understood by one of ordinary skill in the art. The terms "first," "second," and the like in the description and in the claims, do not denote any order, quantity, or importance, but rather are used to facilitate distinguishing between corresponding features. Also, the terms "a" or "an" and the like do not denote a limitation of quantity, but rather denote the presence of at least one. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "both sides", "outside" and the like are used merely to indicate a relative positional relationship, and when the absolute position of the object to be described is changed, the relative positional relationship is changed accordingly.
The technical scheme adopted for solving the technical problems is as follows:
according to the mechanical arm control method based on the self-adaptive variation differential evolution constraint optimization algorithm, after the target position and the target posture of the mechanical arm end effector, namely the drill rod, are obtained, the mechanical arm is subjected to inversion by adopting the self-adaptive variation differential evolution constraint optimization algorithm by taking the shortest stroke as a target function and the pose precision requirement as constraint conditions, and the variation of each joint of the mechanical arm is obtained by solving.
In this embodiment, the step of obtaining the variation of each joint of the mechanical arm by inverting the mechanical arm by using the adaptive variation differential evolution constraint optimization algorithm, as shown in fig. 1, includes:
s1, a forward kinematics model of the mechanical arm is established as a system input, and control parameters of a self-adaptive variation differential evolution algorithm are given: mutation constant F, crossover probability CR, population size N, algebraic counter T, maximum algebraic T.
Wherein, the forward kinematics model of the mechanical arm includes: the homogeneous transformation matrix T9 of the pose of the tail end of the mechanical arm takes a base as a starting end, a No. 0 coordinate system is established at a joint part, and a No. 9 coordinate system is established from the joint part to an end effector in sequence, wherein the coordinate system is a DH coordinate system, wherein the mechanical arm with 8 degrees of freedom is taken as an example, and a DH model is as follows:
θ above 1 To theta 6 The joint angle d is the joint angle from the rotational degree of freedom 1 to the rotational degree of freedom 6 7 To d 8 Free to moveThe length of the degree. Alpha i-1 、a i-1 、d i 、θ i And the initial value is the geometrical relation between the front and back degrees of freedom of the mechanical arm in the DH method model.
S2, randomly initializing a population P= { X in a parameter space 1 ，…，X N ' individual X i ＝{x i1 ，…，x iD Where N represents population size and D represents the number of joints of the robotic arm.
S3, randomly selecting individuals from the population to perform mutation operation to generate a mutation vector V i ＝{V i1 ，…，v iD }。
S4, performing cross operation on the variation vector and the target vector (namely, individuals of the current population) to generate a test vector U i ＝{u i1 ，…，u iD }。
S5, comparing the test vector with the target vector, and selecting a better individual as a new target vector.
And S6, judging whether a preset stopping criterion is met, if yes, ending the algorithm, outputting an optimal individual as a joint variation matrix of the mechanical arm, controlling joint action of the mechanical arm, otherwise, updating the individuals in the population, namely returning to S3, and iterating.
In this embodiment, the step S3 includes:
s31, randomly generating a random number rand1 between 0 and1, comparing the rand1 with the 1-T/T, and selecting a corresponding variation mode according to a judgment result.
S32, if rand1 is less than 1-T/T, selecting variation mode DE/rand/1/bin to generate variation vector, i.eIf rand1 is more than or equal to 1-T/T, a variation mode DE/best/1/bin is selected to generate a variation vector, namelyWherein r is 1 、r 2 、r 3 Is a random integer, and represents the serial number of an individual in a population, X b Best among current generation populationIs a subject of (a).
In this embodiment, the step S4 includes:
s41, randomly generating a random number rand2 between 0 and1, comparing the rand2 with the cross probability CR, and selecting a target vector or a variation vector as a test vector according to a judgment result.
S42, if rand2 < CR, u ij ＝v ij Namely, a variation vector is selected as a test vector; if rand 2. Gtoreq.CR, u ij ＝x ij I.e. the target vector is selected as the test vector.
In this embodiment, the step S5 includes:
s51, setting a fitness function of the shortest travelWherein x is i (k)-x i (k-1) represents the variation of the pose joint angle of the kth target task of the joint i relative to the kth-1 target task; omega i Weight coefficients representing the relative importance of balancing the joints.
S52, setting constraint conditions of the pose of the expected target: a. position constraint conditions: g 1 (X)＝E p -T p Less than or equal to 0; b. attitude constraint conditions: g 2 (X)＝E o -T o And is less than or equal to 0. Wherein E is p Representing position error, T p Representing a position error threshold, E o Representing attitude error, T o Representing a posing error threshold.
S53, setting constraint violation degree G (X). Constraint violation is calculated according to the following formula:
G(X)＝ω 1 G 1 (X)+ω 2 G 2 (X)
wherein G is 1 (X)＝max{0，g 1 (X)}，G 2 (X)＝max{0，g 2 (X)}，ω 1 、ω 2 Weight coefficients respectively representing the position constraint and the attitude constraint.
S54, setting a population constraint allowable relaxation degree epsilon (t). Epsilon (t) represents the limit of individual X constraint violation G (X) when the population evolves to t generations, and is expressed as follows:
where θ represents the proportion of each evolutionary generation of population that allows a reduction in the degree of relaxation; when the population evolves to the t generation, if 0<G (X). Ltoreq.ε (t), then individual X is an acceptable solution; when the population evolves to the t-th generation, individual X is an unacceptable solution if G (X) > ε (t).
S55, evaluating the individual: calculation of test vector X i And the target vector U i And the degree of constraint violation.
If the constraint violation degree of both the trial vector and the target vector is 0, i.e., G (X i )＝G(U i ) =0, then the individual with smaller objective function is selected as the new objective vector.
If the constraint violation of both the trial vector and the target vector is greater than 0, i.e., G (X i )>0 and G (U) i ) And (3) selecting an individual with smaller constraint violation as a new target vector.
If one of the trial vector and the target vector is a constraint violation of 0 and the other constraint violation is greater than 0, i.e., one is a feasible solution and the other is an infeasible solution, then two scenarios are discussed: 1) If the infeasible solution is an acceptable solution, comparing the infeasible solution with the objective function of the feasible solution, and selecting an individual with smaller objective function as a new objective vector. 2) If the infeasible solution is an unacceptable solution, then the feasible solution is selected as the new target vector.
In this embodiment, the step of determining whether the preset stopping criterion is met in the step S6 specifically includes: judging whether the maximum evolution algebra is reached or the convergence accuracy requirement is met.
The application provides a control method of an 8-degree-of-freedom mechanical arm, and the method can be popularized and applied to redundant mechanical arms with different geometric structures. The inverse solution obtained by the method meets the precision requirements of the position and the gesture, and is the inverse solution with the minimum joint variation in infinite groups of inverse solutions.
The above description is only of the preferred embodiments of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.
Claims (5)
1. The mechanical arm control method is characterized by comprising the following steps of:
1) Establishing a forward kinematic model of the mechanical arm as system input, and giving control parameters of a self-adaptive mutation differential evolution algorithm, wherein the control parameters comprise a mutation constant F, a crossover probability CR, a population scale N, an evolution algebra counter T and a maximum evolution algebra T;
2) Randomly initializing a population in a parameter space;
3) Randomly selecting individuals from the population to perform mutation operation to generate a mutation vector, wherein the specific implementation process comprises the following steps: randomly generating a random number rand1 between 0 and1, comparing the sizes of rand1 and 1-T/T, if rand1<1-T/T, a variation pattern DE/rand/1/bin is selected to generate a variation vector, i.eIf rand1 is more than or equal to 1-T/T, a variation pattern DE/best/1/bin is selected to generate a variation vector, namely +.>Wherein r is 1 、r 2 、r 3 Is a random integer, and represents the serial number of an individual in a population, X b For the best individuals in the current generation population, +.>Three individuals randomly extracted from the contemporary population;
4) Performing cross operation on the variation vector and the target vector to generate a test vector;
5) Comparing the test vector with the target vector, and selecting a better individual as a new target vector;
6) Judging whether a preset stopping criterion is met, if yes, ending and outputting an optimal individual to serve as a joint variation matrix of the mechanical arm and control joint action of the mechanical arm, otherwise, returning to the step 3).
2. The method according to claim 1, wherein in step 2), the population is p= { X 1 ,…,X N "and individuals of the population are X i ＝{x i1 ,…,x iD I= … N, N representing population size, D representing the number of joints of the robotic arm.
3. The method according to claim 1, wherein the specific implementation procedure of step 4) includes: randomly generating a random number rand2 between 0 and1, comparing the magnitudes of rand2 and the cross probability CR, if rand2<CR is u ij ＝v ij Namely, a variation vector is selected as a test vector; if rand 2. Gtoreq.CR, u ij ＝x ij I.e. selecting the target vector as the test vector, where u ij Representing test vectors, v ij Representing the variation vector, x ij Representing the target vector.
4. The method according to claim 1, wherein the specific implementation procedure of step 5) includes:
1) Setting the fitness function of the shortest travelWherein x is i (k)-x i (k-1) represents the variation of the pose joint angle of the kth target task of the joint i relative to the kth-1 target task; omega i Weight coefficients representing the relative importance of balancing the joints;
2) Setting constraint conditions of the expected target pose: a. position constraint conditions: g 1 (X)＝E p -T p Less than or equal to 0; b. attitude constraint conditions: g 2 (X)＝E o -T o Less than or equal to 0; wherein E is p Representing position error, T p Representing a position error threshold, E o Representing attitude error, T o Representing a posing error threshold;
3) Setting constraint violation degree G (X): g (X) =p 1 G 1 (X)+p 2 G 2 (X); wherein G is 1 (X)＝max{0，g 1 (X)}，G 2 (X)＝max{0，g 2 (X)}，p 1 、p 2 Weight coefficients respectively representing the position constraint condition and the attitude constraint condition;
4) Setting the allowable relaxation degree epsilon (t) of population constraint:where θ represents the proportion of each evolutionary generation of population that allows a reduction in the degree of relaxation; when the population evolves to the t-th generation, if 0<G (X) is less than or equal to epsilon (t), and then the individual X is an acceptable solution; when the population evolves to the t th generation, if G (X)>Epsilon (t), then individual X is an unacceptable solution;
5) Calculation of test vector X i And the target vector U i Is set to the target function value and the constraint violation degree,
if the constraint violation degree of both the trial vector and the target vector is 0, i.e., G (X i )＝G(U i ) =0, then select the individual with smaller objective function as the new objective vector;
if the violation constraints of both the trial vector and the target vector are greater than 0, i.e., G (X i )>0 and G (U) i )>0, selecting an individual with smaller violating constraint degree as a new target vector;
if one of the trial vector and the target vector is a violation constraint of 0 and the other violation constraint is greater than 0, i.e., one is a feasible solution and the other is an infeasible solution, then: 1) If the infeasible solution is an acceptable solution, comparing the infeasible solution with an objective function of the feasible solution, and selecting an individual with smaller objective function as a new objective vector; 2) If the infeasible solution is an unacceptable solution, then the feasible solution is selected as the new target vector.
5. The method according to claim 1, wherein the predetermined stopping criterion is whether the maximum evolution algebra is reached or whether the convergence accuracy requirement is satisfied.
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| CN111421552B (en) * | 2020-05-09 | 2022-06-07 | 云南电网有限责任公司电力科学研究院 | Cooperative control method for double operating arms of inspection robot |
| CN112588621B (en) * | 2020-11-30 | 2022-02-08 | 山东农业大学 | Agricultural product sorting method and system based on visual servo |
| CN115169250B (en) * | 2022-09-05 | 2022-12-09 | 湖北工业大学 | Microphone array optimization method and system based on improved mixed integer differential evolution |
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