CN109344477A - A kind of 6DOF mechanical arm inverse kinematics method - Google Patents
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Abstract
The invention discloses a kind of 6DOF mechanical arm inverse kinematics methods, it is related to industrial robot field, this method is first with monte carlo method, a certain number of random samples are assigned for joint of mechanical arm space, by calculating the corresponding mechanical arm tail end position of each sample, a part of the sample for wherein meeting target position condition as genetic algorithm initial population is chosen；The other part of genetic algorithm initial population is made of random individual, then the Inverse Kinematics Solution of mechanical arm is solved by genetic algorithm.One aspect of the present invention passes through the initial population of monte carlo method optimized Genetic Algorithm, effectively improves the search speed and search success rate of genetic algorithm；On the other hand the diversity that ensure that genetic groups by the addition of random individual, improves the ability of searching optimum of genetic algorithm.
Description
Technical Field
The invention relates to the field of industrial robots, in particular to a hybrid solving multi-degree-of-freedom mechanical arm inverse kinematics solving method based on the combination of a Monte Carlo method and a genetic algorithm.
Background
The inverse kinematics solution of the mechanical arm is the basis of industrial robot application, is a prerequisite condition of mechanical arm control, and is directly related to tasks such as robot off-line programming, trajectory planning, real-time control and the like. The inverse kinematics plays an important role in the robotics, and the programming control of the robot end effector according to the space pose can be realized only by converting the space pose into a joint variable.
Inverse kinematics of a serial mechanical arm is difficult to solve, and various scholars conduct a great deal of research and study. The solution method of the inverse kinematics solution is mainly divided into an analytical method, a numerical method, a geometric method and the like. If the analytic method is simple and intuitive, the operation speed is high, but only the mechanical arm structure meeting specific geometric conditions can be solved by using the analytic method: i.e. the last 3 joint axes intersect at one point or there are 3 joint axes parallel to each other. Through analysis of a student Doty, only 5 types of 24-type 6-degree-of-freedom orthogonal mechanical arm structures have analytical solutions, and whether analytical solutions exist in other structures cannot be determined. An iterative algorithm for solving joint variables by using a jacobian matrix is a basic idea of a numerical method, and various nonlinear optimization methods are applied to numerical methods of inverse solution, but the characteristics of large operation amount and low convergence speed generally exist. In recent years, some researchers have improved the calculation speed to some extent by combining analysis with numerical calculation. The method relates to the inverse operation of a matrix and the operation of an inverse trigonometric function, and has defects in the aspects of calculation amount, limitation conditions and the like.
Another type of inverse kinematics solution is solved by using an intelligent algorithm, such as a genetic algorithm, a particle swarm algorithm, a neural network, and the like. The intelligent algorithm solves the inverse kinematics, has few limiting conditions and wide application range, but has the defects of slow convergence, local minimum, incapability of ensuring the precision of the result and the like. According to the method, a group of random initial joint angles is used as an initial population, and the result of each iteration is gradually converged to a real solution through continuous iteration updating. However, the selection dependence of the correlation algorithm on the initial population is high, and the result of the calculation is directly influenced by the quality of the initial population.
The D-H matrix (D-H method) is a universal pose calculation method proposed by two scholars of Denavit and Hartenberg in 1955. This method fixes a coordinate system on each link of the robot, and then uses a homogeneous transformation matrix of 4 × 4 to describe the spatial relationship between two adjacent links. The pose of the end effector relative to the base coordinate system can be finally deduced through sequential transformation, so that a kinematic equation of the robot is established. For 6 fromIn the case of a robotic arm, the D-H matrix may be identified as follows, where A isiIs the transformation matrix of the ith link, R is the rotation matrix of 3 x 3, P is the position matrix of 1 x 3, and I is usually the transformation matrix T of a mechanical arm with 1, 6 degrees of freedom6Comprises the following steps:
disclosure of Invention
The invention aims to provide a 6-degree-of-freedom mechanical arm inverse kinematics solving method, so that the defects of low solving speed and low precision of the existing kinematics inverse solution are overcome.
In order to achieve the aim, the invention provides a 6-degree-of-freedom mechanical arm inverse kinematics solving method, which comprises the following steps of:
s1, establishing a D-H matrix of the mechanical arm according to the parameters of the mechanical arm;
s2, determining the threshold value of S3, namely the tail end position and the target position P of the mechanical arm according to the structure of the mechanical arm and the parameters of the mechanical armEThe maximum distance of (d);
s3, giving random angles to all joints of the mechanical arm by adopting a Monte Carlo method to generate random samples, calculating the tail end position of the mechanical arm corresponding to each random sample through the D-H matrix, and reserving the tail end position of the mechanical arm meeting the conditions as a sample;
and S4, taking the sample reserved in S3 as a seed group, adding new random populations to form an initial population of the genetic algorithm, and solving the inverse kinematics by using the genetic algorithm.
Further, the parameters of the mechanical arm include: the length, the torsion angle, the offset and the joint angle of each mechanical arm.
Further, the S3 specifically includes the following steps:
s31, giving random angles to all joints of the mechanical arm to generate random samples;
s32, substituting the random samples into the D-H matrix of S1, and calculating the position of the tail end of the corresponding mechanical arm
S33, judging reserved PMWhile satisfying the following conditions as shown in formula (1);
in the formula (1), thx，thx，thxThe identification of the threshold value in the x, y and z directions;
s34, if the random sample corresponds to the end position PMIf the condition of S33 is met, the corresponding sample is stored to a population array D1;
s35, circulating the operations of S32-S34 until the calculation of all random samples is completed;
and S36, finishing the circulation to obtain a population array D1.
Further, the S4 specifically includes the following steps:
s40, adding a new random sample group D2 of joint angles on the basis of the population group D1 to form an initial population D of the genetic algorithm;
s41, encoding the initial population D;
s42, setting parameters of a genetic algorithm;
s43, calculating a fitness function value of the mechanical arm terminal pose matrix corresponding to each individual in the population;
s44, carrying out genetic selection on individuals in the S41 population according to the fitness function value of S43;
s45, judging whether the genetically selected individuals obtained in S44 meet the crossing probability, and if the genetically selected individuals meet the crossing probability, performing genetic crossing and storing the genetically selected individuals into a new population; if the genetically selected individual does not meet the crossover probability, proceed to S46;
s46, judging whether the genetically selected individuals which do not meet the crossover probability meet the variation probability, if so, performing variation crossover and storing the individuals into a new population, otherwise, removing the individuals;
s47, adding new random individuals on the basis of the new population obtained through the operations of S45 and S46, and enabling the new population to keep the scale of the original population;
s48, judging whether the population obtained in S47 reaches a completion condition, wherein the completion condition comprises a fitness function value Fit of the best individual in the population<The number of epsilon or S43-S47 cycles is within 100-300 times, the achievement of any condition is regarded as the achievement of the completion condition, and the value range of epsilon is 1 x 10-7-2*10-7(ii) a If the completion condition is not met, replacing the population of the previous iteration with the new population obtained in the step S47, and repeating the operations of the step S43-the step S47; if the completion condition is reached, exiting;
and S49, outputting the result, namely the inverse kinematics solution.
Further, the encoding method of S41 is real number encoding.
Further, the selection in S44 adopts a competition selection method, and the individuals with the excessive fitness function value are discarded.
Further, the S45 intersection is a multi-point intersection.
Further, in the step S40, the number of individuals in the population D is set to be T, and the number of individuals in the random population D2 is set to be T2The calculation formula of (2) is as follows:
in the formula (2), T1The number of individuals in population array D1 obtained at S36.
Further, the fitness function in S44 is constructed as shown in formula (3):
Fit＝|ΔP|+|ΔO| (3)
in the formula (3), | Δ P | is a position offset amount, and | Δ O | is an attitude offset amount;
in the formula (4), the reaction mixture is,the end position of the mechanical arm corresponding to the genetic individual, x, y, z coordinates, P, of the end position of the robotic arm corresponding to the genetic individualEIs the target position of the end of the mechanical arm;
in the formula (5), the reaction mixture is,a jth column and an ith row of a manipulator end attitude matrix corresponding to the genetic individual,is the jth column and ith row of the robot arm end target body attitude matrix.
Compared with the prior art, the invention has the following beneficial effects:
1. the 6-degree-of-freedom mechanical arm inverse kinematics solving method avoids the inverse of a calculation matrix and an inverse trigonometric function, has small operand and has no limitation condition.
2. According to the 6-degree-of-freedom mechanical arm inverse kinematics solving method provided by the invention, the initial sample of the genetic algorithm is optimized by the Monte Carlo method, the searching speed and the searching success rate of the genetic algorithm can be effectively improved, meanwhile, part of random samples are reserved to keep the diversity of the population, and the global searching capability of the algorithm is ensured.
3. The 6-degree-of-freedom mechanical arm inverse kinematics solving method provided by the invention is simple, the error is less than 1%, and the operability is strong.
Drawings
In order to more clearly illustrate the technical solution of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only one embodiment of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a schematic structural diagram of UR5 robot;
FIG. 2 is an encoding format of a genetic algorithm;
fig. 3 is a flowchart of S3;
fig. 4 is a flowchart of S4;
FIG. 5 is a diagram illustrating the result of the inverse kinematics solution of the present invention;
fig. 6 is a flowchart of a 6-degree-of-freedom robot arm inverse kinematics solution method according to the present invention.
Detailed Description
The technical solutions in the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the present invention describes in detail the 6-degree-of-freedom robot arm inverse kinematics solution method of the present invention, taking UR5 robot (6-degree-of-freedom robot arm) as an example.
The 6 degree-of-freedom mechanical arm requires to be in an attitude OETo position PE. Wherein,in order to reach the position of the mobile phone,x, y, z coordinates of the target position at the tail end of the mechanical arm; attitude OEThe rotation amount of the mechanical arm is calculated,the rotation angle of the end of the mechanical arm to the coordinate axis of the base.
The main parameters of each joint of the UR5 mechanical arm are as follows: a isiFor the length of the ith link, αiIs the torsion angle of the ith connecting rod, diIs the offset of the connecting rod, thetaiThe joint angle corresponding to the ith connecting rod.
Table 1 UR5 main arm parameters
| i | ai(m) | αi(°) | di(m) | θi |
| 1 | 0 | 90 | 0.08916 | (-360,360) |
| 2 | -0.425 | 0 | 0 | (-360,360) |
| 3 | -0.39225 | 0 | 0 | (-360,360) |
| 4 | 0 | -90 | 0.10915 | (-360,360) |
| 5 | 0 | -90 | 0.09456 | (-360,360) |
| 6 | 0 | 0 | 0.0823 | (-360,360) |
As shown in fig. 1, the 6-degree-of-freedom mechanical arm inverse kinematics solution method provided by the invention comprises the following steps:
and S1, establishing a D-H matrix of the mechanical arm according to the parameters of the mechanical arm.
S2, determining the threshold value of S3 according to the structure of the mechanical arm and the parameters of the mechanical arm, wherein the threshold value is the tail end and the target position P of the mechanical armEThe parameters of the robotic arm include: length, twist angle, offset and joint angle of each mechanical arm. In this embodiment, the threshold th in three directions x, y and zx，thy，thzAll take 0.1 cm.
S3, random angles are given to all joints of the mechanical arm by adopting a Monte Carlo method to generate random samples, the tail end position of the mechanical arm corresponding to each random sample is calculated through a D-H matrix, and only the tail end position of the mechanical arm meeting the conditions is reserved as a sample, namely a population group D1. In this example, the number of samples is 20 ten thousand. According to the characteristics of the mechanical arm of the UR5 robot, the rotation angle value range of all 6 joints is [0,360 ]. The sample data form is as follows: [ theta ] of1,θ2,θ3,θ4,θ5,θ6]. As shown in fig. 3, S3 specifically includes the following steps:
s31, giving random angles to all joints of the mechanical arm, and generating a random sample of the joint angles;
s32, substituting the random sample of the joint angle into the D-H matrix of S1, and calculating the tail end position corresponding to the random sample of the joint angle
S33, judging reserved PMWhile satisfying the following conditions as shown in formula (1);
in the formula (1), thx，thy，thzThe identification of the threshold value in the x, y and z directions;
s34, determining the end position P corresponding to the random sample of the joint angleMIf the condition of S33 is met, the corresponding sample is stored in a population array D1;
s35, circulating the operations of S32-S34 until the calculation of all random samples is completed;
and S36, finishing the circulation, and obtaining a population array D1 meeting the condition of S33.
S4, based on the population array D1 retained in S36, adding a new joint angle population D2, combining into an initial population D of the genetic algorithm, and obtaining an inverse solution of kinematics by using the genetic algorithm, as shown in fig. 4, S4 specifically includes the following steps:
s40, adding a new random sample D2 of joint angles on the basis of the population array D1 to form an initial population D of the genetic algorithm; setting the number of individuals in the population D as T, and the number T of individuals in the population D22Determined by equation (2):
in the formula (2), T1The number of individuals in population array D1 obtained at S36;
s41, encoding the initial population D in a real number encoding mode, wherein J is shown in figure 21-J66 joints corresponding to the robot arm, J11、J12And J13The values of the hundred, ten and ones positions of the angle of the joint 1 respectively;
s42, setting parameters of a genetic algorithm, wherein in the embodiment, the cross probability is 0.8, and the mutation probability is 0.4;
and S43, calculating a fitness function value of the mechanical arm terminal pose matrix corresponding to each individual in the population. The pose matrix of the tail end of the mechanical arm is calculated by D-H, and the structure of the fitness function is shown as a formula (3):
Fit＝|ΔP|+|ΔO| (3)
in the formula (3), | Δ P | is a position offset amount, and | Δ O | is an attitude offset amount;
in the formula (4), the reaction mixture is,the end position of the mechanical arm corresponding to the genetic individual, x, y, z coordinates, P, of the end position of the robotic arm corresponding to the genetic individualEIs the target position of the end of the mechanical arm;
in the formula (5), the reaction mixture is,a jth column and an ith row of a manipulator end attitude matrix corresponding to the genetic individual,the ith row is the jth column of the attitude matrix of the target body at the tail end of the mechanical arm;
s44, carrying out genetic selection on individuals in the S41 population according to the fitness function value of S43, wherein a competition selection method is selected in the embodiment, and individuals with overlarge fitness function values are discarded;
s45, judging whether the genetically selected individuals obtained in S44 meet the crossing probability, if so, performing genetic crossing and storing the genetically selected individuals in a new population; if the genetically selected individual does not meet the crossover probability, proceed to S46; the embodiment adopts multipoint intersection;
s46, judging whether the genetically selected individuals which do not meet the crossover probability meet the variation probability, if so, performing variation crossover and storing the individuals into a new population, otherwise, removing the individuals;
s47, adding new random individuals on the basis of the new population obtained through the operations of S45 and S46, and enabling the new population to keep the scale of the original population;
s48, judging whether the population individuals obtained in the S47 reach the completion conditions, wherein the completion conditions comprise fitness function values Fit<The number of epsilon or S43-S47 cycles is within 100-300 times, the achievement of any condition is regarded as the achievement of the completion condition, and the value range of epsilon is 1 x 10-7-2*10-7(ii) a If the completion condition is not met, replacing the population of the previous iteration with a new population, and repeating the operations of S43-S47; if the completion condition is reached, exiting; the completion condition of this embodiment is the fitness function value Fit<E, e is 0.0000002, and the iteration number is 300;
s49, outputting a result, that is, a kinematic inverse solution, as shown in fig. 5, where an abscissa is an iteration number, and an ordinate is a fitness function value, it can be found from fig. 5 that the kinematic inverse solution of the mechanical arm can be obtained through about 40 iterations in this embodiment, and an error of the inverse solution is approximately equal to zero, that is, an error of a numerical value after iteration is less than 1%, so that the operability of the present invention is strong.
In summary, the 6-degree-of-freedom mechanical arm inverse kinematics solving method provided by the invention has the advantages that the initial sample of the genetic algorithm is generated by adopting the Monte Carlo method, the convergence rate of the genetic algorithm is improved by optimizing the initial sample of the genetic algorithm, the diversity of the sample is kept by the random sample, and the global searching capability of the genetic algorithm is ensured, so that the inverse kinematics solving method provided by the invention has the advantages of high speed and high precision, and is suitable for the situations of off-line and on-line track planning.
The above disclosure is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of changes or modifications within the technical scope of the present invention, and shall be covered by the scope of the present invention.
Claims (9)
1. A6-degree-of-freedom mechanical arm inverse kinematics solving method is characterized by comprising the following steps: the method comprises the following steps:
s1, establishing a D-H matrix of the mechanical arm according to the parameters of the mechanical arm;
s2, determining the threshold value of S3, namely the tail end position and the target position P of the mechanical arm according to the structure of the mechanical arm and the parameters of the mechanical armEThe maximum distance of (d);
s3, giving random angles to all joints of the mechanical arm by adopting a Monte Carlo method to generate random samples, calculating the tail end position of the mechanical arm corresponding to each random sample through the D-H matrix, and reserving the tail end position of the mechanical arm meeting the conditions as a sample;
and S4, taking the sample reserved in S3 as a seed group, adding new random populations to form an initial population of the genetic algorithm, and solving the inverse kinematics by using the genetic algorithm.
2. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 1, wherein: the parameters of the mechanical arm comprise: the length, the torsion angle, the offset and the joint angle of each mechanical arm.
3. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 1, wherein: the S3 specifically includes the following steps:
s31, giving random angles to all joints of the mechanical arm to generate random samples;
s32, substituting the random samples into the D-H matrix of S1, and calculating the position of the tail end of the corresponding mechanical arm
S33, judging reserved PMWhile satisfying the following conditions as shown in formula (1);
in the formula (1), thx，thx，thxThe identification of the threshold value in the x, y and z directions;
s34, if the random sample corresponds to the end position PMIf the condition of S33 is met, the corresponding sample is stored to a population array D1;
s35, circulating the operations of S32-S34 until the calculation of all random samples is completed;
and S36, finishing the circulation to obtain a population array D1.
4. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 1, wherein: the S4 specifically includes the following steps:
s40, adding a new random sample group D2 of joint angles on the basis of the population group D1 to form an initial population D of the genetic algorithm;
s41, encoding the initial population D;
s42, setting parameters of a genetic algorithm;
s43, calculating a fitness function value of the mechanical arm terminal pose matrix corresponding to each individual in the population;
s44, carrying out genetic selection on individuals in the S41 population according to the fitness function value of S43;
s45, judging whether the genetically selected individuals obtained in S44 meet the crossing probability, and if the genetically selected individuals meet the crossing probability, performing genetic crossing and storing the genetically selected individuals into a new population; if the genetically selected individual does not meet the crossover probability, proceed to S46;
s46, judging whether the genetically selected individuals which do not meet the crossover probability meet the variation probability, if so, performing variation crossover and storing the individuals into a new population, otherwise, removing the individuals;
s47, adding new random individuals on the basis of the new population obtained through the operations of S45 and S46, and enabling the new population to keep the scale of the original population;
s48, judging whether the population obtained in S47 reaches a completion condition, wherein the completion condition comprises a fitness function value Fit of the best individual in the population<The number of epsilon or S43-S47 cycles is within 100-300 times, the achievement of any condition is regarded as the achievement of the completion condition, and the value range of epsilon is 1 x 10-7-2*10-7(ii) a If the completion condition is not met, replacing the population of the previous iteration with the new population obtained in the step S47, and repeating the operations of the step S43-the step S47; if the completion condition is reached, exiting;
and S49, outputting the result, namely the inverse kinematics solution.
5. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 4, wherein: the encoding mode of S41 is real number encoding.
6. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 4, wherein: and selecting in the S44 by adopting a competition selection method, and discarding individuals with overlarge fitness function values.
7. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 4, wherein: the S45 intersection is a multipoint intersection.
8. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 4, wherein: in S40, the number of individuals in the population D is set to be T, and the number of individuals in the random population D2 is set to be T2The calculation formula of (2) is as follows:
in the formula (2), T1The number of individuals in population array D1 obtained at S36.
9. The 6-degree-of-freedom mechanical arm inverse kinematics solution method according to claim 4, wherein: the fitness function in S44 is constructed as shown in equation (3):
Fit＝|ΔP|+|△O| (3)
in the formula (3), | Δ P | is a position offset amount, and | Δ O | is an attitude offset amount;
in the formula (4), the reaction mixture is,the end position of the mechanical arm corresponding to the genetic individual,
x, y, z coordinates, P, of the end position of the robotic arm corresponding to the genetic individualEIs the target position of the end of the mechanical arm;
in the formula (5), the reaction mixture is,a jth column and an ith row of a manipulator end attitude matrix corresponding to the genetic individual,is the jth column and ith row of the robot arm end target body attitude matrix.
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