CN115741712A - Laser sensor based joint robot kinematic parameter identification method - Google Patents
Laser sensor based joint robot kinematic parameter identification method Download PDFInfo
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Abstract
The invention aims to solve the problem that the existing method for identifying the kinematic parameters of the joint robot adopts a laser tracker to measure the differential motion of a target ball arranged at the tail end of the robot so as to identify the kinematic parameters of the robot; or a special calibration block is adopted to identify the kinematic parameters, so that the problems of complicated calibration steps and high price of calibration equipment exist, and the method for identifying the kinematic parameters of the joint robot based on the laser sensor is provided. According to the invention, the laser sensor is arranged at the tail end of the joint robot, a weight is suspended in the working space of the robot, and the identification of the kinematic parameters of the joint robot is realized by using a parameter identification method of a genetic algorithm based on the laser sensor, so that the calibration process is simpler, the absolute positioning precision of the robot is improved, the calibration time is shortened, and the calibration efficiency is improved.
Description
Technical Field
The invention belongs to the technical field of industrial robots, and particularly relates to a laser sensor-based joint robot kinematic parameter identification method.
Background
Along with the continuous expansion of the application range and the task complexity of the industrial robot in industrial production, the requirements on the position and posture precision of the industrial robot are higher and higher. At present, the industrial robot has high repeated positioning precision which reaches 0.1mm magnitude. However, the absolute positioning accuracy is low, in the order of 1cm, which severely limits the application range of industrial robots. The positioning accuracy of an industrial robot is low for a number of reasons, the most important of which is the parameter deviation of the geometry in the kinematic model. Calibration techniques are effective methods to compensate for these parameter deviations and are therefore a focus of research. The calibration is to identify the accurate parameters of the robot model by applying an advanced measurement means and a model-based parameter identification method, thereby improving the positioning precision of the robot.
For the joint robot, errors in the manufacturing and installation process and long-time abrasion can cause the actual kinematic parameters of the joint robot to be inconsistent with theoretical values, so that the absolute positioning accuracy of the robot is poor. At present, aiming at a kinematic parameter identification method of a joint robot, the kinematic parameter of the robot is mostly identified by adopting a laser tracker to measure the differential motion of a target ball arranged at the tail end of the robot; or a special calibration block is adopted to identify the kinematic parameters, the calibration steps are complicated, and the price of calibration equipment is high.
For example, chinese patent CN114800526a discloses an industrial robot calibration method based on laser tracker system establishment through point-line-surface, establishes a robot error model, and uses mathematical theory to deduce an error transfer formula, and gives preparation work before data acquisition, and based on the laser tracker point-line-surface coordinate system establishment method and related cautions, in the parameter identification process, gives a derivation process of singular value decomposition least square method, gives an execution flow of program algorithm, and meanwhile, obtains DH compensation parameters through a forward test set, verifies the validity of DH compensation parameters through a reverse verification set, and realizes improvement of absolute positioning accuracy of the industrial robot. However, the laser tracker is expensive, the installation steps are complicated, the calibration precision is influenced by the reference coordinate system, and once the reference coordinate system is incorrectly established, the calibration precision can be seriously influenced.
For example, chinese patent CN105066808a discloses a simple calibration device for kinematic parameters of an industrial robot and a calibration method thereof, the calibration device includes a calibration block and a calibration rod, the calibration block has two mutually perpendicular calibration planes, the calibration rod is fixedly installed at the end of a robot body in an offset manner, and a dial indicator is installed at the end of the calibration rod along an axis. The calibration method comprises the steps that a small ball of a measuring head of the dial gauge is in contact with a calibration plane at more than three different positions, and the normal direction of the calibration plane is calculated; after two calibration plane normal directions are obtained, according to the two normal vertical constraints, a constraint equation containing calibration parameters can be listed, the position of a calibration block is changed, different contact points are selected, a series of constraint equations can be obtained, and a least square method is used for obtaining a calibration result of the kinematic parameters of the industrial robot. However, the method relies heavily on the premise that the two calibration surfaces on the calibration block are planes and are strictly perpendicular, and when the condition cannot be met, the calibration effect is difficult to improve.
For example, chinese patent CN109304730a discloses a robot kinematic parameter calibration method based on a laser range finder, the calibration device includes a laser range finder and a calibration plate, the surface of the calibration plate is a plane, the calibration plate is fixed in the robot working space, and the laser range finder is installed at the end of the robot. The calibration method is to control the robot to move, so that the calibration plate is positioned in the measuring range of the laser range finder, and the joint angle value of each joint and the reading value of the laser range finder are collected once when the tail end is positioned at a different position. And after obtaining a plurality of groups of measurement data, obtaining a plurality of points according to the obtained mapping relation and the plurality of groups of measurement data, and determining the kinematic parameter error of the robot according to the obtained plurality of points and the coplanarity condition. But the method has higher requirements on the planeness of the surface of the calibration plate, and is often difficult to meet in practice; meanwhile, the precision requirement of the method on the transformation matrix from the terminal joint coordinate system to the laser range finder coordinate system is harsh, and in engineering practice, when a tool coordinate system is calibrated by adopting a multipoint method, the precision often cannot meet the requirement.
Disclosure of Invention
The invention aims to solve the problem that the existing method for identifying the kinematic parameters of the joint robot adopts a laser tracker to measure the differential motion of a target ball arranged at the tail end of the robot so as to identify the kinematic parameters of the robot; or a special calibration block is adopted to identify the kinematic parameters, so that the problems of complicated calibration steps and high price of calibration equipment exist, and the method for identifying the kinematic parameters of the joint robot based on the laser sensor is provided.
In order to achieve the purpose, the invention adopts the technical scheme that:
a joint robot kinematic parameter identification method based on a laser sensor is characterized by comprising the following steps:
The auxiliary device comprises a laser sensor, a bracket and a weight hung on the bracket through a rope; the laser sensor is fixedly arranged on a flange at the tail end of the joint robot, and the heavy object is positioned in the working space of the joint robot;
2.1, moving the tail end of the joint robot through a manual operator to enable the tail end of the joint robot to approach a rope and ensure that the tail end of the joint robot is in a scanning range of a laser sensor;
2.2, scanning and sampling for N times at different positions of the rope, reading and recording coordinate values p of sampling points scanned to the rope by the laser sensor under the coordinate system of the laser sensor Si And the values of the respective joint angles when the robot is at that position, i =1, …, N;
and 5, utilizing the angle values of all joints obtained in the step 2, nominal kinematic parameters of all joints and kinematic error parameters of all joints to obtain coordinate values p of N sampling points in a laser sensor coordinate system Si Conversion to coordinate values p in the base coordinate system Bi ；
Step 6, sorting the N sampling points in ascending order according to the coordinate values of the X axis under the base coordinate system to obtain a point set under the base coordinate system;
step 7, setting initial values of kinematic parameter errors delta alpha, delta d and delta a of each joint according to the point set under the base coordinate system obtained in the step 6, and calculating to obtain a total error in a kinematic parameter error range;
and 8, taking the minimization of the total error E as an optimization objective function of the optimization algorithm, carrying out the optimization algorithm by using the set calculation times, and taking a vector group corresponding to the minimum value in the calculated objective function values or a vector group corresponding to the objective function value smaller than a set threshold value Q as final error values of all the joint kinematics parameters.
Further, in step 5, the coordinate value p of the sampling point in the laser sensor coordinate system Si Conversion into coordinate values p in the base coordinate system Bi The method specifically comprises the following steps:
in the formula, p Bi The coordinate value of the ith sampling point under the base system is represented; p is a radical of Si The coordinate value of the ith sampling point in the coordinate system of the laser sensor is represented; i is more than or equal to 1 and less than or equal to N;
0 A 1 a transformation matrix representing the base coordinate system to the 1 st coordinate system;
j A j+1 representing a transformation matrix from a j coordinate system to a j +1 coordinate system, wherein each element in the m-1 matrix with j being more than or equal to 0 and less than or equal to m is a function of kinematic parameters of connecting rod distortion alpha, connecting rod offset d, connecting rod length a and joint angle theta; the concrete form is as follows:
wherein, c θ j+1 Represents cos θ j+1 ，sθ j+1 Denotes sin θ j+1 ；
d 0 A 1 Is shown becauseDifferential motion from a base coordinate system to a 1 st coordinate system caused by kinematic parameter errors;
d j A j+1 representing differential motion from a j coordinate system to a j +1 coordinate system caused by kinematic parameter errors, wherein each element in the matrix is a function of the kinematic parameter errors, namely a connecting rod torsion error delta alpha, a connecting rod offset error delta d, a connecting rod length error delta a, and the kinematic parameters, namely a connecting rod torsion alpha, a connecting rod offset d, a connecting rod length a and a joint angle theta; the concrete form is as follows:
m T S a transformation matrix representing the end joint coordinate system to the laser sensor coordinate system.
Further, in step 7, the total error E in the error range of the kinematic parameters is:
in the formula, x i And y i Respectively representing the X-axis coordinate value and the Y-axis coordinate value of the sorted ith sampling point in the base coordinate system; x is the number of N-i+1 And y N-i+1 And the X-axis coordinate value and the Y-axis coordinate value of the N-i +1 th sampling point in the base coordinate system are shown.
Further, in step 7, the kinematic parameter error range is: -0.5. Ltoreq. DELTA.alpha. Ltoreq.0.5; Δ d is more than or equal to 0.5 and less than or equal to 0.5; -0.5. Ltoreq. DELTA.a. Ltoreq.0.5.
Further, in step 7, the initial values of the joint kinematic parameter errors, i.e., the link twist error Δ α, the link offset error Δ d, and the link length error Δ a, are set to 0.
Furthermore, in step 2, the number N of the sampling points is an even number, and grouping calculation is facilitated when calculating the total error E within the kinematic parameter error range.
Further, in step 8, the threshold Q = E 0 /200；
Wherein E is 0 And calculating the total error in the kinematic parameter error range when the kinematic parameter errors of all joints, namely the connecting rod torsion error delta alpha, the connecting rod offset error delta d and the connecting rod length error delta a, are all 0.
Further, in step 3, the modeling method of the kinematic model is an improved DH method, a 5 parameter MDH method, a CPC model, an S model, or a POE model.
Further, in step 8, the optimization algorithm is a genetic algorithm.
Further, in step 1, the larger the mass of the weight is, the more accurate the weight is, the more uniform the rope material for suspending the weight is, and the larger the rigidity is, the better the rigidity is.
Compared with the prior art, the invention has the following beneficial technical effects:
according to the method for identifying the kinematic parameters of the joint robot based on the laser sensor, the laser sensor is mounted at the tail end of the joint robot without introducing extra measuring equipment or a special calibration block, a weight is suspended in the working space of the robot, and then the method for identifying the kinematic parameters of the joint robot based on the laser sensor by using a genetic algorithm is adopted, so that the identification of the kinematic parameters of the joint robot is realized, the calibration process is simple, the absolute positioning precision of the robot is improved, the calibration time is shortened, and the calibration efficiency is improved.
Drawings
FIG. 1 is a flowchart illustrating an embodiment of a method for identifying kinematic parameters of a joint robot based on a laser sensor according to the present invention;
FIG. 2 is a schematic structural diagram of a joint robot in the practice of the present invention;
FIG. 3 is a schematic diagram of a motion coordinate system of a joint robot modeled by using improved D-H kinematics in the implementation of the present invention;
reference numerals:
1-laser sensor, 2-bracket, 3-rope and 4-weight.
Detailed Description
To make the objects, advantages and features of the present invention more apparent, a method for identifying kinematic parameters of a laser sensor-based joint robot according to the present invention is described in detail with reference to the accompanying drawings and specific embodiments. It should be understood by those skilled in the art that these embodiments are only for explaining the technical principle of the present invention and are not intended to limit the scope of the present invention.
A joint robot kinematic parameter identification method based on a laser sensor comprises the following steps:
As shown in fig. 1, the auxiliary device comprises a laser sensor 1, a bracket 2 and a weight 4 suspended from the bracket by a rope 3. The laser sensor is fixedly installed on a flange at the tail end of the joint robot by using the adapter, and the heavy object is positioned in the working space of the joint robot. The larger the mass of the weight is, the more accurate the weight is, the more uniform the rope material for hanging the weight is, and the larger the rigidity is, the better the rope material is.
2.1, moving the tail end of the joint robot through a manual operator to enable the tail end of the joint robot to approach to a rope and ensure that the tail end of the joint robot is in the scanning range of the laser sensor.
2.2, repeating N times of scanning and sampling at different positions of the rope, reading and recording the coordinate value p of the sampling point scanned to the rope by the laser sensor under the coordinate system of the laser sensor Si And the angle value of each joint when the robot is at that position; the number of sampling points N is an even number, i =1, …, N.
The modeling methods of the robot kinematics model commonly used include an improved DH method, a 5-parameter MDH method, a CPC model, an S model, a POE model and the like, the classic DH method is simple in principle and easy to understand, the classic DH method is most widely applied in the field of industrial robots compared with other modeling methods, and the improved DH model of the joint robot is established by the improved DH method in the implementation.
The improved DH model establishes a space coordinate system of each connecting rod of the robot by establishing a joint coordinate system on each connecting rod joint of the industrial robot and representing each connecting rod by four parameters. For the 6-joint robot shown in fig. 1, a kinematic modeling is performed by using a modified D-H method, and a motion coordinate system thereof is shown in fig. 2.
The method comprises the steps of defining 6 joints which are sequentially connected from bottom to top to be a first joint, a second joint, an.
For each joint, there are 4 kinematic parameters, link twist α, link offset d, link length a, joint angle θ, respectively. Assuming that besides the joint angle theta, other kinematic parameters have errors which can be respectively expressed as delta alpha, delta d and delta a, the three variables are called kinematic parameter errors, and assuming that the positioning error of the tip is caused by the kinematic parameter error of each joint.
Whatever the way the laser sensor is mounted at the end of the robot, the cable remains parallel to the Z-axis in the base coordinate system, and therefore, theoretically, whatever the transformation matrix from the end joint coordinate system to the laser sensor coordinate system 6 T S The X value and the Y value of each sampling point on the rope in the coordinate value under the base system are equal, so that when the method in the patent is used, excessive pursuit of a conversion matrix is not needed 6 T S High accuracy of the method.
Step 5, obtaining the angle value of each joint, the nominal kinematic parameter of each joint and the kinematic error parameter of each joint by utilizing the step 1, and enabling the coordinate values p of the N sampling points to be under the coordinate system of the laser sensor Si Conversion into coordinate values p in the base coordinate system Bi ；
The nominal kinematic parameters of each connecting shaft can be obtained from the arm length parameters and the coordinate system conversion relation in the modeling process. Nominal arm length parameters for the robot are available from the manufacturer, and nominal link twist and nominal link offset are obtained during kinematic modeling of the robot. The kinematic parameter error is very small compared with the nominal kinematic parameter, and the actual transformation matrix can be regarded as the nominal transformation matrix plus the differential transformation caused by the kinematic parameter error, so that the transformation of a certain point in the laser sensor coordinate system to the base coordinate system can be expressed as:
p Bi ＝( 0 A 1 +d 0 A 1 )·( 1 A 2 +d 1 A 2 )·...·( j A j+1 +d j A j+1 )·...( 5 A 6 +d 5 A 6 )· 6 T S ·p Si
in the formula, p Bi The coordinate value of the ith sampling point under the base standard is represented; p is a radical of Si A coordinate value representing the ith point in a laser sensor coordinate system; i is more than or equal to 1 and less than or equal to N;
0 A 1 a transformation matrix representing the base coordinate system to the 1 st coordinate system;
j A j+1 representing a transformation matrix from a jth coordinate system to a j +1 th coordinate system, wherein j is more than or equal to 0 and less than or equal to 5, and each element in the matrix is a function of the kinematic parameters alpha, d, a and theta; the concrete form is as follows:
in the formula, c θ j+1 Represents cos θ j+1 ，sθ j+1 Denotes sin θ j+1 ；
d 0 A 1 Representing differential motion from a base coordinate system to a 1 st coordinate system due to kinematic parameter errors;
d j A j+1 representing the differential motion from the j-th coordinate system to the j + 1-th coordinate system due to kinematic parameter errors, each element in the matrix being a function of the kinematic parameter errors Δ α, Δ d, Δ a;
the concrete form is as follows:
6 T S a transformation matrix representing the end joint coordinate system to the laser sensor coordinate system.
Step 6, sorting the N sampling points in ascending order according to the coordinate values of the X axis under the base coordinate system to obtain a point set under the base coordinate system;
in fact, due to the error between the nominal kinematic parameters and the actual kinematic parameters, the X coordinate values of the n points are not equal, and the Y coordinate values are not equal.
And 7, setting initial values of kinematic parameter errors delta alpha, delta d and delta a of each joint according to the point set under the base coordinate system obtained in the step 6, and calculating to obtain a total error E in a kinematic parameter error range. The total error when the kinematic error parameters of the joints are all 0 is recorded as E 0 ；
A method for converting a certain point under a laser sensor coordinate system to a base coordinate system when a group of kinematic parameter errors are given is provided, and a total error E can be obtained according to a point set under the base coordinate system:
in the formula, x i And y i Respectively representing the X-axis coordinate value and the Y-axis coordinate value of the sorted ith sampling point in the base coordinate system; x is the number of N-i+1 And y N-i+1 And representing the X-axis coordinate value and the Y-axis coordinate value under the base coordinate system of the N-i +1 th sampling point after sorting. Two farther sampling point data are selected to calculate errors, and results obtained by multiple times of optimization algorithm calculation are more accurate.
And 8, taking the minimization of the total error E as an optimization target of the optimization algorithm, performing the optimization algorithm by using the set calculation times, and taking a vector group corresponding to the minimum value in the calculated objective function values or a vector group corresponding to the objective function value smaller than a set threshold value Q as final error values of each joint kinematic parameter.
In this embodiment, a genetic algorithm, specifically a genetic algorithm tool box in a MATLAB optimization tool box, is selected to solve for each joint kinematic parameter error. When the genetic algorithm is used for solving the kinematic parameter errors of all joints, nonlinear constraint, linear equality constraint and linear inequality constraint do not exist.
The total error E is taken as the objective function of the genetic algorithm, i.e. the fitness function in the MATLAB genetic algorithm toolbox. The kinematic parameter errors delta alpha, delta d and delta a of each joint are variables to be solved, and the initial values of the kinematic parameter errors delta alpha, delta d and delta a are 0; because the kinematic parameter error is small and is generally within 0.5, the upper limit and the lower limit of each kinematic parameter error are respectively set to be 0.5 and-0.5.
Taking error minimization as an optimization target of the optimization algorithm, calculating by using a multiple genetic optimization algorithm to obtain the minimum value of the total error E in the error range of the kinematic parameters, or after calculation, enabling the value of the fitness function E to be smaller than a set threshold Q = E 0 At/200, the respective joint kinematic parameter errors Δ α, Δ d, Δ a are used as final respective joint kinematic parameter error values.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, and not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the present invention.
Claims (9)
1. A joint robot kinematic parameter identification method based on a laser sensor is characterized by comprising the following steps:
step 1, building an auxiliary device
The auxiliary device comprises a laser sensor, a bracket and a weight hung on the bracket through a rope; the laser sensor is fixedly arranged on a flange at the tail end of the joint robot, and the heavy object is positioned in the working space of the joint robot;
step 2, obtaining coordinate information of sampling points
2.1, moving the tail end of the joint robot through a manual operator to enable the tail end of the joint robot to approach a rope and ensure that the tail end of the joint robot is in a scanning range of a laser sensor;
2.2, scanning and sampling for N times at different positions of the rope, reading and recording coordinate values p of sampling points scanned to the rope by the laser sensor under the coordinate system of the laser sensor Si And the values of the respective joint angles when the robot is at that position, i =1, …, N;
step 3, establishing a kinematics model of the joint robot;
step 4, calibrating the laser sensor by using a multipoint method, and obtaining a conversion matrix from the tail end joint coordinate system to the laser sensor coordinate system m T S M is the number of joints of the joint robot;
and 5, utilizing the angle values of all joints obtained in the step 2, nominal kinematic parameters of all joints and kinematic error parameters of all joints to obtain coordinate values p of N sampling points in a laser sensor coordinate system Si Conversion into coordinate values p in the base coordinate system Bi ；
Step 6, sorting the N sampling points in ascending order according to the coordinate values of the X axis under the base coordinate system to obtain a point set under the base coordinate system;
step 7, setting initial values of kinematic parameter errors delta alpha, delta d and delta a of each joint according to the point set under the base coordinate system obtained in the step 6, and calculating to obtain a total error in a kinematic parameter error range;
and 8, taking the minimization of the total error E as an optimization objective function of the optimization algorithm, carrying out the optimization algorithm by using the set calculation times, and taking a vector group corresponding to the minimum value in the calculated objective function values or a vector group corresponding to the objective function value smaller than a set threshold value Q as final error values of all the joint kinematics parameters.
2. The laser sensor-based joint robot kinematic parameter identification method according to claim 1, wherein:
in step 5, the coordinate value p of the sampling point under the coordinate system of the laser sensor Si Conversion into coordinate values p in the base coordinate system Bi The method specifically comprises the following steps:
p Bi ＝( 0 A 1 +d 0 A 1 )·( 1 A 2 +d 1 A 2 )·...·( j A j+1 +d j A j+1 )·...( m-1 A m +d m-1 A m )· m T S ·p Si
in the formula, p Bi The coordinate value of the ith sampling point under the base system is represented; p is a radical of Si The coordinate value of the ith sampling point in the coordinate system of the laser sensor is represented; i is more than or equal to 1 and less than or equal to N;
0 A 1 a transformation matrix representing the base coordinate system to the 1 st coordinate system;
j A j+1 representing a transformation matrix from a j coordinate system to a j +1 coordinate system, wherein each element in the m-1 matrix with j being more than or equal to 0 and less than or equal to m is a function of kinematic parameters of connecting rod distortion alpha, connecting rod offset d, connecting rod length a and joint angle theta; the concrete form is as follows:
wherein, c θ j+1 Represents cos θ j+1 ，sθ j+1 Denotes sin θ j+1 ；
d 0 A 1 Representing differential motion from a base coordinate system to a 1 st coordinate system due to kinematic parameter errors;
d j A j+1 representing differential motion from the jth coordinate system to the (j + 1) th coordinate system caused by kinematic parameter errors, wherein each element in the matrix is kinematic parameter errors, namely a connecting rod torsion error delta alpha, a connecting rod offset error delta d, a connecting rod length error delta a and a kinematic parameter errorA function of the rod twist α, the link offset d, the link length a, the joint angle θ; the concrete form is as follows:
m T S a transformation matrix representing the end joint coordinate system to the laser sensor coordinate system.
3. The laser sensor-based joint robot kinematic parameter identification method according to claim 2, wherein:
in step 7, the total error E in the kinematic parameter error range is:
in the formula, x i And y i Respectively representing the X-axis coordinate value and the Y-axis coordinate value of the sorted ith sampling point in the base coordinate system; x is the number of N-i+1 And y N-i+1 And the X-axis coordinate value and the Y-axis coordinate value of the N-i +1 th sampling point in the base coordinate system are shown.
4. The laser sensor-based joint robot kinematic parameter identification method according to claim 3, wherein:
in step 7, the kinematic parameter error range is: -0.5. Ltoreq. DELTA.alpha. Ltoreq.0.5; Δ d is more than or equal to-0.5 and less than or equal to 0.5; -0.5. Ltoreq. DELTA.a. Ltoreq.0.5.
5. The laser sensor-based joint robot kinematic parameter identification method according to claim 4, wherein:
in step 7, the initial values of the joint kinematic parameter errors, namely the connecting rod torsion error delta alpha, the connecting rod offset error delta d and the connecting rod length error delta a, are set to be 0.
6. The laser sensor-based joint robot kinematic parameter identification method according to claim 5, wherein:
in step 2, the number N of the sampling points is an even number.
7. The laser sensor based joint robot kinematic parameter identification method according to any one of claims 1 to 6, wherein:
in step 8, the threshold Q = E 0 200；
Wherein E is 0 And calculating the total error in the kinematic parameter error range when the kinematic parameter errors of all joints, namely the connecting rod torsion error delta alpha, the connecting rod offset error delta d and the connecting rod length error delta a, are all 0.
8. The laser sensor-based joint robot kinematic parameter identification method according to claim 7, wherein:
in step 3, the modeling method of the kinematic model is an improved DH method, a 5-parameter MDH method, a CPC model, an S model or a POE model.
9. The laser sensor-based joint robot kinematic parameter identification method according to claim 8, wherein:
in step 8, the optimization algorithm is a genetic algorithm.
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