CN113696184A - Method for constructing visual motion capability map for flexibility of serial mechanical arm - Google Patents

Method for constructing visual motion capability map for flexibility of serial mechanical arm Download PDF

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CN113696184A
CN113696184A CN202111074584.3A CN202111074584A CN113696184A CN 113696184 A CN113696184 A CN 113696184A CN 202111074584 A CN202111074584 A CN 202111074584A CN 113696184 A CN113696184 A CN 113696184A
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sphere
mechanical arm
working space
flexibility
coordinate system
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CN113696184B (en
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赵京东
赵智远
杨国财
赵亮亮
杨晓航
蒋再男
谢宗武
刘宏
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Harbin Institute of Technology
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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
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1653—Programme controls characterised by the control loop parameters identification, estimation, stiffness, accuracy, error analysis
    • 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
    • B25J9/1605—Simulation of manipulator lay-out, design, modelling of manipulator

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Abstract

A method for constructing a visual kinematic capability map for the flexibility of a serial mechanical arm relates to a method for constructing a kinematic capability map of a mechanical arm. Establishing a positive kinematics model of the mechanical arm to obtain a positive kinematics equation; solving an achievable working space; performing voxelization processing on the reachable working space by using a sphere, and representing the position information of discrete points in the reachable working space by using a sphere center coordinate; discrete points are uniformly distributed on the outer surface of the sphere, and the coordinate relation between the sphere center coordinate and the sphere discrete points is established to disperse the posture of the end effector reaching the sphere center position; judging the accessibility of all poses at the sphere center position of the sphere, solving accessibility probability, and representing the motion flexibility of the mechanical arm at the point; and visualizing the spheres with different probability intervals to obtain a motion capability map. The flexible motion capability of the serial mechanical arm at different positions in the reachable working space can be visually checked and evaluated, and the flexible working space obtained by solving is more accurate.

Description

Method for constructing visual motion capability map for flexibility of serial mechanical arm
Technical Field
The invention relates to a method for constructing a mechanical arm motion capability map, in particular to a method for constructing a motion capability map for visualizing the flexibility of a serial mechanical arm, and belongs to the technical field of mechanical arm motion capability analysis.
Background
The series mechanical arm is widely applied to the fields of industrial production, aerospace, deep sea exploration, medical service and the like, and is designed into different structures according to requirements to complete various types of tasks. The working space is used as an important kinematic index and is generally used for evaluating the motion capability of the series mechanical arm so as to guide tasks such as configuration design, structural parameter optimization, motion planning and the like of the series mechanical arm.
The workspace comprises a reachable workspace, which is a collection of location points that the end effector of the robotic arm can reach in at least one pose, and a smart workspace, which is a collection of location points that the end effector of the robotic arm can reach in any pose. The reachable working space of the series mechanical arm is obtained by analyzing the forward kinematics solution of the series mechanical arm, the solution process is simple, and the method is mainly used for evaluating the working capacity of the mechanical arm at present. However, the reachable workspace can only represent position information of points that the end effector of the robot arm can reach, and cannot represent pose information to reach these points. When the motion capability of the mechanical arm is evaluated, the capability of the mechanical arm reaching the same operation point in different tail end postures in the working area of the mechanical arm is more concerned, namely the flexible motion capability of the mechanical arm. For example, in order to ensure successful grasping of an object while performing a grasping task, it is necessary for the end effector of the robot arm to reach the grasping point in some pose, not just simply to reach the point. Therefore, the method has more significance for evaluating the motion capability of the mechanical arm by adopting a smart working space. However, limited by the structural features of the robot arm and the range of motion of each joint, the smart working space of the tandem robot arm in practical application does not exist basically, and therefore, the evaluation of the motion capability of the robot arm by using the flexible working space similar to the smart working space becomes a research hotspot with more practical significance. A flexible workspace refers to a collection of location points that an end effector of a robotic arm can reach in as many poses as possible, which is a subset of the reachable workspace. At present, indexes such as operability, direction operability, minimum singular value and condition number are mostly adopted to analyze the flexibility of the mechanical arm at each position in a working area, and then the flexible working space is obtained by solving. However, the above indexes are derived from a jacobian matrix of the mechanical arm, and since the jacobian matrix relates the joint velocity to the cartesian velocity of the end of the mechanical arm, all the derived indexes are dimensional indexes, but a dimensionless index is generally desirable for evaluating the motion capability of the mechanical arm. In addition, the cartesian speed at the end of the mechanical arm mixes the translation speed and the rotation speed, so that the interpretability of the indexes is reduced, and the accuracy of the evaluation of the flexible motion capability of the mechanical arm is adversely affected.
In summary, for a serial mechanical arm with wide application, it is urgently needed to improve a working space method for evaluating the motion capability of the serial mechanical arm, so that the working space method can represent not only position information of an end effector of the mechanical arm reaching a certain point in a working area, but also posture information of the end effector reaching the point, and compared with simple index analysis, an intuitive visualization scheme is needed, and detailed visualization inspection and analysis can be performed on the flexible motion capability of the mechanical arm in the whole working area, which is very important for guiding tasks such as configuration design, structural parameter optimization, motion planning and the like of the serial mechanical arm.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides a method for constructing a mobility map for visualizing the flexibility of a series mechanical arm, which can not only represent the position information of points which can be reached by an end effector of the mechanical arm, but also represent the attitude information of the points, the flexibility of the motion is represented by using the accessibility probability of the pose, and the flexible working space obtained by solving is more accurate.
In order to achieve the purpose, the invention adopts the following technical scheme: a method for constructing a visual flexible motion capability map of a serial mechanical arm comprises the following steps:
the method comprises the following steps: establishing a positive kinematics model of the series mechanical arm to obtain a positive kinematics equation of the series mechanical arm;
step two: solving by combining a Monte Carlo method with a positive kinematic equation of the serial mechanical arm and kinematic parameters of the serial mechanical arm to obtain a reachable working space, and visually displaying the reachable working space through MATLAB software;
step three: performing voxelization processing on the reachable working space by using a sphere, and representing the position information of discrete points in the reachable working space by using the sphere center coordinates of the sphere;
step four: discrete points are uniformly distributed on the outer surface of the sphere, and the posture of the end effector of the serial mechanical arm reaching the sphere center position is dispersed by establishing the coordinate relation between the sphere center coordinate and the sphere discrete points;
step five: judging the accessibility of all poses at the sphere center position of the sphere by adopting an inverse kinematics solving method, solving to obtain the pose accessibility probability of the point, and expressing the motion flexibility of the serial mechanical arm at the point by using the probability;
step six: and visualizing the spheres in different probability intervals to obtain a movement capacity map representing the flexibility of the serial mechanical arm.
Compared with the prior art, the invention has the beneficial effects that: the method can visually check and evaluate the flexible motion capability of the serial mechanical arm at different positions in the reachable working space, has universality for the serial mechanical arm in the construction process, and compared with the traditional method, the constructed motion capability map not only shows the position information of the points which can be reached by the mechanical arm end effector, but also shows the posture information of the points, and describes the motion capability of the serial mechanical arm at different positions in the working area more abundantly, thereby effectively reducing the area for searching effective paths in task planning, and simultaneously obviously improving the success rate in executing tasks. In addition, the pose accessibility probability is a dimensionless index, compared with the traditional method for analyzing the motion flexibility of the mechanical arm by using indexes such as operability, direction operability, minimum singular value and condition number, the obtained flexible working space is more accurate in solving, the physical significance of the flexible working space is more clear, and the method plays a more important role in guiding tasks such as configuration design, structural parameter optimization and motion planning of the serial mechanical arm.
Drawings
FIG. 1 is a schematic diagram of a series seven degree-of-freedom redundant robotic arm in an embodiment of the present invention;
FIG. 2 is a schematic view of a positive kinematic model of the robotic arm of FIG. 1;
FIG. 3 is a schematic diagram of a cube discretized into a small cube enveloping the reachable workspace of the robotic arm of FIG. 1;
FIG. 4 is a schematic illustration of the numbering of the small squares of FIG. 3;
FIG. 5 is a schematic illustration of drawing a sphere fit within the small cube of FIG. 3 to obtain an accessible workspace;
FIG. 6 is a schematic illustration of discrete points generated on the outer surface of the sphere in FIG. 5;
FIG. 7 is a schematic diagram of the coordinate system established for the discrete points in FIG. 6 and the pose discretization;
FIG. 8 is a semi-sectional view of a reachability graph corresponding to the flexibility index of the robotic arm of FIG. 1 in the probability interval [0,0.2 ];
fig. 9 is a half-sectional view of a reachability graph corresponding to the flexibility index of the robot arm of fig. 1 in the probability interval (0.2, 0.8);
FIG. 10 is a semi-sectional view of a reachability graph corresponding to the flexibility index of the robotic arm of FIG. 1 in the probability interval [0.8,1 ];
fig. 11 is a top view of fig. 10.
Detailed Description
The technical solutions in the present invention will be described clearly and completely with reference to the accompanying 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 invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
A method for constructing a visual flexible motion capability map of a serial mechanical arm comprises the following steps:
the method comprises the following steps: establishing a positive kinematics model of the series mechanical arm to obtain a positive kinematics equation thereof
The positive kinematic model is preferably established by adopting a Craig method, a Base coordinate system of the serial mechanical arm is expressed as Base, and a fixed coordinate system of each joint of the serial mechanical arm is expressed as { x }nynznD is the number of joints, a coordinate system of a reference point of the mechanical arm end effector is represented by TCP, and a joint angle of an nth joint of the serial mechanical arm is represented by thetanThe positive kinematic equation solved is expressed as:
Figure BDA0003261770720000051
wherein θ ═ θ1,...,θn]TA vector of the joint angle is represented,
Figure BDA0003261770720000052
represents the pose of the coordinate system TCP in the Base coordinate system Base,
Figure BDA0003261770720000053
representing a coordinate system x0y0z0The pose in the Base coordinate system Base,
Figure BDA0003261770720000054
representing a coordinate system xnynznIn a coordinate system { x }n-1yn-1zn-1The pose in (c) is set by the position,
Figure BDA0003261770720000055
representing the coordinate system TCP in the coordinate system { xnynznPose in (1).
Step two: the Monte Carlo method is adopted to combine the positive kinematic equation of the serial mechanical arm and the kinematic parameter solution of the serial mechanical arm to obtain the reachable working space
The reachable working space is preferably the method provided in Monte Carlo method improvement and volume solving [ J ] of the robot working space solution and the method provided in the step of optics precision engineering, 2018,26(11):2703 + Jun 2713, which is a general numerical method for solving the reachable working space of the robot and can solve the precise reachable working space. According to the definition of the reachable working space, the reachable working space of the series mechanical arm is obtained by the method in combination with the formula (1) and the kinematic parameters, and is visually displayed through MATLAB software, wherein the kinematic parameters refer to D-H parameters corresponding to the positive kinematic model established in the first step.
Step three: voxelization processing is carried out on the reachable working space by adopting a sphere, and the position information of discrete points in the reachable working space is represented by the sphere center coordinates of the sphere
In particular, the method comprises the following steps of,
step three, firstly: w is used for the reachable working space obtained in the step twoRDenotes that W isRCompletely enveloping the cube, wherein the edge length L of the cube is preferably selected according to L which is 2L, wherein L represents the longest length of the straightened serial mechanical arm, the center of the cube coincides with the origin of a base coordinate system in the positive kinematics model established in the step one, the directions of the length, the width and the height of the cube are respectively parallel to the directions of three axes of the base coordinate system, and the origin coordinate of the base coordinate system is represented as OB(0,0,0), the coordinates of the eight vertices of the cube with respect to the base coordinate system are:
[(-l,-l,-l),(l,-l,-l),(l,l,-l),(-l,l,-l),(-l,-l,l),(l,-l,l),(l,l,l),(-l,l,l)] (2)；
step three: uniformly dividing the cube in the step three into u equal parts along the length direction, the width direction and the height direction, wherein the cube is divided into u equal parts3Small cube, the edge length L of the small cubeSL/u, this process is called the process of voxel of the cube, each small cube representing a voxel, each small cube being numbered starting from the first small cube in the lower left corner of the cube, column by column and row by row, the resulting number being stored in the matrix Num _ 1;
step three: and generating an inscribed Sphere in each small cube according to the numbering sequence in the third step and the second step, wherein the radius r of the inscribed Sphere is equal to L/2u, the Sphere center coordinate of each inscribed Sphere is calculated and stored in the matrix Sphere, and the number of the small cube corresponding to the W-th row of the Q-th column of the H-th layer is j equal to W + u (Q-1) + u2(H-1), center O of a small cube inscribed sphere corresponding to number jCThe coordinates relative to the base coordinate system are:
Figure BDA0003261770720000061
step three and four: traversing all the small cubes according to the numbering sequence in the step two, checking the number of the reachable working space points in each small cube, finding out the small cubes with the number of the reachable working space points being not 0, and storing the corresponding numbers in a matrix Num _ 2;
step three and five: and extracting the Sphere center coordinates of the inscribed Sphere of the small cube corresponding to the number in the matrix Num _2 from the matrix Sphere, drawing the Sphere according to all the extracted inscribed spheres through MATLAB software, and fitting the result to obtain the reachable working space of the serial mechanical arm, wherein the Sphere center coordinates of the Sphere represent the position information of discrete points in the reachable working space.
Step four: discrete points are uniformly distributed on the outer surface of the sphere, and the posture of the mechanical arm end effector reaching the sphere center position is dispersed by establishing the coordinate relation between the sphere center coordinate and the sphere discrete points
In particular, the method comprises the following steps of,
step four, firstly: the discrete points are preferably distributed using SAFFE.B., KUIJLAAARSA.B.J.distributing and manipulating on a sphere, the physical intellignencer [ J]1997,19(1):5-11 ", the spiral point equipartition algorithm generates N uniformly distributed discrete points on the outer surface of each sphere drawn in the third step and the fifth step, and calculates the position vector P of the kth discrete point on the outer surface of the sphere of the small cube corresponding to the serial number j relative to the base coordinate system by using the spherical coordinatesk(1≤k≤N)：
Figure BDA0003261770720000071
Figure BDA0003261770720000076
Figure BDA0003261770720000072
Figure BDA0003261770720000073
Wherein the content of the first and second substances,
Figure BDA0003261770720000077
d is a constant representing the pitch of the helix;
step four and step two: establishing a coordinate system at each discrete Point generated in the step four and the step one, and using PointkRepresents the coordinate system at the k discrete Point, and the connecting line between the sphere center and the Point represents the coordinate system PointkThe direction from the center of the sphere to the discrete Point is the positive direction of the z axis, the x axis and the y axis are tangent to the spherical surface at the discrete Point k, and the specific direction passes through the coordinate system PointkAnd (3) determining a rotation matrix relative to the spherical center coordinate system, wherein the direction of the spherical center coordinate system is consistent with the direction of the Base coordinate system Base, and the rotation matrix can be calculated by combining the spherical coordinate system with the discrete points generated in the first step and the second step:
Figure BDA0003261770720000075
step four and step three: dispersing the corresponding posture of the dispersed Point k around the coordinate system PointkThe z-axis of the rotating shaft is rotated at equal intervals, and the interval value is delta to obtain
Figure BDA0003261770720000081
Group poses, wherein the g-th group pose is relative to the coordinate system PointkAnd base coordinate systemRotation matrices respectively
Figure BDA0003261770720000082
And
Figure BDA0003261770720000083
expressed, they are calculated by the following formulas:
Figure BDA0003261770720000084
Figure BDA0003261770720000085
the coordinate system is established and the postures are dispersed by adopting the same method for other discrete points on the spherical surface, and the position of each sphere center is obtained
Figure BDA0003261770720000086
Group attitude representing attitude information of the robot arm end effector to the position of the center of sphere, P for the position vector of the center of sphere with respect to the base coordinate systemcAnd if so, the position matrix of the mechanical arm end effector reaching the sphere center is represented as follows:
Figure BDA0003261770720000087
step five: adopting an inverse kinematics solving method to judge the accessibility of all poses at the sphere center position of the sphere and solving to obtain the pose accessibility probability of the point, and using the probability to express the motion flexibility of the serial mechanical arm at the point
In particular, the method comprises the following steps of,
step five, first: solving the inverse kinematics solution corresponding to the pose matrix reaching the sphere center, preferably adopting the inverse kinematics solution TRAC-IK proposed in 'BEESON P, BARRETT0A.TRAC-IK: An open-source library for improved solution of genetic inverse kinematics.2015IEEE-RAS 15th International reference on human subjects (Humanoids) [ C ],2015, 928-935', wherein the method is a general numerical method for calculating the inverse solution, has the characteristics of high solving success rate and high solving speed, and is used for traversing and solving the inverse solution of each group of pose in the formula (11);
step five two: solving the accessibility probability of the pose reaching the sphere center, wherein N.M groups of poses are scattered at each sphere center position in the fourth step, the number of poses which can be successfully solved by traversing the inverse solution of each group of poses in the fifth step is represented by S, and the accessibility probability R of the pose corresponding to the sphere center position is represented as:
Figure BDA0003261770720000091
wherein, R is a dimensionless index, and the numerical value of R represents the flexible motion capability of the serial mechanical arm reaching the position of the sphere center.
Step six: visualizing spheres with different probability intervals to obtain a movement capacity map representing the flexibility of the serial mechanical arm
The pose accessibility probability R is divided into a plurality of probability intervals according to actual task requirements, spheres corresponding to the probability intervals are respectively visually displayed through MATLAB to obtain a movement capacity map representing the flexibility of the serial mechanical arm, a semi-section representation method is preferably adopted in order to clearly see the internal condition of the capacity map in the visualization process, and the flexibility analysis cannot be influenced after the section.
Examples
Step one, combining the series seven-degree-of-freedom redundant mechanical arm shown in figure 1, adopting a Craig method to establish a positive kinematics model of the arm as shown in figure 2, wherein a coordinate system { x ] in the model0y0z0Denotes the Base coordinate system Base, coordinate system xnynznDenotes a fixed coordinate system of each joint, where z is 1n(n ═ 1.., 7.) is the axis of rotation of each joint, the coordinate system TCP and the coordinate system { x } of the robot arm end effector reference point7y7z7Completely superimposed, represented for simplicity by the coordinate system x7y7z7Denotes, thetanDenotes the nth joint angle, θ ═ θ1,...,θ7]TExpressing a joint angle vector, and solving to obtain a positive kinematic equation of the arm as follows:
Figure BDA0003261770720000092
wherein the content of the first and second substances,
Figure BDA0003261770720000101
Figure BDA0003261770720000102
anrepresents an edge xnAxis from znThe axis moving to zn+1Distance of axis, αnDenotes a winding xnAxis from znRotation of the shaft to zn+1Distance of the axes, dnIs shown along znAxis from xn-1The shaft being moved to xnDistance of the shaft;
referring to FIG. 2, the D-H parameters corresponding to the model are shown in Table 1, and the values of the parameters in the Table are substituted into the positive kinematic equation to calculate
Figure BDA0003261770720000103
The specific numerical value of (1).
TABLE 1 mechanical arm D-H parameters
Figure BDA0003261770720000104
And step two, combining the Monte Carlo method improvement and volume solving of the robot working space with the positive kinematic equation and the D-H parameters shown in the table 1 according to the definition of the reachable working space and by adopting the improved Monte Carlo method provided in the Monte Carlo method improvement and volume solving of the robot working space, and solving to obtain the accurate reachable working space of the arm.
Step three, as shown in fig. 3, enveloping the arm and the reachable working space with a cube whose edge length L is 3.552(m), where the center of the cube coincides with the origin of the base coordinate system in the positive kinematic model, the directions of the length, width, and height of the cube are respectively parallel to the directions of the three axes of the base coordinate system, and the coordinates of the eight vertices of the cube with respect to the base coordinate system are respectively:
Figure BDA0003261770720000111
the cube is uniformly divided into u-50 equal parts along the length, width and height directions, the cube is divided into 125000 small cubes, and the edge length L of the small cubesS0.07104(m), numbering each small cube starting from the first small cube at the bottom left corner of the cube, proceeding sequentially in a row-by-row, column-by-column, row-by-row manner, and as a result, as shown in fig. 4, storing the obtained numbers in a matrix Num _1, wherein the coordinate axis X direction represents the row direction, the coordinate axis Y direction represents the column direction, the coordinate axis Z direction represents the layer direction, and t represents the number of layers;
generating inscribed spheres in each small cube according to the numbering sequence in a matrix Num _1, wherein the radius r of each inscribed Sphere is 0.03552(m), calculating the Sphere center coordinate of each inscribed Sphere and storing the Sphere center coordinate in the matrix Sphere, wherein the number j of the small cube corresponding to the No. Q, No. W row of the H-th layer is W +50(Q-1) +2500(H-1), and the coordinate of the Sphere center of the inscribed Sphere of the small cube corresponding to the number j relative to the base coordinate system is:
Figure BDA0003261770720000112
traversing all the small cubes according to the numbering sequence in the matrix Num _1, checking the number of the reachable working space points in each small cube, finding out the small cubes of which the number of the reachable working space points is not 0, and storing the corresponding numbers in the matrix Num _ 2;
the coordinates of the center of the inscribed Sphere of the small cube corresponding to the number in the matrix Num _2 are extracted from the matrix Sphere, all spheres are drawn through MATLAB software, the reachable working space of the arm is obtained through fitting results, as shown in FIG. 5, and the coordinates of the center of the Sphere represent the position information of discrete points in the reachable working space.
Step four, as shown in fig. 6 and 7, a spiral point uniform distribution algorithm is adopted to generate N-100 uniformly distributed discrete points on the outer surface of each sphere shown in fig. 5, a position vector of a kth discrete point on the outer surface of the inscribed sphere corresponding to the serial number j is calculated by adopting the spherical coordinates shown in fig. 7 relative to the base coordinate system, the pitch D of the spiral line is 20, and the coordinate system { X in fig. 7 is that0Y0Z0Denotes the coordinates of the center of the sphere, which is related to the base coordinate system { x }0y0z0The postures of the fingers are completely consistent, O0Coordinate system { X ] representing the position of the center of sphere1Y1Z1Denotes the coordinate system Point of the kth discrete Pointk，O1Indicating the position of the k-th discrete point,
Figure BDA0003261770720000121
representing the zenith angle in a spherical coordinate system,
Figure BDA0003261770720000122
expressing the azimuth angle in the spherical coordinate system, and obtaining the coordinate system Point through the formula (8)kRelative to the coordinate system of the center of sphere { X0Y0Z0Rotation matrix of
Figure BDA0003261770720000123
Dispersing the corresponding posture of the dispersed Point k around the coordinate system PointkIs rotated at equal intervals along the z-axis, the interval being taken as
Figure BDA0003261770720000124
Obtaining M-12 group postures, wherein the g-th group posture is relative to the coordinate system PointkAnd the rotation matrix of the base coordinate system are obtained by calculation through a formula (9) and a formula (10) respectively;
the coordinate system is established and the postures are dispersed for the rest of the discrete points on the spherical surface by the same method, 1200 groups of postures are obtained for each sphere center position, posture information indicating that the end effector of the mechanical arm reaches the sphere center position is represented, and a posture matrix of the end effector of the mechanical arm reaching the sphere center is obtained through solving by a formula (11).
And step five, traversing and solving the inverse solution of each group of position and posture in the formula (11) by adopting a TRAC-IK method, and then solving the position and posture accessibility probability of reaching each sphere center position through the formula (12).
Step six, as shown in fig. 8 to 11, dividing the pose reachability probability R at each sphere center position into 3 probability intervals: [0,0.2], (0.2,0.8) and [0.8,1], a motion capability map indicating the flexibility of the arm is obtained by visualizing and displaying spheres corresponding to the above 3 probability intervals by MATLAB, wherein FIG. 8 is a half-sectional view of the reachability map corresponding to the flexibility index of the arm in the probability interval [0,0.2], FIG. 9 is a half-sectional view of the reachability map corresponding to the flexibility index of the arm in the probability interval (0.2,0.8), FIG. 10 is a half-sectional view of the reachability map corresponding to the flexibility index of the arm in the probability interval [0.8,1], and FIG. 11 is a top view of FIG. 10.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof. The present embodiments are therefore to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference sign in a claim should not be construed as limiting the claim concerned.
Furthermore, it should be understood that although the present description refers to embodiments, not every embodiment may contain only a single embodiment, and such description is for clarity only, and those skilled in the art should integrate the description, and the embodiments may be combined as appropriate to form other embodiments understood by those skilled in the art.

Claims (7)

1. A method for constructing a visual flexible motion capability map of a serial mechanical arm is characterized by comprising the following steps: the method comprises the following steps:
the method comprises the following steps: establishing a positive kinematics model of the series mechanical arm to obtain a positive kinematics equation of the series mechanical arm;
step two: solving by combining a Monte Carlo method with a positive kinematic equation of the serial mechanical arm and kinematic parameters of the serial mechanical arm to obtain a reachable working space, and visually displaying the reachable working space through MATLAB software;
step three: performing voxelization processing on the reachable working space by using a sphere, and representing the position information of discrete points in the reachable working space by using the sphere center coordinates of the sphere;
step four: discrete points are uniformly distributed on the outer surface of the sphere, and the posture of the end effector of the serial mechanical arm reaching the sphere center position is dispersed by establishing the coordinate relation between the sphere center coordinate and the sphere discrete points;
step five: judging the accessibility of all poses at the sphere center position of the sphere by adopting an inverse kinematics solving method, solving to obtain the pose accessibility probability of the point, and expressing the motion flexibility of the serial mechanical arm at the point by using the probability;
step six: and visualizing the spheres in different probability intervals to obtain a movement capacity map representing the flexibility of the serial mechanical arm.
2. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 1, wherein the kinetic energy map comprises the following steps: and in the first step, the positive kinematic model of the serial mechanical arm is established by adopting a Craig method.
3. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 1, wherein the kinetic energy map comprises the following steps: and the kinematic parameters of the serial mechanical arm in the second step are D-H parameters corresponding to the positive kinematic model established in the first step.
4. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 1, wherein the kinetic energy map comprises the following steps: the third step is specifically as follows:
s1, completely enveloping the reachable working space obtained through solving by using a cube, wherein the center of the cube is superposed with the origin of a base coordinate system in the positive kinematic model, and the directions of the length, the width and the height of the cube are respectively parallel to the directions of three axes of the base coordinate system;
s2, dividing the cube into u along the length, width and height directions3Each small cube represents a voxel, each small cube is numbered from the first small cube at the lower left corner of the cube in a layer-by-layer, column-by-column and line-by-line mode, and the obtained number is stored in a matrix Num _ 1;
s3, generating inscribed spheres in each small cube according to the numbering sequence, calculating the Sphere center coordinates of each inscribed Sphere and storing the Sphere center coordinates in a matrix Sphere;
s4, traversing all the small cubes according to the numbering sequence, checking the number of the reachable working space points in each small cube, finding out the small cubes with the number of the reachable working space points not being 0, and storing the corresponding numbers in a matrix Num _ 2;
s5, extracting the spherical center coordinates of the inscribed Sphere of the small cube corresponding to the number in the matrix Num _2 from the matrix Sphere, drawing the Sphere according to all the extracted inscribed spheres through MATLAB software, and fitting the result to obtain the reachable working space of the serial mechanical arm, wherein the spherical center coordinates of the Sphere represent the position information of discrete points in the reachable working space.
5. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 4, wherein the kinetic energy map comprises the following steps: the concrete method of the fourth step is as follows:
s1, generating uniformly distributed discrete points on the outer surface of each voxel processed by adopting a spiral point uniform distribution algorithm;
s2, establishing a coordinate system at each discrete point, wherein a connecting line of the sphere center and the discrete points represents a z-axis of the coordinate system, the direction from the sphere center to the discrete points is the positive direction of the z-axis, the x-axis and the y-axis are tangent to the spherical surface at the discrete points, and the direction is determined by a rotation matrix of the coordinate system relative to the sphere center coordinate system;
and S3, dispersing the corresponding postures of each discrete point, rotating around the z axis of the coordinate system at equal intervals to obtain a plurality of groups of postures, and solving a posture matrix of the end effector of the serial mechanical arm reaching the sphere center.
6. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 1, wherein the kinetic energy map comprises the following steps: the concrete method for solving the reachability probability of the position posture in the fifth step is that an inverse kinematics solving method TRAC-IK is adopted to solve the inverse solution of the position posture at the sphere center position of the sphere in a traversing way, the number of the position postures successfully solved by the inverse solution is represented by S, the discrete number at each sphere center position in the fourth step is N.M groups, and then the reachability probability R of the position posture corresponding to the sphere center position is represented as
Figure FDA0003261770710000031
7. The method for constructing the kinetic energy map for visualizing the flexibility of the serial mechanical arm according to claim 1, wherein the kinetic energy map comprises the following steps: and in the sixth step, the motion capability map divides the pose accessibility probability into a plurality of probability intervals according to the actual task requirement, and spheres corresponding to the probability intervals are respectively displayed in a visualized mode through MATLAB and are represented by a semi-section method.
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