CN115284253B - Parallel six-axis robot pose inverse solution method - Google Patents
Parallel six-axis robot pose inverse solution method Download PDFInfo
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- CN115284253B CN115284253B CN202111665940.9A CN202111665940A CN115284253B CN 115284253 B CN115284253 B CN 115284253B CN 202111665940 A CN202111665940 A CN 202111665940A CN 115284253 B CN115284253 B CN 115284253B
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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
- B25J9/003—Programme-controlled manipulators having parallel kinematics
- B25J9/0045—Programme-controlled manipulators having parallel kinematics with kinematics chains having a rotary joint at the base
Abstract
The invention relates to a parallel six-axis robot pose inverse solution method,the position of a terminal moving platform coordinate system relative to a static platform base coordinate system is given by the structural parameters of a parallel six-axis robot O OP and attitude value O R P Solving for the extension of the cylinder piston rod (cylinder position vector O ΒΑ i ) At the same time, satisfies fifteen angle values (Θ UQi ，Θ AOi ，Θ ABi ) The working space of the tail end static platform of the robot can be limited by limiting the fifteen angle values within the preset threshold range, so that the working space of the robot is increased to the maximum extent; meanwhile, when the static platform reaches a designated pose, the parallel six-axis robot can bear the designed rated load in the working space range.
Description
Technical Field
The invention relates to the technical field of robots, in particular to a parallel six-axis robot pose inverse solution method.
Background
Compared with a serial robot, the parallel robot has the characteristics of high rigidity, high precision and large load self weight, has wide application in the fields of positioning platforms, simulation equipment, entertainment equipment and the like, and has great potential in automatic processing application scenes. In order to develop a novel control system of the parallel robot and realize the basic motion of the parallel robot, an inverse solution algorithm is a problem which needs to be solved at first. The inverse solution algorithm can be used for kinematic simulation before development of the model and guiding the model selection of parts. For example, when a working space is given, it is checked whether the extension value of the piston rod of the electric cylinder is within an allowable range.
One common method for limiting the working space of a parallel six-axis robot is to calculate the pose of the end moving platform by periodically calling a forward solution algorithm, and limit the working space range by limiting the shape of the pose, and as shown in fig. 1, the working space of the parallel six-axis robot is generally composed of 3 parts, namely an irregular sphere space, a cylinder space and a bottom space. Because the irregular sphere at the top is difficult to build a mathematical model, difficult to judge and limit by using a positive solution, generally only a cylindrical space (easy to model) is utilized, so that the accessible working space of the robot is small, and the working space cannot be fully utilized.
Disclosure of Invention
Aiming at the problems existing in the prior art, the invention aims to provide a pose inverse solution method for a parallel six-axis robot, which supplements angle values at fifteen rotary joints and realizes the limitation of the working space of the robot by limiting the fifteen angle values.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the six-axis robot comprises a static platform, a movable platform, six Hooke hinge assemblies, six electric cylinder assemblies and three cross shaft assemblies, wherein the Hooke hinge assemblies are arranged on the static platform, the cross shaft assemblies are arranged on the movable platform, one end of each electric cylinder assembly is arranged on the Hooke hinge assembly, and the other end of each electric cylinder assembly is rotationally connected to the cross shaft assembly through a bearing pin shaft;
the method comprises the following steps:
1. constructing geometric elements and kinematic elements;
B i i=1 to 6 represents the origin of the hook, and B is as follows i I=1 to 6 points are arranged in the center of a cross shaft of the Hooke joint;
{ O } is the base coordinate system; establishing a rectangular coordinate system { O } on the static platform, and setting an origin O of the coordinate system at B 1 ～B 6 On a determined plane and located at B 1 ～B 6 The determined circle center position of the circle is arranged on the OB in the y-axis direction 1 ,OB 2 The angular bisector position of the line segment, at this time, the six hook hinges are symmetrical relative to the y axis; the z axis is arranged upwards, and the x axis can be automatically determined according to a right-hand rule;
R b representation B 1 ～B 6 The radius of the determined circle is called the 'hook hinge virtual circle radius';
O OB 1 ～ O OB 6 representing vector OB 1 ～OB 6 A representation with { O } as a reference frame; O OB i called "Hooke's joint position vector", specifically refers to the ith Hooke's joint origin B starting from the base coordinate system origin O i I=1 to 6 is a vector of the end point;
β i i=1 to 6 represents O OB i The angle with the Y-axis of the base coordinate system { O } is referred to as the "Hooke's hinge offset angle";
U i the origin of the intersecting axis is that the axes of two cylindrical surfaces of the intersecting axis part form an intersection point, and the intersection point is U i ，i＝1～3；
R Q Radius values representing circles determined by three intersecting axis origins are referred to as "intersecting axis virtual circle radii";
{ P } is the moving platform coordinate system; establishing a rectangular coordinate system { P }, wherein the origin P of { P } is positioned at U on the movable platform i I=1 to 3, and is located on three U' s i The circle center position of the circle is determined; u (U) 2 In the negative direction of the y-axis, U 1 ,U 3 Symmetrical with respect to the y-axis, the z-axis is upward, and the x-axis can be determined by right-hand rules;
o D i i=1 to 3 is a "cross axis transverse axis vector", which takes a base coordinate system as a reference system;
δ i i=1 to 3 represents o D i The angle of the vector to the Y-axis of { P }, called o D i Vector distribution angle;
Q i i=1 to 3 represents the origin of the lug, which means the sum U on the lug part i I=1 to 3 corresponds to the overlapping point;
o BQ i i=1 to 6 is called a "hook hinge-axis ear vector", and a base coordinate system { O } is used as a reference system;
{Q i i=1 to 3 and O R Qi i=1 to 3 each represents "an axis ear coordinate system" and "a rotation matrix of the axis ear coordinate system with respect to the base coordinate system { O };
the distribution angle of the shaft lug original points is called as a shaft lug distribution angle;
P PQ i : the expression "position vector of the axis ear origin distributed on the moving platform with the moving platform coordinate system { P } as the reference system";
O OP is a given position, and represents a position vector of an origin P of the moving platform coordinate system { P } relative to an origin O of the static platform coordinate system;
O R P for a given pose, representing a rotation matrix of the moving platform coordinate system { P } relative to the stationary platform coordinate system { O };
A 1 ～A 6 representing the hinge center of the pin shaft;
Ο ΒΑ i : the representation is composed of O R P And O OP, according to the "electric cylinder position vector" obtained by the pose inverse solution algorithm, taking a base coordinate system { O } as a reference system;
Qj QA i i=1 to 6,j =1 to 3: an axis ear-rotation center vector in an axis ear coordinate system { Q j Is a reference frame in which Q1 QA 2 ， Q1 QA 3 In { Q 1 In the process of }, Q2 QA 4 ， Q2 QA 5 in { Q 2 In the process of }, Q3 QA 1 ， Q3 QA 6 in { Q 3 Inner part;
O QA i i=1 to 6: an axial ear-rotation center vector, taking a base coordinate system { O } as a reference system; theta (theta) UQi A vector of angular values representing the shaft ear piece and the cross-shaft housing, wherein i = 1,2,3, represents the angular values of 3 cross-shaft assemblies;
Θ AOi an angle value vector of the cross shaft relative to the Hooke's lower base is represented, wherein i=1-6, and the angle value of the Hooke's assembly at 6 is represented;
Θ ABi a vector of angular values representing the cross-axis relative to the base on the hook, where i=1 to 6, represents the hook assembly at 6An angle value;
Θ UQM : representing Θ UQi A threshold value of (2); theta (theta) AOM : representing Θ AOi A threshold value of (2); theta (theta) ABM : representing Θ ABi A threshold value of (2);
BI 1 ～BI 3 : representing Hooke's hinge horizontal vector, representing the vector formed by connecting two Hooke's hinge origins; BI (BI) 1 Representation B 2 Pointing to B 3 Vectors of BI 2 Representation B 4 Pointing to B 5 Vectors of BI 3 Representation B 6 Pointing to B 1 Is a vector of (2);
OI 1 ～OI 3 representing a Hooke's joint midpoint vector, representing a vector whose base coordinate system origin points to the midpoint of two Hooke joints, where OI 1 Origin O of base coordinate system points to B 1 And B 6 Midpoint of the connection, OI 2 Origin O of base coordinate system points to B 2 And B 3 Midpoint of the connection, OI 3 Origin O of base coordinate system points to B 4 And B 5 A midpoint of the connection line;
2. pose inverse solution process
Step 1: calculating vectors O OB 1 ～ O OB 6 The method comprises the steps of carrying out a first treatment on the surface of the According to the ' Hooke ' virtual circle radius ' R b The Hooke's hinge position offset angle beta i, i=1-6, and then pass through R according to the coordinate rotation theorem in robotics theory b Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the Hooke hinge position vector O OB 1 ～ O OB 6 ；
Step 2: calculating vectors P PQ i I=1 to 3; according to the 'cross-axis virtual circle radius' R Q The distribution angle of the axis ear origin is i=1-6, and then the axis ear origin passes through R according to the coordinate rotation theorem in the robotics theory Q Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the axis ear position vector P PQ i ，i＝1～3；
Step 3: calculating Hooke's hinge-axis ear vector o BQ i I=1 to 6; according to a known quantity "givenPosition' O OP, known quantity "given gesture" O R P The tab position vector PPQi obtained in step 2, i=1 to 3, the hook position vector obtained above O OB 1 ～ O OB 6 Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the robotics theory, the Hooke hinge-axial ear vector is obtained through the following formula o BQ i ,i＝1～6；
Step 4: computing cross axis vectors o D i I=1 to 3, and is obtained as follows: "given pose" according to a known quantity " O R P Vector distribution angle delta i Then according to the coordinate rotation theorem in the robotics theory, through " O R P Multiplying the Y-axis unit vector by the rotation angle matrix calculation formula around the Z axis to obtain a cross axis transverse axis vector o D i ，i＝1～3；
Step 5: calculation of O R Qi I=1 to 3, expressed as O R Qi ＝[ O x Qi O y Qi O z Qi ]， O x Qi ， O y Qi ， O z Qi Is a split axis of a rectangular coordinate system and accords with the right hand rule, so that the following needs to be respectively calculated: [ O x Q1 O y Q1 O z Q1 ]，[ O x Q2 O y Q2 O z Q2 ]，[ O x Q3 O y Q3 O z Q3 ]9 factors in total; according to Hooke's hinge-axis ear vector, the components can be obtained through the calculation of the cross multiplication, modulo and division of the vector o z Q1 The method comprises the steps of carrying out a first treatment on the surface of the According to the previous step o z Q1 And the cross axis transverse axis vector obtained as described above o D 1 By cross-multiplication of vectors o z Q1 × o D 1 Find modulo| o z Q1 × o D 1 After division calculation, the components can be obtained o y Q1 The method comprises the steps of carrying out a first treatment on the surface of the Based on the obtained Z component and Y component, a score can be obtained according to the right hand ruleMeasuring amount o x Q1 The method comprises the steps of carrying out a first treatment on the surface of the Is obtained by the same method o x Q2 o y Q2 o z Q2 o x Q3 o y Q3 o z Q3 ；
Step 6: calculation of Qj QA i ，i＝1～6，j＝1～3：
Q3 QA 1 ＝ Q1 QA 3 ＝ Q2 QA 5 ＝[-QAX-QAY 0] T
Q1 QA 2 ＝ Q2 QA 4 ＝ Q3 QA 6 ＝[QAX QAY 0] T
Step 7: calculation of O QA i I=1 to 6; rotation matrix of the shaft ear coordinate system obtained by using the above o R Qi I=1 to 3, and the above-obtained axial lug-rotation center vector Qj QA i I=1 to 6,j =1 to 3, and the coordinate transformation theorem in the robot kinematics theory is adopted o R Qi Multiplied by Qj QA i Can calculate the axial ear-rotation center vector taking the base coordinate system { O } as the reference system " Qj QA i ，i＝1～6；
Step 8: solving for O BA i I=1 to 6; using the obtained axial ear-rotation center vector with the base coordinate system { O } as a reference system Qj QA i I=1 to 6 and the hook-axis ear vector obtained as described above o BQ i I=1 to 6, and then using basic operation of vectors, the position vector of the electric cylinder can be obtained by the following formula, and the vector is a position inverse solution;
step 9: calculating Θ UQi I=1 to 3, the included angle being expressed as a cross axis transverse axis vector O D i And the x-axis direction of the axis ear coordinate system O x Qi Is included in the plane of the first part; the method is obtained by the following formula:
Θ UQ1 ＝arccos( O D 1 · O x Q1 )
Θ UQ2 ＝arccos( O D 2 · O x Q2 )
Θ UQ3 ＝arccos( O D 3 · O x Q3 )
step 10: judging theta UQi Whether or not it satisfies a threshold value smaller than a threshold value set in advance, namely Θ UQi ≤Θ UQΜ I=1 to 3, if not, stopping the solving process and reporting abnormality;
step 11: calculating Θ ABi I=1 to 3, which can be obtained by the following formula:
step 12: judging theta ABi Whether or not to satisfy a threshold value theta smaller than a preset value ABM I.e. theta ABi ≤Θ ABΜ I=1 to 6, if not, stopping the solving process and reporting an abnormality;
step 13: calculating OI i I=1 to 3, which can be obtained by the following formula:
step 14: calculating Θ AOi I=1 to 6, and can be obtained by the following formula:
step 15: judging theta AOi Whether or not to satisfy a threshold value theta smaller than a preset value AOM I.e. theta AOi ≤Θ AOΜ I=1 to 6, if not, stopping the solving process and reporting the abnormality.
o D i The vector distribution angle is:
the distribution angle of the axle ear original points is:
in the step 1, the vector O OB 1 ～ O OB 6 The expression is as follows:
in the step 2, the vector P PQ i The expression of i=1 to 3 is as follows:
in the step 3, hooke's joint-axis ear vector o BQ i The expression of i=1 to 6 is as follows:
o BQ 1 ＝ O OP+ O R P * P PQ 3 - O OB 1
o BQ 2 ＝ O OP+ O R P * P PQ 1 - O OB 2
o BQ 3 ＝ O OP+ O R P * P PQ 1 - O OB 3
o BQ 4 ＝ O OP+ O R P * P PQ 2 - O OB 4
o BQ 5 ＝ O OP+ O R P * P PQ 2 - O OB 5
o BQ 6 ＝ O OP+ O R P * P PQ 3 - O OB 6 。
in the step 4, the cross axis and the horizontal axis vector o D i The expression of i=1 to 3 is as follows:
in the step 5 of the above-mentioned process, O R Qi each factor expression of i=1 to 3 is as follows:
in the step 7 of the above-mentioned process, O QA i the expression of i=1 to 6 is as follows:
O QA 1 ＝ O R Q3 * Q3 QA 1
O QA 2 ＝ O R Q1 * Q1 QA 2
O QA 3 ＝ O R Q1 * Q1 QA 3
O QA 4 ＝ O R Q2 * Q2 QA 4
O QA 5 ＝ O R Q2 * Q2 QA 5
O QA 6 ＝ O R Q3 * Q3 QA 6
the saidIn the step 8 of the process, the process is carried out, O BA i the expression of i=1 to 6 is as follows:
O BA i ＝ O BQ i + O QA i
wherein i=1 to 6.
After the scheme is adopted, the invention gives the structural parameters of the parallel six-axis robot, and the position of the terminal movable platform coordinate system relative to the static platform base coordinate system O OP and attitude value O R P Solving for the extension of the cylinder piston rod (cylinder position vector Ο ΒΑ i ) At the same time, satisfies fifteen angle values (Θ UQi ，Θ AOi ，Θ ABi ) The working space of the tail end static platform of the robot can be limited by limiting the fifteen angle values within the preset threshold range, so that the working space of the robot is increased to the maximum extent; meanwhile, when the static platform reaches a designated pose, the parallel six-axis robot can bear the designed rated load in the working space range.
Drawings
FIG. 1 is a schematic diagram of a working space of a parallel six-axis robot;
FIG. 2 is a schematic diagram of a parallel six-axis robot;
FIG. 3 is a schematic diagram of a rotating structure of six-axis parallel robots J1-J12;
FIG. 4 is a schematic diagram of a rotating structure of a parallel six-axis robot J13-J30;
FIG. 5 is a schematic layout of a parallel six-axis robotic Hooke's joint assembly;
FIG. 6 is a schematic diagram of a parallel six-axis robot cross-axis assembly;
FIG. 7 is a schematic illustration of an arrangement of cross-shaft assemblies;
FIG. 8 is a cross-shaft schematic view of a Hooke's joint assembly;
FIG. 9 is a schematic illustration of a Hooke's joint assembly arrangement and establishment of a base coordinate system;
FIG. 10 is a schematic diagram of Hooke's joint position vector;
FIG. 11 is a schematic illustration of a cross-axis part;
FIG. 12 is a schematic diagram of a moving platform coordinate system setup;
FIG. 13 is a schematic diagram of the construction of the elements of the mobile platform;
FIG. 14 is a schematic view of a cross-axis origin;
fig. 15 is a schematic diagram of a PQ vector;
FIG. 16 is a schematic view of BQ vectors;
FIG. 17 is a schematic diagram of a { Q } coordinate system;
FIG. 18 is a schematic diagram of coordinates and vectors at a cross-axis assembly;
FIG. 19 is a diagram of Ο ΒΑ i A schematic diagram;
FIG. 20 is a schematic diagram of a { U } coordinate system;
FIG. 21 is a schematic view of angular vectors of the lug component and the cross-shaft housing;
FIG. 22 is a schematic view of angle vectors of the cross-shaft relative to the lower base and the upper base of the Hooke's joint;
FIG. 23 is a Hooke's hinge horizontal vector schematic;
FIG. 24 is a Hooke's hinge midpoint vector.
Detailed Description
As shown in fig. 2, the parallel six-axis robot according to the present invention includes a stationary platform 10, a movable platform 20, six hook assemblies, six electric cylinder assemblies and three cross-axis assemblies 50, wherein the hook assemblies are mounted on the stationary platform 10, the cross-axis assemblies 50 are mounted on the movable platform 20, one ends of the electric cylinder assemblies are mounted on the hook assemblies, and the other ends of the electric cylinder assemblies are rotatably connected to the cross-axis assemblies 50 through bearing pins.
The six electric cylinder assemblies are sequentially defined as a first electric cylinder assembly 41, a second electric cylinder assembly 42, a third electric cylinder assembly 43, a fourth electric cylinder assembly 44, a fifth electric cylinder assembly 45 and a sixth electric cylinder assembly 46 in a counterclockwise direction; the six hook assemblies are sequentially defined as a first hook assembly 31, a second hook assembly 32, a third hook assembly 33, a fourth hook assembly 34, a fifth hook assembly 35 and a sixth hook assembly 36; three cross-shaft assemblies 50 are defined in sequence as a first cross-shaft assembly 51, a second cross-shaft assembly 52 and a third cross-shaft assembly 53. The second and third cylinder assemblies 42, 43, the second and third hookes and the first cross axle assembly 51 form a first control assembly, one ends of the second and third cylinder assemblies 42, 43 are mounted on the second and third hookes assemblies 32, 33, respectively, and the other ends are connected to the first cross axle assembly 51. The fourth cylinder assembly 44, the fifth cylinder assembly 45, the fourth hook joint, the fifth hook joint and the second cross-shaft assembly 52 form a second control assembly, one end of the fourth cylinder assembly 44 and one end of the fifth cylinder assembly 45 are respectively arranged on the fourth hook joint assembly 34 and the fifth hook joint assembly 35, and the other end of the fourth cylinder assembly 44 and the fifth cylinder assembly 45 are connected to the second cross-shaft assembly 52. The sixth cylinder assembly 46, the first cylinder assembly 41, the sixth hook assembly 36, the first hook assembly 31, and the third cross shaft assembly 53 form a third control assembly, and one ends of the sixth cylinder assembly 46 and the first cylinder assembly 41 are respectively connected to the sixth hook assembly 36 and the first hook assembly 31, and the other ends are connected to the third cross shaft assembly 53.
Each Hooke's hinge assembly fixedly connected with the static platform is provided with 2 rotary joints so as to realize that the cylinder body of the electric cylinder assembly has 2 rotary degrees of freedom relative to the static platform and 12 rotary degrees of freedom, and the rotary shafts are J1-J12 in figure 3; each electric cylinder is provided with 1 translational joint, so that one translational degree of freedom of a piston rod of the electric cylinder relative to the cylinder body is realized, and 6 translational degrees of freedom are altogether provided, and the moving axis is shown as J13-J18 in figure 4; 2 single-shaft rotary joints are arranged at the bottom of each shaft lug part to realize that each shaft lug has 1 degree of freedom of rotation relative to 2 connected piston rods, and the total number of degrees of freedom of rotation is 6, and the rotary shafts are J19-J24 in figure 4; each cross-shaft assembly has 2 rotational joints that enable single axis rotation of the shaft ear relative to the cross-shaft housing, for a total of 3 degrees of freedom, with the rotational axes being J25-J27 in fig. 4. The cross shaft shell can also realize single-shaft rotation relative to the movable platform, and the total freedom is 3, and the rotation shafts are J28-J30 in FIG. 4. J25-J27 are perpendicular to J28-J30 in one-to-one correspondence. The rotational degrees of freedom described above can be achieved by designing a shafting mechanism, and the translational degrees of freedom described above are achieved using electric cylinders.
The Hooke's lower base of each Hooke's hinge subassembly all passes through the screw and is connected with quiet platform. The installation angle of the hook assembly is specific and can be considered as the arrangement of the hook rotation centers (B1-B6): (a) The intersection points (B1-B6) of the two rotation shafts of the cross shaft of the Hooke's joint assembly, namely the rotation centers of the Hooke's joints, B1-B6 should be arranged on a circle taking the point O as the center of a circle. (b) The angular bisectors OY1 of the images OB1 and OB2 are set to 120 ° for OY2 and OY3 and OY 1. OB3 and OB4 are axisymmetric with respect to ray OY2, and B5 and B6 are axisymmetric with respect to ray OY 3. (c) The fixed shaft axes of the cross shafts of the second and third hook assemblies should be at 30 degrees to the OY1 line, the fixed shaft axes of the cross shafts of the fourth and fifth hook assemblies should be at 90 degrees to the OY1 line, and the fixed shaft axes of the cross shafts of the hook assemblies 1 and 6 should be at 30 degrees to the OY1 line, as shown in fig. 5.
The Hooke hinge upper seat of each Hooke hinge assembly is connected with the electric cylinder through a screw. The pin hole axis of the pin shaft hole on the fork frame at the top end of the piston rod is parallel to the axis of the swing shaft of the Hooke hinge assembly.
Each cross shaft assembly is connected with the movable platform through a screw. The mounting position and mounting angle of the cross-shaft assembly on the movable platform are specific: (a) The intersection points of the axis of the central shaft and the cylindrical axis of the shaft lug are set as Q1-Q3, and correspond to the cross shaft assemblies 1-3 respectively. (b) And a P point is arranged on the movable platform, and Q1-Q3 are uniformly distributed on a circle taking the P point as a circle center. (c) the central axis should be perpendicular to OQ 1-OQ 3, respectively.
Based on the parallel six-axis robot, the invention discloses a pose inverse solution method of the parallel six-axis robot, which comprises two parts of geometric element and kinematic element construction and pose inverse solution process. The method comprises the following steps:
1. geometric element and kinematic element construction
This section is used to define the aggregate elements and build kinematic elements required in the parallel six-axis robot position inverse solution method of the present invention.
B i I=1 to 6 represents the origin of the hook, and B is as follows i The i=1 to 6 points are arranged in the center of the cross shaft of the Hooke joint. As shown in fig. 5 and 8.
{ O } is the base coordinate system. Establishing a rectangular coordinate system { O } on the static platform, and setting an origin O of the coordinate systemIs arranged at B 1 ～B 6 On a determined plane and located at B 1 ～B 6 The determined circle center position of the circle is arranged on the OB in the y-axis direction 1 ,OB 2 The angular bisector position of the line segment, at which time the six hook hinges are symmetrical with respect to the y-axis. The z axis is set up upwards and the x axis can be automatically determined according to the right hand rule, the final coordinate system as shown in fig. 9.
R b Representation B 1 ～B 6 The radius of the circle is determined, as shown in fig. 9, and is called the "hook virtual circle radius".
O OB 1 ～ O OB 6 Representing vector OB 1 ～OB 6 The representation with { O } as the reference frame is shown in FIG. 10. O OB i Called "Hooke's joint position vector", specifically refers to the ith Hooke's joint origin B starting from the base coordinate system origin O i I=1 to 6 is the vector of the end point, and the reference coordinate system is { O }.
β i I=1 to 6 represents O OB i The angle with the Y-axis of the base coordinate system { O } is shown in FIG. 10. Referred to as the "hook hinge offset angle".
U i The origin of the intersecting axis is that the axes of two cylindrical surfaces of the intersecting axis part form an intersection point, and the intersection point is U i I=1 to 3, as shown in fig. 11 and 20.
R Q The radius values of the circles determined by the three intersecting axis origins are shown in fig. 7. Referred to as the "cross-axis virtual circle radius".
{ P } is the moving platform coordinate system. And establishing a rectangular coordinate system { P } on the movable platform. Origin P of { P } is located at U i I=1 to 3, and is located on three U' s i The center position of the circle is determined. The y-axis of { P } is set as shown, where U 2 In the negative direction of the y-axis, U 1 ,U 3 Symmetrical with respect to the y-axis, the z-axis is oriented upwards and the x-axis can be determined using the right hand rule. As shown in fig. 12.
o D i I=1 to 3 are "cross axis transverse axis vectors", which are referenced to a base coordinate system, as shown in fig. 13.
δ i I=1 to 3 represents o D i The angle of the vector to the Y-axis of { P }, called o D i The angle of the vector distribution,as shown in fig. 13.
Q i I=1 to 3 represents the axial ear origin. Shaft lug part upper and U i The point where i=1 to 3 corresponds to and overlaps is Q i I=1 to 3, as shown in fig. 6, 14 to 15.
o BQ i I=1 to 6 is called "hook hinge-axis ear vector", and the reference system is the base coordinate system { O }, as shown in fig. 16.
{Q i I=1 to 3 and O R Qi i=1 to 3 each represents a rotation matrix of the "axial ear coordinate system" and the "axial ear coordinate system" with respect to the base coordinate system { O }. The origin of the coordinate system is fixedly connected with the origin Q of the shaft lug i ，{Q i The xyz three axes of are shown in figure 17,
the distribution angle of the original axle ear points is called as axle ear distribution angle,as shown in fig. 15.
P PQ i : the expression "position vector of the axis ear origin distributed on the moving platform with the moving platform coordinate system { P } as the reference system" is shown in fig. 15;
O OP is a given position, representing a position vector of an origin P of the moving platform coordinate system { P } with respect to an origin O of the stationary platform coordinate system, which is a known term, as shown in fig. 19;
O R P for a given pose, a rotation matrix of the moving platform coordinate system { P } relative to the stationary platform coordinate system { O } is represented, this term being a known term, as shown in FIG. 19;
A 1 ～A 6 indicating the pin hinge center. Zero at the shaft lugIn the piece 1 (the shaft lug part 2 and the shaft lug part 3), two pin hinge center points A 2 (Point A) 4 Point A 6 ) And point A 3 (Point A) 5 Point A 1 ) Relative to { Q 1 }({Q 2 }，{Q 3 Y-axis symmetrical arrangement of point a }) 2 (Point A) 4 Point A 6 ) And point A 3 (Point A) 5 Point A 1 ) Placed at { Q 1 }({Q 2 }，{Q 3 }) with QAX a 2 And A 3 In { Q 1 The absolute offset value of the X-axis direction of the X-axis is called "X-absolute offset value", and A is represented by QAY 2 And A 3 In { Q 1 The absolute offset value in the Y-axis direction of } is referred to as "Y absolute offset value". As shown in fig. 18 and 19.
Ο ΒΑ i : the representation is composed of O R P And O OP, the "cylinder position vector" obtained by the pose inverse solution algorithm is based on the base coordinate system { O } as the reference system, as shown in FIG. 19.
Qj QA i I=1 to 6,j =1 to 3: an axis ear-rotation center vector in an axis ear coordinate system { Q j And is the reference frame. Wherein the method comprises the steps of Q1 QA 2 ， Q1 QA 3 In { Q 1 In the process of }, Q2 QA 4 ， Q2 QA 5 in { Q 2 In the process of }, Q3 QA 1 ， Q3 QA 6 in { Q 3 And within. As shown in fig. 18 and 19.
O QA i I=1 to 6: the axial ear-rotation center vector takes a basic coordinate system { O } as a reference system. As shown in fig. 18.
Θ UQi : a vector of angular values representing the angle of the shaft ear piece to the cross-shaft housing, where i=1, 2,3, represents the angular value of the cross-shaft assembly at 3, such as shown in fig. 21;
Θ AOi : a vector of angular values representing the cross relative to the lower base of the hook, where i=1 to 6, represents the angular value of the hook assembly at 6, such as shown in fig. 22;
Θ ABi : indicating the cross axle relative to Hooke's jointAn angle value vector of the upper base, wherein i=1 to 6, represents the angle value of the hook component at 6, for example, as shown in fig. 22;
Θ UQM : representing Θ UQi A threshold value of (2);
Θ AOM : representing Θ AOi A threshold value of (2);
Θ ABM : representing Θ ABi A threshold value of (2);
BI 1 ～BI 3 : representing the hook hinge horizontal vector. A vector formed by connecting two hook origins: BI (BI) 1 Representation B 2 Pointing to B 3 Vectors of BI 2 Representation B 4 Pointing to B 5 Vectors of BI 3 Representation B 6 Pointing to B 1 Is a vector of (a). As shown in fig. 23.
OI 1 ～OI 3 : representing the hook hinge midpoint vector. A vector representing the origin of the base coordinate system pointing to the midpoint of the two hook hinges, where OI 1 Origin O of base coordinate system points to B 1 And B 6 Midpoint of the connection, OI 2 Origin O of base coordinate system points to B 2 And B 3 Midpoint of the connection, OI 3 Origin O of base coordinate system points to B 4 And B 5 The midpoint of the connection line. As shown in fig. 24.
2. Pose inverse solution process
Step 1: calculating vectors O OB 1 ～ O OB 6 . According to the ' Hooke ' virtual circle radius ' R b The Hooke's hinge position offset angle beta i, i=1-6, and then pass through R according to the coordinate rotation theorem in robotics theory b Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the Hooke hinge position vector O OB 1 ～ O OB 6 。
Step 2: calculating vectors P PQ i I=1 to 3. According to the 'cross-axis virtual circle radius' R Q Shaft lugThe origin distribution angle i=1 to 6, and then according to the coordinate rotation theorem in the robotics theory, the origin distribution angle i=1 to 6 passes through R Q Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the axis ear position vector P PQ i ，i＝1～3。
Step 3: calculating Hooke's hinge-axis ear vector o BQ i I=1 to 6. "given position" according to a known quantity " O OP, known quantity "given gesture" O R P The tab position vector PPQi obtained in step 2, i=1 to 3, the hook position vector obtained above O OB 1 ～ O OB 6 Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the robotics theory, the Hooke hinge-axial ear vector is obtained through the following formula o BQ i ,i＝1～6。
o BQ 1 ＝ O OP+ O R P * P PQ 3 - O OB 1
o BQ 2 ＝ O OP+ O R P * P PQ 1 - O OB 2
o BQ 3 ＝ O OP+ O R P * P PQ 1 - O OB 3
o BQ 4 ＝ O OP+ O R P * P PQ 2 - O OB 4
o BQ 5 ＝ O OP+ O R P * P PQ 2 - O OB 5
o BQ 6 ＝ O OP+ O R P * P PQ 3 - O OB 6
Step 4: calculating the crossoverAxis-transverse axis vector o D i I=1 to 3, and is obtained as follows: "given pose" according to a known quantity " O R P Vector distribution angle delta i Then according to the coordinate rotation theorem in the robotics theory, through " O R P Multiplying the Y-axis unit vector by the rotation angle matrix calculation formula around the Z axis to obtain a cross axis transverse axis vector o D i ，i＝1～3。
Step 5: calculation of O R Qi I=1 to 3. Can be expressed as O R Qi ＝[ O x Qi O y Qi O z Qi ]， O x Qi ， O y Qi ， O z Qi Is a split axis of a rectangular coordinate system and accords with the right hand rule, so that the following needs to be respectively calculated: [ O x Q1 O y Q1 O z Q1 ]，[ O x Q2 O y Q2 O z Q2 ]，[ O x Q3 O y Q3 O z Q3 ]9 factors in total. According to Hooke's hinge-axis ear vector o BQ 3 And o BQ 2 by cross-multiplication of vectors o BQ 3 ×(- o BQ 2 ) Find modulo| o BQ 3 ×(- o BQ 2 ) After division calculation, the components can be obtained o z Q1 The method comprises the steps of carrying out a first treatment on the surface of the According to the previous step o z Q1 And the cross axis transverse axis vector obtained as described above o D 1 By cross-multiplication of vectors o z Q1 × o D 1 Find modulo| o z Q1 × o D 1 After division calculation, the components can be obtained o y Q1 . From the Z component and Y component obtained above, the components can be obtained according to the right hand rule o x Q1 . Is obtained by the same method o x Q2 o y Q2 o z Q2 o x Q3 o y Q3 o z Q3 . The specific formula can be obtained as follows:
/>
step 6: calculation of Qj QA i ，i＝1～6,j＝1～3：
Q3 QA 1 ＝ Q1 QA 3 ＝ Q2 QA 5 ＝[-QAX -QAY 0] T
Q1 QA 2 ＝ Q2 QA 4 ＝ Q3 QA 6 ＝[QAX QAY 0] T
Step 7: calculation of O QA i I=1 to 6. Rotation matrix of the shaft ear coordinate system obtained by using the above o R Qi I=1 to 3, and the above-obtained axial lug-rotation center vector Qj QA i I=1 to 6,j =1 to 3, and the coordinate transformation theorem in the robot kinematics theory is adopted o R Qi Multiplied by Qj QA i Can calculate the axial ear-rotation center vector taking the base coordinate system { O } as the reference system " Qj QA i ，i＝1～6。
O QA 1 ＝ O R Q3 * Q3 QA 1
O QA 2 ＝ O R Q1 * Q1 QA 2
O QA 3 ＝ O R Q1 * Q1 QA 3
O QA 4 ＝ O R Q2 * Q2 QA 4
O QA 5 ＝ O R Q2 * Q2 QA 5
O QA 6 ＝ O R Q3 * Q3 QA 6
Step 8: solving for O BA i I=1 to 6, using the obtained axial ear-rotation center vector with the reference system { O } as the reference system Qj QA i I=1 to 6 and the hook-axis ear vector obtained as described above o BQ i And i=1 to 6, and then using the basic operation of the vector, the cylinder position vector can be obtained by the following formula, and the vector is the position inverse solution. The method can be obtained by the following formula:
O BA i ＝ O BQ i + O QA i
wherein i=1 to 6.
Step 9: calculating Θ UQi I=1 to 3, which angle can be expressed as a cross axis-transversal axis vector O D i And the x-axis direction of the axis ear coordinate system O x Qi Is included in the bearing. The method can be obtained by the following formula:
Θ UQ1 ＝arccos( O D 1 · O x Q1 )
Θ UQ2 ＝arccos( O D 2 · O x Q2 )
Θ UQ3 ＝arccos( O D 3 · O x Q3 )
step 10: judging theta UQi Whether or not it satisfies a threshold value smaller than a threshold value set in advance, namely Θ UQi ≤Θ UQΜ I=1 to 3, if not, stopping the solving process and reporting abnormality;
step 11: calculating Θ ABi I=1 to 3, and can be obtained by the following formula.
/>
Step 12: judging theta ABi Whether or not to satisfy a threshold value theta smaller than a preset value ABM I.e. theta ABi ≤Θ ABΜ I=1 to 6, if not, stopping the solving process and reporting an abnormality;
step 13: calculating OI i I=1 to 3, which can be obtained by the following formula:
step 14: calculating Θ AOi I=1 to 6, and can be obtained by the following formula.
Step 15: judging theta AOi Whether or not to satisfy a threshold value theta smaller than a preset value AOM I.e. theta AOi ≤Θ AOΜ I=1 to 6, if not, stopping the solving process and reporting the abnormality.
In summary, the invention gives the structural parameters of the parallel six-axis robot, and the position of the terminal moving platform coordinate system relative to the static platform base coordinate system O OP and attitude value O R P Solving for the extension of the cylinder piston rod (cylinder position vector Ο ΒΑ i ) At the same time, satisfies fifteen angle values (Θ UQi ，Θ AOi ，Θ ABi ) The working space of the tail end static platform of the robot can be limited by limiting the fifteen angle values within the preset threshold range, so that the working space of the robot is increased to the maximum extent; meanwhile, when the static platform reaches a designated pose, the parallel six-axis robot can bear the designed rated load in the working space range.
The foregoing embodiments of the present invention are not intended to limit the technical scope of the present invention, and therefore, any minor modifications, equivalent variations and modifications made to the above embodiments according to the technical principles of the present invention still fall within the scope of the technical proposal of the present invention.
Claims (9)
1. A parallel six-axis robot pose inverse solution method is characterized in that: the six-axis robot comprises a static platform, a movable platform, six Hooke hinge assemblies, six electric cylinder assemblies and three cross shaft assemblies, wherein the Hooke hinge assemblies are arranged on the static platform, the cross shaft assemblies are arranged on the movable platform, one end of each electric cylinder assembly is arranged on each Hooke hinge assembly, and the other end of each electric cylinder assembly is rotationally connected to the cross shaft assembly through a bearing pin shaft;
the method comprises the following steps:
1. constructing geometric elements and kinematic elements;
B i i=1 to 6 represents the origin of the hook, and B is as follows i I=1 to 6 points are arranged in the center of a cross shaft of the Hooke joint;
{ O } is the base coordinate system; establishing a rectangular coordinate system { O } on the static platform, and setting an origin O of the coordinate system at B 1 ～B 6 On a determined plane and located at B 1 ～B 6 The determined circle center position of the circle is arranged on the OB in the y-axis direction 1 ,OB 2 The angular bisector position of the line segment, at this time, the six hook hinges are symmetrical relative to the y axis; the z axis is arranged upwards, and the x axis can be automatically determined according to a right-hand rule;
R b representation B 1 ～B 6 The radius of the determined circle is called the 'hook hinge virtual circle radius';
O OB 1 ～ O OB 6 representing vector OB 1 ～OB 6 A representation with { O } as a reference frame; O OB i called "Hooke's joint position vector", specifically refers to the ith Hooke's joint origin B starting from the base coordinate system origin O i I=1 to 6 is a vector of the end point;
β i i=1 to 6 represents O OB i The angle with the Y-axis of the base coordinate system { O } is referred to as the "Hooke's hinge offset angle";
U i the origin of the intersecting axis is that the axes of two cylindrical surfaces of the intersecting axis part form an intersection point, and the intersection point is U i ，i＝1～3；
R Q Radius values representing circles determined by three intersecting axis origins are referred to as "intersecting axis virtual circle radii";
{ P } is the moving platform coordinate system; establishing a rectangular coordinate system { P }, wherein the origin P of { P } is positioned at U on the movable platform i I=1 to 3, and is located on three U' s i The circle center position of the circle is determined; u (U) 2 In the negative direction of the y-axis, U 1 ,U 3 Symmetrical with respect to the y-axis, the z-axis is upward, and the x-axis can be determined by right-hand rules;
o D i i=1 to 3 is a "cross axis transverse axis vector", which takes a base coordinate system as a reference system;
δ i i=1 to 3 represents o D i The angle of the vector to the Y-axis of { P }, called o D i Vector distribution angle;
Q i i=1 to 3 represents the origin of the lug, which means the sum U on the lug part i I=1 to 3 corresponds to the overlapping point;
o BQ i i=1 to 6 is called a "hook hinge-axis ear vector", and a base coordinate system { O } is used as a reference system;
{Q i i=1 to 3 and O R Qi i=1 to 3 each represents "an axis ear coordinate system" and "a rotation matrix of the axis ear coordinate system with respect to the base coordinate system { O };
the distribution angle of the shaft lug original points is called as a shaft lug distribution angle;
P PQ i : the expression "position vector of the axis ear origin distributed on the moving platform with the moving platform coordinate system { P } as the reference system";
O OP is a given position, and represents a position vector of an origin P of the moving platform coordinate system { P } relative to an origin O of the static platform coordinate system;
O R P for a given pose, representing a rotation matrix of the moving platform coordinate system { P } relative to the stationary platform coordinate system { O };
A 1 ～A 6 representing the hinge center of the pin shaft; hinge center point A of two pin shafts 2 And A 3 、A 4 And A 5 、A 6 And A 1 Relative to { Q i Y-axis symmetrical arrangement, denoted A by QAX 2 And A 3 、A 4 And A 5 、A 6 And A 1 In { Q i The absolute offset value of the X-axis direction of the X-axis is called "X-absolute offset value", and A is represented by QAY 2 And A 3 、A 4 And A 5 、A 6 And A 1 In { Q i An absolute offset value in the Y-axis direction of }, referred to as "Y absolute offset value";
Ο ΒΑ i : the representation is composed of O R P And O OP, according to the "electric cylinder position vector" obtained by the pose inverse solution algorithm, taking a base coordinate system { O } as a reference system;
QjQA i i=1 to 6,j =1 to 3: an axis ear-rotation center vector in an axis ear coordinate system { Q j Is a reference frame in which Q1 QA 2 ， Q1 QA 3 In { Q 1 In the process of }, Q2 QA 4 ， Q2 QA 5 in { Q 2 In the process of }, Q3 QA 1 ， Q3 QA 6 in { Q 3 Inner part;
O QA i i=1 to 6: an axial ear-rotation center vector, taking a base coordinate system { O } as a reference system; theta (theta) UQi A vector of angular values representing the shaft ear piece and the cross-shaft housing, wherein i = 1,2,3, represents the angular values of 3 cross-shaft assemblies;
Θ AOi an angle value vector of the cross shaft relative to the Hooke's lower base is represented, wherein i=1-6, and the angle value of the Hooke's assembly at 6 is represented;
Θ ABi indicating the cross axle relative toAn angle value vector of a base on the Hooke hinge, wherein i=1-6, and the angle value of the Hooke hinge assembly at 6 positions is represented;
Θ UQM : representing Θ UQi A threshold value of (2); theta (theta) AOM : representing Θ AOi A threshold value of (2); theta (theta) ABM : representing Θ ABi A threshold value of (2);
BI 1 ～BI 3 : representing Hooke's hinge horizontal vector, representing the vector formed by connecting two Hooke's hinge origins; BI (BI) 1 Representation B 2 Pointing to B 3 Vectors of BI 2 Representation B 4 Pointing to B 5 Vectors of BI 3 Representation B 6 Pointing to B 1 Is a vector of (2);
OI 1 ～OI 3 representing a Hooke's joint midpoint vector, representing a vector whose base coordinate system origin points to the midpoint of two Hooke joints, where OI 1 Origin O of base coordinate system points to B 1 And B 6 Midpoint of the connection, OI 2 Origin O of base coordinate system points to B 2 And B 3 Midpoint of the connection, OI 3 Origin O of base coordinate system points to B 4 And B 5 A midpoint of the connection line;
2. pose inverse solution process
Step 1: calculating vectors O OB 1 ～ O OB 6 The method comprises the steps of carrying out a first treatment on the surface of the According to the ' Hooke ' virtual circle radius ' R b The Hooke's hinge position offset angle beta i, i=1-6, and then pass through R according to the coordinate rotation theorem in robotics theory b Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the Hooke hinge position vector O OB 1 ～ O OB 6 ；
Step 2: calculating vectors P PQ i I=1 to 3; according to the 'cross-axis virtual circle radius' R Q The distribution angle of the axis ear origin is i=1-6, and then the axis ear origin passes through R according to the coordinate rotation theorem in the robotics theory Q Multiplying the rotation angle matrix calculation formula around the Z axis by the Y axis unit vector to obtain the axis ear position vector P PQ i ，i＝1～3；
Step 3: calculating Hooke's hinge-ear(Vector) o BQ i I=1 to 6; "given position" according to a known quantity " O OP, known quantity "given gesture" O R P The tab position vector PPQi obtained in step 2, i=1 to 3, the hook position vector obtained above O OB 1 ～ O OB 6 Then according to the coordinate rotation theorem and the basic operation theorem of the vector in the robotics theory, the Hooke hinge-axial ear vector is obtained through the following formula o BQ i ,i＝1～6；
Step 4: computing cross axis vectors o D i I=1 to 3, and is obtained as follows: "given pose" according to a known quantity " O R P Vector distribution angle delta i Then according to the coordinate rotation theorem in the robotics theory, through " O R P Multiplying the Y-axis unit vector by the rotation angle matrix calculation formula around the Z axis to obtain a cross axis transverse axis vector o D i ，i＝1～3；
Step 5: calculation of O R Qi I=1 to 3, expressed as O R Qi ＝[ O x Qi O y Qi O z Qi ]， O x Qi ， O y Qi ， O z Qi Is a split axis of a rectangular coordinate system and accords with the right hand rule, so that the following needs to be respectively calculated: [ O x Q1 O y Q1 O z Q1 ]，[ O x Q2 O y Q2 O z Q2 ]，[ O x Q3 O y Q3 O z Q3 ]9 factors in total; according to Hooke's hinge-axis ear vector, the components can be obtained through the calculation of the cross multiplication, modulo and division of the vector o z Q1 The method comprises the steps of carrying out a first treatment on the surface of the According to the previous step o z Q1 And the cross axis transverse axis vector obtained as described above o D 1 By cross-multiplication of vectors o z Q1 × o D 1 Find modulo| o z Q1 × o D 1 After division calculation, the components can be obtained o y Q1 The method comprises the steps of carrying out a first treatment on the surface of the According to the upper partThe obtained Z component and Y component can obtain components according to the right hand rule o x Q1 The method comprises the steps of carrying out a first treatment on the surface of the Is obtained by the same method o x Q2 o y Q2 o z Q2 o x Q3 o y Q3 o z Q3 ；
Step 6: calculation of Qj QA i ，i＝1～6，j＝1～3：
Q3 QA 1 ＝ Q1 QA 3 ＝ Q2 QA 5 ＝[-QAX -QAY 0] T
Q1 QA 2 ＝ Q2 QA 4 ＝ Q3 QA 6 ＝[QAX QAY 0] T
Step 7: calculation of O QA i I=1 to 6; rotation matrix of the shaft ear coordinate system obtained by using the above o R Qi I=1 to 3, and the above-obtained axial lug-rotation center vector Qj QA i I=1 to 6,j =1 to 3, and the coordinate transformation theorem in the robot kinematics theory is adopted o R Qi Multiplied by Qj QA i Can calculate the axial ear-rotation center vector taking the base coordinate system { O } as the reference system " Qj QA i ，i＝1～6；
Step 8: solving for O BA i I=1 to 6; using the obtained axial ear-rotation center vector with the base coordinate system { O } as a reference system Qj QA i I=1 to 6 and the hook-axis ear vector obtained as described above o BQ i I=1 to 6, and then using basic operation of vectors, the position vector of the electric cylinder can be obtained by the following formula, and the vector is a position inverse solution;
step 9: calculating Θ UQi I=1 to 3, the included angle being expressed as a cross axis transverse axis vector O D i And the x-axis direction of the axis ear coordinate system O x Qi Is included in the plane of the first part; the method is obtained by the following formula:
Θ UQ1 ＝arccos( O D 1 · O x Q1 )
Θ UQ2 ＝arccos( O D 2 · O x Q2 )
Θ UQ3 ＝arccos( O D 3 · O x Q3 )
step 10: judging theta UQi Whether or not it satisfies a threshold value smaller than a threshold value set in advance, namely Θ UQi ≤Θ UQΜ I=1 to 3, if not, stopping the solving process and reporting abnormality;
step 11: calculating Θ ABi I=1 to 3, which can be obtained by the following formula:
step 12: judging theta ABi Whether or not to satisfy a threshold value theta smaller than a preset value ABM I.e. theta ABi ≤Θ ABΜ I=1 to 6, if not, stopping the solving process and reporting an abnormality;
step 13: calculating OI i I=1 to 3, which can be obtained by the following formula:
step 14: calculating Θ AOi I=1 to 6, and can be obtained by the following formula:
step 15: judging theta AOi Whether or not to satisfy less than advanceSet threshold value theta AOM I.e. theta AOi ≤Θ AOΜ I=1 to 6, if not, stopping the solving process and reporting the abnormality.
2. The parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: o D i the vector distribution angle is:
the distribution angle of the axle ear original points is:
3. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 1, the vector O OB 1 ～ O OB 6 The expression is as follows:
4. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 2, the vector P PQ i The expression of i=1 to 3 is as follows:
5. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 3, hooke's joint-axis ear vector o BQ i The expression of i=1 to 6 is as follows:
o BQ 1 ＝ O OP+ O R P * P PQ 3 - O OB 1
o BQ 2 ＝ O OP+ O R P * P PQ 1 - O OB 2
o BQ 3 ＝ O OP+ O R P * P PQ 1 - O OB 3
o BQ 4 ＝ O OP+ O R P * P PQ 2 - O OB 4
o BQ 5 ＝ O OP+ O R P * P PQ 2 - O OB 5
o BQ 6 ＝ O OP+ O R P * P PQ 3 - O OB 6 。
6. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 4, the cross axis and the horizontal axis vector o D i The expression of i=1 to 3 is as follows:
7. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 5 of the above-mentioned process, O R Qi each factor expression of i=1 to 3 is as follows:
O x Q1 ＝ O y Q1 × O z Q1
O x Q3 ＝ O y Q3 × O z Q3
O x Q3 ＝ O y Q3 × O z Q3 。
8. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 7 of the above-mentioned process, O QA i the expression of i=1 to 6 is as follows:
O QA 1 ＝ O R Q3 * Q3 QA 1
O QA 2 ＝ O R Q1 * Q1 QA 2
O QA 3 ＝ O R Q1 * Q1 QA 3
O QA 4 ＝ O R Q2 * Q2 QA 4
O QA 5 ＝ O R Q2 * Q2 QA 5
O QA 6 ＝ O R Q3 * Q3 QA 6
9. the parallel six-axis robot pose inverse solution method according to claim 1, wherein the method comprises the following steps: in the step 8 of the above-mentioned process, O BA i the expression of i=1 to 6 is as follows:
O BA i ＝ O BQ i + O QA i
wherein i=1 to 6.
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