CN113967906B - Parallel six-axis robot position and posture correction method based on additional encoder - Google Patents

Parallel six-axis robot position and posture correction method based on additional encoder Download PDF

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CN113967906B
CN113967906B CN202111408697.2A CN202111408697A CN113967906B CN 113967906 B CN113967906 B CN 113967906B CN 202111408697 A CN202111408697 A CN 202111408697A CN 113967906 B CN113967906 B CN 113967906B
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axis
electric cylinder
coordinate system
hooke
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CN113967906A (en
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郭鹏
刘珍亮
谢双胜
黄朋生
潘桐
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Borunte Robot Co Ltd
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Borunte Robot Co Ltd
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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
    • 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
    • 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning

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Abstract

The invention relates to a parallel six-axis robot position and posture correction method based on an additional encoder, which is characterized in that five angle encoders are arranged at specific joints of a robot, angle values of 5 positions can be additionally read, and the position and posture values of a movable platform coordinate system relative to a static platform base coordinate system are solved by combining structural parameters of a given parallel six-axis robot and the elongation of an electric cylinder piston rod at any moment. Because more information can be obtained through five encoders, the difficulty of solving a positive solution can be reduced, and in the operation process, only elementary matrix multiplication operation, namely simple multiplication and addition operation, is performed, so that the calculation efficiency is effectively improved.

Description

Parallel six-axis robot position and posture correction method based on additional encoder
Technical Field
The invention relates to the technical field of industrial robots, in particular to a parallel six-axis robot position and posture correction method based on an additional encoder.
Background
The parallel robot is a robot with a brand new structure, has the advantages of higher rigidity, higher precision, better bearing capacity and the like compared with the traditional industrial robot, and almost relates to many fields of modern advanced technology. The method 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 the motion analysis of the parallel robot, the positions of the driving parts are given, and the pose of the moving platform is solved to obtain a pose positive solution, which has profound significance for the working space analysis and the error compensation of the robot mechanism. The position and attitude information of the movable platform can be used for limiting the working position of the movable platform of the robot, namely the control system continuously judges the position and attitude in the running process, and when the position and attitude information exceeds the set limit of a user, the robot is alarmed and stopped.
The existing parallel robot pose positive solution method has large calculation amount and low calculation efficiency.
Disclosure of Invention
The invention aims to provide a parallel six-axis robot pose correction method based on an additional encoder, so as to reduce the calculation amount of pose correction solution and improve the calculation efficiency.
In order to achieve the purpose, the invention adopts the technical scheme that:
a parallel six-axis robot position and posture correction method based on an additional encoder comprises a static platform, a movable platform, six hook hinge assemblies, six electric cylinder assemblies and three cross shaft assemblies, wherein the hook hinge assemblies are mounted on the static platform, the cross shaft assemblies are mounted on the movable platform, one ends of the electric cylinder assemblies are mounted on the hook hinge assemblies, and the other ends of the electric cylinder assemblies are rotatably connected to the cross shaft assemblies through bearing pin shafts;
the six electric cylinder assemblies are sequentially defined as a first electric cylinder assembly, a second electric cylinder assembly, a third electric cylinder assembly, a fourth electric cylinder assembly, a fifth electric cylinder assembly and a sixth electric cylinder assembly in the anticlockwise direction; the six Hooke joint components are sequentially defined as a first Hooke joint component, a second Hooke joint component, a third Hooke joint component, a fourth Hooke joint component, a fifth Hooke joint component and a sixth Hooke joint component; the three cross shaft assemblies are sequentially defined as a first cross shaft assembly, a second cross shaft assembly and a third cross shaft assembly; the second electric cylinder assembly, the third electric cylinder assembly, the second hook joint, the third hook joint and the first cross shaft assembly form a first control assembly, one end of the second electric cylinder assembly and one end of the third electric cylinder assembly are respectively arranged on the second hook joint assembly and the third hook joint assembly, and the other end of the second electric cylinder assembly and one end of the third electric cylinder assembly are connected to the first cross shaft assembly; a fourth electric cylinder assembly, a fifth electric cylinder assembly, a fourth hook joint, a fifth hook joint and a second cross shaft assembly form a second control assembly, one end of the fourth electric cylinder assembly and one end of the fifth electric cylinder assembly are respectively arranged on the fourth hook joint assembly and the fifth hook joint assembly, and the other end of the fourth electric cylinder assembly and one end of the fifth electric cylinder assembly are connected to the second cross shaft assembly; a sixth electric cylinder assembly, a first electric cylinder assembly, a sixth hook joint assembly, a first hook joint assembly and a third cross shaft assembly form a third control assembly, one end of the sixth electric cylinder assembly and one end of the first electric cylinder assembly are respectively connected with the sixth hook joint assembly and the first hook joint assembly, and the other end of the sixth electric cylinder assembly and one end of the first electric cylinder assembly are connected with the third cross shaft assembly;
the method comprises the following steps:
firstly, five angle encoders are mounted on an optional group of a first control assembly, a second control assembly and a third control assembly of the robot to read joint angle values;
specifically, an angle encoder is respectively arranged on a Hooke joint upper base and a Hooke joint lower base of a left Hooke joint assembly of the selected control assembly, and is recorded as a first angle encoder and a second angle encoder, and the angle encoders are used for measuring the rotating angles of a fixed shaft part and a swinging shaft part of the Hooke joint assembly relative to the Hooke joint lower base and the Hooke joint upper base respectively and are recorded as j theta 1 And j θ 2 (ii) a An angle encoder is arranged on a Hooke joint upper base of a Hooke joint assembly on the right side of the selected control assembly and is recorded as a third angle encoder; the method is used for measuring the rotation angle of the swing shaft part of the Hooke joint relative to the Hooke joint upper base of the Hooke joint assembly and is recorded as j theta 3 (ii) a An angle encoder is arranged in the cross shaft assembly of the selected control assembly and is recorded as a fourth angle encoder for measuring the angle value of the shaft part of the shaft lug of the cross shaft assembly relative to the cross shaft shell and recorded as j theta 4 (ii) a An angle encoder is arranged at the position, connected with the selected control assembly, of the movable platform, is recorded as a fifth angle encoder and is used for measuring the rotation angle value of the movable platform relative to the cross shaft assembly, and is recorded as j theta 5 ；
Then, solving the pose of the moving platform according to the following steps:
s1, constructing kinematic elements of a parallel six-axis robot;
B i i = 1-6 is a Hooke hinge origin which is respectively arranged at the centers of the cross shafts of the six Hooke hinge components;
establishing a base coordinate system { O } on the static platform, wherein the origin O of the coordinate system is set at B 1 ～B 6 On a certain plane and located at B 1 ～B 6 Determining the circle center position of the circle; in the y-axis direction atOB 1 ,OB 2 The angular bisector position of the line segment is set, the z axis is upward, and the x axis is determined according to the right-hand rule; r b Is represented by B 1 ～B 6 The radius of the determined circle is called as the radius of the virtual circle of the Hooke's hinge; O OB 1 ～ O OB 6 ： O OB i the position vector of the Hooke's joint is expressed, specifically, the ith Hooke's joint origin B is expressed by taking the origin of the base coordinate system as the starting point i I = 1-6 as the vector of the terminal point, and the reference coordinate system is a base coordinate system;
β i i =1 to 6 is a hook hinge offset angle, indicating O OB i An angle to the Y-axis of the base coordinate system { O };
R Q the radius is called as the virtual circle radius of the crossed shaft and represents the radius value of the circle determined by the original points of the three crossed shaft components;
Q i i = 1-3 is the origin of the axle ear of the cross axle assembly, the upper part of the axle ear is U i I =1 to 3 corresponds to the overlapping point and is set as Q i ，i＝1～3；
{Q i I = 1-3 represents an axis ear coordinate system, and the origin of the coordinate system is fixedly connected with the origin Q of the axis ear i ，{Q i The z axis of the hinge is along the axis direction of the shaft part of the shaft lug, the y axis is along the connecting line direction of two points of the hinge of the pin shaft, and the x axis is determined according to the right-hand rule;
U i i = 1-3 is the origin of the crossed shaft, and the axes of the two cylindrical surfaces of the crossed shaft part form an intersection point;
{U i i =1 to 3, and represents a cross-axis coordinate system whose origin is a cross-axis origin U i The z-axis is along the axial direction of the shaft part of the shaft lug, the y-axis is along the axial direction of the central shaft, and the x-axis is determined according to the right-hand rule;
{ P } is a moving platform coordinate system, and the origin P of the coordinate system { P } is located at U i I =1 to 3 on a plane defined by three U' s i Determining the circle center position of the circle; the y-axis of the coordinate system { P } is set as: u shape 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 is determined by a right-hand rule;
Figure BDA0003364332160000031
i =1 to 3 represents the distribution angle of the pivot points
Figure BDA0003364332160000032
O OP position of the movable platform, which represents the position vector of the origin P of the movable platform coordinate system { P } relative to the origin O of the stationary platform coordinate system;
O R P representing a rotation matrix of a movable platform coordinate system { P } relative to a static platform coordinate system { O } for the attitude of the movable platform;
A 1 ～A 6 is the hinge center of the pin shaft, A 2 And A 3 Corresponding to the first cross-shaft assembly, A 4 And A 5 Corresponding to the second cross-shaft assembly, A 6 And A 1 Corresponding to the third cross shaft assembly;
Ο ΒΑ i representing the position vector of the electric cylinder, and taking a base coordinate system { O } as a reference system;
s2, on the cross shaft of the second hook joint component, using the center B of the cross shaft 2 Establishing a Hooke coordinate system { B2} for an origin, wherein the origin is fixed at the center of the cross shaft, namely the intersection point of the axis of the fixed shaft part and the axis of the swinging shaft part, the y-axis of the Hooke coordinate system { B2} is pointed to a Hooke assembly at the right end along the axis of the fixed shaft part, the z-axis is the same as the z-axis of { O }, and the x-axis can be obtained by right-hand determination;
s3, establishing an electric cylinder coordinate system { L2} on a Hooke joint upper base of the second Hooke joint component, wherein the origin of the electric cylinder coordinate system is superposed with the origin of the Hooke joint coordinate system { B2}, the z axis is vertical to a plane determined by the axis of the fixed shaft part and the axis of the swinging shaft part of the second Hooke joint component and faces upwards, the x axis faces the same direction as the x axis of the { B2} along the axis of the swinging shaft part, and the y axis can be obtained by right-hand rule;
s4, center B of second hook joint component 2 From the center B of the third Hooke's hinge component 3 Is denoted by b 23 ：
Figure BDA0003364332160000033
S5, solving the pose of the { B2} coordinate system by taking the { O } as a reference system: O P B2 indicates the position of the origin of B2, O R B2 indicating the attitude of B2, O T B2 representing a pose matrix;
Figure BDA0003364332160000041
s6, solving the pose of the electric cylinder coordinate system (L2) by taking (O) as a reference system, B2 R L2 indicating the attitude of L2 with respect to B2, O T L2 representing a pose matrix:
Figure BDA0003364332160000042
Figure BDA0003364332160000043
O T L2 and the 1 st to 3 rd rows and the 1 st to 3 rd columns of O R L2 ；
S7, using { O } as reference system, solving A 2 Position of the point:
Figure BDA0003364332160000044
s8, solving A by taking { O } as a reference system 3 Position of the point:
Figure BDA0003364332160000045
s9, solving for { Q 1 Pose with respect to { O }, using O T Q1 It is shown that, L2 N 23 the vector indicating the point A2 points to the point A3, using { L2} as the reference system,
L2 N 23 ＝ L2 P A3 - L2 P A2 ；
solving a rule according to a normal vector of the two-dimensional vector, and L2 N 23 the unit vector of the vertical is L2 N ⊥23 ；
α 23 Represent L2 N 23 And z-axis of { L2}, i.e. vector z L2 ＝[0 0 1] T An included angle value;
L2 A o23 is represented by A 2 Point sum A 3 A center point position vector of the point;
L2 P Q1 a position vector representing the origin of { Q1} in a { L2} coordinate system;
Figure BDA0003364332160000051
s10, solving { U 1 Pose with respect to { O }, using O T U1 Represents:
Figure BDA0003364332160000052
Q1 P U1 ＝[0 0 0]
Figure BDA0003364332160000053
s12, solving for { P 1 Pose with respect to { O }, using O T P1 It is shown that,
Figure BDA0003364332160000054
s13, solving O OP and O R P ：
P1 P P ＝[-R Q 0 0]
Figure BDA0003364332160000061
Figure BDA0003364332160000062
O T P the matrix formed by the 1 st to 3 rd rows and the 1 st to 3 rd columns is O R P ， O T P The vector formed by the 1 st to 3 rd lines and the 4 th column of (A) is O OP。
After the scheme is adopted, the five angle encoders are arranged at the specific joints of the robot, the angle values of 5 positions can be additionally read, and the position and attitude values of the movable platform coordinate system relative to the static platform base coordinate system are solved by combining the structural parameters of the given parallel six-axis robot and the elongation of the electric cylinder piston rod at any moment. Because more information can be obtained through five encoders, the difficulty of solving a positive solution can be reduced, and in the operation process, only elementary matrix multiplication operation, namely simple multiplication and addition operation, is performed, so that the calculation efficiency is effectively improved.
Drawings
FIG. 1 is a general assembly view of a parallel six-axis robot of the present invention;
FIG. 2 is an exploded view of the assembly of the parallel six-axis robot of the present invention;
FIG. 3 is a schematic view of the robot rotation axes J1-J12 of the present invention;
FIG. 4 is a schematic view of the robot rotation axis J13-J30 according to the present invention;
FIG. 5 is a layout view of a hook joint assembly of the present invention;
FIG. 6 is a schematic view of a cross of the present invention;
FIG. 7 is a schematic structural view of a cross-shaft assembly of the present invention;
FIG. 8 is a layout view of the cross-shaft assembly of the present invention;
FIG. 9 is a schematic diagram of the establishment of a base coordinate system according to the present invention;
FIG. 10 is a schematic view of a Hooke's hinge position vector according to the present invention;
FIG. 11 is a schematic view of the origin of the cross-axis of the present invention;
FIG. 12 is a schematic diagram of the mobile platform coordinate system setup according to the present invention;
FIG. 13 is a schematic diagram of the establishment of various elements on the mobile platform according to the present invention;
FIG. 14 is a schematic diagram of the origin of the cross-axis of the present invention;
FIG. 15 is a diagram of a PQ vector according to the present invention;
FIG. 16 is a schematic view of the Q-coordinate system of the present invention;
FIG. 17 is a schematic diagram of the elements of the Q-coordinate system of the present invention;
FIG. 18 shows the present invention Ο ΒΑ i A schematic diagram;
FIG. 19 is a schematic view of a U coordinate system of the present invention;
FIG. 20 is a schematic view of an angular encoder measurement of the present invention;
FIG. 21 is a schematic view of the installation of the angular encoder of the present invention;
FIG. 22 is a schematic diagram illustrating the establishment of a coordinate system at a second hook-and-loop assembly according to an embodiment of the present invention;
FIGS. 23-24 are schematic diagrams illustrating the establishment of a coordinate system at a first cross-axle assembly in an embodiment of the present invention;
FIG. 25 is a flow chart of the present invention.
Description of reference numerals:
a stationary platform 10;
a movable platform 20;
a first hook hinge assembly 31; a second hook hinge assembly 32; a third hook hinge assembly 33; a fourth hook hinge assembly 34; a fifth hook hinge assembly 35; a sixth hook hinge assembly 36;
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; a sixth electric cylinder assembly 46;
a cross-shaft assembly 50; a first cross-shaft assembly 51; a second cross-shaft assembly 52; third cross-shaft assembly 53;
a first angle encoder 61; a second angle encoder 62; a third angle encoder 63; a fourth angle encoder 64; a fifth angular encoder 65.
Detailed Description
Referring to fig. 1 and 2, the parallel six-axis robot of the present invention includes a static platform 10, a dynamic platform 20, six hooke joint assemblies, six electric cylinder assemblies, and three crossing axis assemblies 50, wherein the hooke joint assemblies are mounted on the static platform 10, the crossing axis assemblies 50 are mounted on the dynamic platform 20, one end of the electric cylinder assemblies is mounted on the hooke joint assemblies, and the other end of the electric cylinder assemblies is rotatably connected to the crossing axis assemblies 50 through force-bearing pin shafts.
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 the anticlockwise direction; the six Hooke joint components are sequentially defined as a first Hooke joint component 31, a second Hooke joint component 32, a third Hooke joint component 33, a fourth Hooke joint component 34, a fifth Hooke joint component 35 and a sixth Hooke joint component 36; the three cross-shaft assemblies 50 are defined in turn as a first cross-shaft assembly 51, a second cross-shaft assembly 52 and a third cross-shaft assembly 53. The second electric cylinder assembly 42, the third electric cylinder assembly 43, the second hooke joint, the third hooke joint and the first cross shaft assembly 51 form a first control assembly, one end of the second electric cylinder assembly 42 and one end of the third electric cylinder assembly 43 are respectively arranged on the second hooke joint assembly 32 and the third hooke joint assembly 33, and the other end of the second electric cylinder assembly 42 and the other end of the third electric cylinder assembly 43 are connected to the first cross shaft assembly 51. The fourth electric cylinder assembly 44, the fifth electric cylinder assembly 45, the fourth hooke joint, the fifth hooke joint and the second cross shaft assembly 52 form a second control assembly, one end of the fourth electric cylinder assembly 44 and one end of the fifth electric cylinder assembly 45 are respectively installed on the fourth hooke joint assembly 34 and the fifth hooke joint assembly 35, and the other end of the fourth electric cylinder assembly 44 and the fifth hooke joint assembly is connected to the second cross shaft assembly 52. The sixth electric cylinder assembly 46, the first electric 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, one end of the sixth electric cylinder assembly 46 and one end of the first electric cylinder assembly 41 are respectively connected with the sixth hook assembly 36 and the first hook assembly 31, and the other end of the sixth electric cylinder assembly 46 and the other end of the first electric cylinder assembly 41 are connected with the third cross shaft assembly 53.
As shown in fig. 3-4, each hooke joint assembly fixedly connected to the stationary platform 10 has two rotational joints, so that the cylinder body of the electric cylinder assembly has two rotational degrees of freedom, twelve rotational degrees of freedom, and rotating shafts J1 to J12, relative to the stationary platform 10; each electric cylinder is provided with a translation joint, so that one translation degree of freedom of a piston rod of the electric cylinder relative to the cylinder body is realized, six translation degrees of freedom are realized, and the moving shaft is J13-J18; the bottom of each shaft lug part is provided with 2 single-shaft rotary joints so as to realize that each shaft lug has 1 rotary freedom degree relative to the connected 2 piston rods, and the rotary freedom degrees are 6, and the rotary shafts are J19-J24 in figure 4; each crossed shaft assembly has 2 rotary joints, can realize the single-shaft rotation of the shaft lug relative to the crossed shaft shell, and has 3 degrees of freedom in total, and the rotary shaft is J25-J27. The cross shaft shell can also rotate relative to the moving platform 20 in a single shaft, 3 degrees of freedom are achieved, and the rotating shaft is J28-J30. J25-J27 are vertical to J28-J30 in one-to-one correspondence. The rotational degrees of freedom can be realized by designing a shafting mechanism, and the translational degrees of freedom are realized by using an electric cylinder.
As shown in fig. 5 to 25, the lower hooke joint base of each hooke joint assembly is connected to the stationary platform 10 by a screw, and the installation angle of the hooke joint assembly is specific and can be considered as the setting of the hooke joint rotation centers (B1 to B6): (a) Intersection points (B1-B6) of two rotating shafts of the cross shaft of the Hooke hinge assembly, namely the rotating center of the Hooke hinge, and B1-B6 are arranged on a circle with the point O as the center of a circle. (b) An angle bisector OY1 of OB1 and OB2 is drawn, and OY2 and OY3 are both 120 ° to 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 axes of the fixed shaft parts of the cross shafts of the Hooke's joint assembly 2 and the Hooke's joint assembly 3 form 30 degrees with the OY1 line, the axes of the fixed shaft parts of the cross shafts of the Hooke's joint assembly 4 and the Hooke's joint assembly 5 form 90 degrees with the OY1 line, and the axes of the fixed shaft parts of the cross shafts of the Hooke's joint assembly 1 and the Hooke's joint assembly 6 form 30 degrees with the OY1 line.
And the Hooke joint upper seat of each Hooke joint assembly is connected with the electric cylinder through a screw. The 'pin hole axis' of the pin hole on the fork frame at the top end of the piston rod is parallel to the axis of the swing shaft part of the hook hinge assembly.
Each cross-shaft assembly is connected to the movable platform 20 by screws. The mounting position and mounting angle of the cross-axle assembly on the moveable platform 20 are specific: (a) The intersection points of the axis of the central shaft and the 'shaft lug cylindrical axis' of the shaft lug are set to be Q1-Q3 and respectively correspond to the cross shaft assembly 1-the cross shaft assembly 3. (b) A point P is arranged on the movable platform 20, and Q1-Q3 are uniformly distributed on a circle with the point P as the center of circle. (c) the central shaft axis is perpendicular to OQ 1-OQ 3.
Based on the robot structure, the invention discloses a parallel six-axis robot position and posture correction method based on an additional encoder.
Specifically, an angle encoder is respectively arranged on a Hooke joint upper base and a Hooke joint lower base of a left Hooke joint assembly of the selected control assembly, and is recorded as a first angle encoder 61 and a second angle encoder 62, and the angle encoders are used for measuring the rotating angles of a fixed shaft part and a swinging shaft part of the Hooke joint assembly relative to the Hooke joint lower base and the Hooke joint upper base respectively and are recorded as j theta 1 And j θ 2 . And an angle encoder is arranged on the Hooke joint upper base of the Hooke joint assembly on the right side of the selected control assembly and is recorded as a third angle encoder 63. The method is used for measuring the rotation angle of the swing shaft part of the Hooke joint relative to the Hooke joint upper base of the Hooke joint assembly and is recorded as j theta 3 . An angle encoder, marked as a fourth angle encoder 64, is mounted inside the cross shaft assembly of the selected control assembly and is used for measuring the angle value of the shaft part of the shaft lug of the cross shaft assembly relative to the cross shaft shell, marked as j theta 4 . An angle encoder, designated as a fifth angle encoder 65, is mounted on the movable platform 20 at a position connected to the selected control assembly for measuring a rotation angle value, designated as j θ, of the movable platform 20 relative to the cross-shaft assembly 5 。
After the angle encoder is installed, the length L = [ L1L 2L 3L 4L 5L 6 ] of the electric cylinder of the vector at any time is known]L1 to l6 represent Ο ΒΑ 1 ～ Ο ΒΑ 6 Let l1= count the light Ο ΒΑ 1 |，...，l6＝| Ο ΒΑ 6 L. The angle value j theta can be read by five angle encoders 1 ～jθ 5 Using J theta = [ J theta ] 1 jθ 2 jθ 3 jθ 4 jθ 5 ]And (4) showing. Then, the pose positive solution problem of the parallel six-axis robot is described as follows: the forward solution problem can be described as: knowing the values of L and J theta, the position of the movable platform 20 is solved O OP and attitude of the moving platform 20 O R P The value of (c). In the embodiment, five angle encoders are mounted on the first control assembly, and the angle encoders are mounted on the second hook joint assembly 32, the third hook joint assembly 33 and the first cross shaft assembly 51 respectively. Therefore, the pose solution of the movable platform 20 specifically comprises the following steps:
s1, constructing kinematic elements of a parallel six-axis robot:
B i and i = 1-6 is the origin of the Hooke's joint, and the origin is respectively arranged at the centers of the cross shafts of the six Hooke's joint components.
{ O } is the base coordinate system. A rectangular coordinate system { O } is established on the stationary platform 10, and the origin O of the coordinate system is set at B 1 ～B 6 On a defined plane and located at B 1 ～B 6 The center position of the circle is determined, and the y-axis direction is arranged at OB 1 ,OB 2 The angular plane of the line segment is divided into line positions, and at the moment, the six hook hinge assemblies are symmetrical relative to the y axis; the z axis is arranged upwards, and the x axis can be automatically determined according to the right-hand rule, so that the final coordinate system is obtained.
R b Is represented by B 1 ～B 6 The radius of the determined circle is called as the radius of the virtual circle of the Hooke's joint.
O OB 1 ～ O OB 6 ： O OB i : the Hooke's joint position vector specifically represents the ith Hooke's joint origin B with the origin of the base coordinate system as the starting point i I =1 to 6 as the vector of the end point, and the reference coordinate system is the base coordinate system.
β i I =1 to 6 is a hook hinge offset angle, and represents O OB i Angle to the Y-axis of the base coordinate system { O }.
R Q Referred to as the "cross-axis virtual circle radius," represents the radius value of the circle defined by the three cross-axis assembly origins.
Q i I = 1-3 is the axle ear origin of the cross axle assembly, and the axle ear is connected with U i I =1 to 3 corresponds to the overlapping point and is set as Q i ，i＝1～3。
{Q i I =1 to 3 denotes an axis ear coordinate system. The origin of the coordinate system is fixedly connected with the origin Q of the shaft lug i ，{Q i And (4) xyz three axes of the shaft lug, wherein the z axis is along the axis direction of the shaft part of the shaft lug, the y axis is along the direction of a connecting line of two points of the hinge of the pin shaft, and the x axis is determined according to the right-hand rule.
U i The axis of two cylindrical surfaces of the crossed shaft part forms a crossing point which is the origin of the crossed shaft and is set as U i ，i＝1～3。
{U i And i =1 to 3, which represents a cross-axis coordinate system. The origin of the coordinate system is the origin U of the crossed shaft i The z-axis is along the axial direction of the shaft portion of the shaft lug, the y-axis is along the axial direction of the central shaft, and the x-axis is determined according to the right-hand rule.
{ P } is the moving platform 20 coordinate system. A rectangular coordinate system { P } is established on the movable platform 20, and the origin P of the coordinate system { P } is located at U i I =1 to 3 on a plane defined by three U' s i And determining the center position of the circle. Y-axis of coordinate system { P }, 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 up, and the x-axis can be determined with the right-hand rule.
Figure BDA0003364332160000101
i =1 to 3 represents the distribution angle of the pivot points
Figure BDA0003364332160000102
O The position of the OP movable platform 20 represents a position vector of the origin P of the coordinate system { P } of the movable platform 20 relative to the origin O of the coordinate system of the stationary platform 10.
O R P The attitude of the movable platform 20 represents a rotation matrix of the coordinate system { P } of the movable platform 20 with respect to the coordinate system { O } of the stationary platform 10.
A 1 ～A 6 In the hinge of the pin shaftHeart, A 2 And A 3 Corresponding to first cross-shaft assembly 51, A 4 And A 5 Corresponding second cross-shaft assembly 52, A 6 And A 1 Corresponding to third cross-shaft assembly 53. Two pin hinge center points A 2 (Point A) 4 Point A 6 ) And point A 3 (Point A) 5 Point A 1 ) Point relative to { Q 1 }({Q 2 }，{Q 3 ) } about the Y axis of the substrate, point A 2 (Point A) 4 Point A of 6 ) And point A 3 (Point A) 5 Point A 1 ) Is placed in { Q 1 }({Q 2 }，{Q 3 }) in the XY plane, A is represented by QAX 1 And A 2 In { Q 1 Absolute offset value in the X-axis direction of (A) }, QAY denotes A 1 And A 2 In { Q 1 Absolute offset value in the Y-axis direction.
Ο ΒΑ i The electric cylinder position vector is expressed by taking a base coordinate system { O } as a reference system.
S2, on the cross shaft of the second hook joint component 32, using the center B of the cross shaft 2 A Hooke joint coordinate system { B2} is established for an original point, the original point is fixed in the center of the cross shaft, namely the intersection point of the axis of the fixed shaft part and the axis of the swinging shaft part, the y axis of the Hooke joint coordinate system { B2} is pointed to a Hooke joint assembly at the right end along the axis of the fixed shaft part, the z axis is the same as the z axis of { O }, and the x axis can be obtained by right-hand rule determination. { B2} is represented by a solid line.
S3, establishing an electric cylinder coordinate system { L2} on the Hooke hinge upper base of the second Hooke hinge assembly 32, wherein the origin of the electric cylinder coordinate system is coincident with the origin of the Hooke hinge coordinate system { B2}, the z-axis is perpendicular to a plane determined by the axis of the fixed shaft part and the axis of the swinging shaft part of the second Hooke hinge assembly 32 and faces upwards, the x-axis is in the same direction with the x-axis of the { B2} along the axis of the swinging shaft part, and the y-axis can be obtained by a right-hand rule. { L2} is indicated by a dotted line.
S4, center B of left Hooke 'S joint component (second Hooke' S joint component 32) 2 From the center B of the right hook joint assembly (third hook joint assembly 33) 3 Is denoted as b 23 Calculating to obtain:
Figure BDA0003364332160000111
and S5, solving the pose of the { B2} coordinate system by taking the { O } as a reference system. As will be shown below, in the following, O P B2 indicates the position of the origin of B2, O R B2 the attitude of B2 is represented, O T B2 a pose matrix is represented.
O P B2 ＝R b ·[-sin(30°) cos(30°) 0] T
Figure BDA0003364332160000112
Figure BDA0003364332160000113
And S6, solving the pose of the electric cylinder coordinate system { L2} by taking the { O } as a reference system. As will be shown below, in the following, B2 R L2 indicating the attitude of L2 with respect to B2, O T L2 a pose matrix is represented.
Figure BDA0003364332160000114
Figure BDA0003364332160000115
O T L2 And the 1 st to 3 rd rows and the 1 st to 3 rd columns of O R L2 。
S7, using { O } as reference system, solving A 2 Position of the point:
L2 P A2 ＝[0 0 l2] T
O P A2 ＝ O R L2 · L2 P A2
s7, solving A by taking { O } as a reference system 3 Position of the point:
Figure BDA0003364332160000116
O P A3 ＝ O T L2 · L2 P A3
s8, solving for { Q 1 Pose with respect to { O }, using O T Q1 And (4) showing. L2 N 23 The vector indicating the point A2 points to the point A3, using { L2} as the reference system,
L2 N 23 ＝ L2 P A3 - L2 P A2
according to the normal vector solving rule of the two-dimensional vector, the sum can be obtained L2 N 23 The unit vector of the vertical is L2 N ⊥23 。
α 23 To represent L2 N 23 And z-axis of { L2}, i.e. vector z L2 ＝[0 0 1] T Included angle value.
L2 A o23 Is represented by A 2 Point sum A 3 The center point position vector of the point.
L2 P Q1 A position vector representing the origin of { Q1} in the { L2} coordinate system.
The above-mentioned geometric elements. { Q 1 Denoted by a solid line, { U } 1 Indicated with a dashed line.
Figure BDA0003364332160000121
Figure BDA0003364332160000122
Figure BDA0003364332160000123
L2 P Q1 ＝ L2 A o23 + L2 N ⊥23 ·QAY
Figure BDA0003364332160000124
S9, solving { U 1 Pose with respect to { O }, using O T U1 And (4) showing.
Figure BDA0003364332160000125
Q1 P U1 ＝[0 0 0]
Figure BDA0003364332160000126
S10, solving for { P 1 Pose with respect to { O }, using O T P1 And (4) showing. { P 1 Denoted by a dotted line, { U } 1 Denoted by solid lines.
Figure BDA0003364332160000131
U1 P P1 ＝[0 0 0]
Figure BDA0003364332160000132
S11, solving O OP and O R P 。
P1 P P ＝[-R Q 0 0]
Figure BDA0003364332160000133
Figure BDA0003364332160000134
O T P the matrix formed by the 1 st to 3 rd rows and the 1 st to 3 rd columns is O R P ， O T P The vector formed by the 1 st to 3 rd lines and the 4 th column of (A) is O OP。
In conclusion, the five angle encoders are arranged at specific joints of the robot, the angle values of 5 positions can be read additionally, and the position and attitude values of the coordinate system of the movable platform 20 relative to the base coordinate system of the static platform 10 are solved by combining the structural parameters of the given parallel six-axis robot and the extension amount of the piston rod of the electric cylinder at any moment. Because more information can be obtained through five encoders, the difficulty of solving a positive solution can be reduced, and in the operation process, only elementary matrix multiplication operation, namely simple multiplication and addition operation, is performed, so that the calculation efficiency is effectively improved.
The above description is only exemplary of the present invention and is not intended to limit the technical scope of the present invention, so that any minor modifications, equivalent changes and modifications made to the above exemplary embodiments according to the technical spirit of the present invention are within the technical scope of the present invention.

Claims (1)

1. A parallel six-axis robot position and posture correction method based on an additional encoder is characterized in that: the parallel six-axis robot comprises a static platform, a movable platform, six hook hinge assemblies, six electric cylinder assemblies and three cross shaft assemblies, wherein the hook hinge assemblies are arranged on the static platform, the cross shaft assemblies are arranged on the movable platform, one ends of the electric cylinder assemblies are arranged on the hook hinge assemblies, and the other ends of the electric cylinder assemblies are rotationally connected to the cross shaft assemblies through bearing pin shafts;
the six electric cylinder assemblies are sequentially defined as a first electric cylinder assembly, a second electric cylinder assembly, a third electric cylinder assembly, a fourth electric cylinder assembly, a fifth electric cylinder assembly and a sixth electric cylinder assembly in the anticlockwise direction; the six Hooke joint components are sequentially defined as a first Hooke joint component, a second Hooke joint component, a third Hooke joint component, a fourth Hooke joint component, a fifth Hooke joint component and a sixth Hooke joint component; the three cross shaft assemblies are sequentially defined as a first cross shaft assembly, a second cross shaft assembly and a third cross shaft assembly; the second electric cylinder assembly, the third electric cylinder assembly, the second hook joint, the third hook joint and the first cross shaft assembly form a first control assembly, one end of the second electric cylinder assembly and one end of the third electric cylinder assembly are respectively arranged on the second hook joint assembly and the third hook joint assembly, and the other end of the second electric cylinder assembly and one end of the third electric cylinder assembly are connected to the first cross shaft assembly; a fourth electric cylinder assembly, a fifth electric cylinder assembly, a fourth hook joint, a fifth hook joint and a second cross shaft assembly form a second control assembly, one end of the fourth electric cylinder assembly and one end of the fifth electric cylinder assembly are respectively arranged on the fourth hook joint assembly and the fifth hook joint assembly, and the other end of the fourth electric cylinder assembly and one end of the fifth electric cylinder assembly are connected to the second cross shaft assembly; a sixth electric cylinder assembly, a first electric cylinder assembly, a sixth hook joint assembly, a first hook joint assembly and a third cross shaft assembly form a third control assembly, one end of the sixth electric cylinder assembly and one end of the first electric cylinder assembly are respectively connected with the sixth hook joint assembly and the first hook joint assembly, and the other end of the sixth electric cylinder assembly and one end of the first electric cylinder assembly are connected with the third cross shaft assembly;
the method comprises the following steps:
firstly, five angle encoders are mounted on an optional group of a first control assembly, a second control assembly and a third control assembly of the robot to read joint angle values;
specifically, an angle encoder is respectively arranged on a Hooke joint upper base and a Hooke joint lower base of a left Hooke joint assembly of the selected control assembly, and is recorded as a first angle encoder and a second angle encoder, and the angle encoders are used for measuring the rotating angles of a fixed shaft part and a swinging shaft part of the Hooke joint assembly relative to the Hooke joint lower base and the Hooke joint upper base respectively and are recorded as j theta 1 And j θ 2 (ii) a An angle encoder is arranged on a Hooke joint upper base of a Hooke joint assembly on the right side of the selected control assembly and is recorded as a third angle encoder; the method is used for measuring the rotation angle of the swing shaft part of the Hooke joint relative to the Hooke joint upper base of the Hooke joint assembly and recording as j theta 3 (ii) a An angle encoder is arranged in the cross shaft assembly of the selected control assembly and is recorded as a fourth angle encoder for measuring the angle value of the shaft part of the shaft lug of the cross shaft assembly relative to the cross shaft shell and recorded as j theta 4 (ii) a Connected with selected control components on a moving platformAn angle encoder is arranged at the position of the movable platform, is recorded as a fifth angle encoder and is used for measuring the rotation angle value of the movable platform relative to the cross shaft component and is recorded as j theta 5 ；
Then, solving the pose of the movable platform according to the following steps:
s1, constructing kinematic elements of a parallel six-axis robot;
B i i = 1-6 is a Hooke hinge origin which is respectively arranged at the centers of the cross shafts of the six Hooke hinge components;
establishing a base coordinate system { O } on the static platform, wherein the origin O of the coordinate system is arranged at B 1 ～B 6 On a certain plane and located at B 1 ～B 6 Determining the circle center position of the circle; in the y-axis direction at OB 1 ,OB 2 The angular bisector position of the line segment is set, the z axis is upward, and the x axis is determined according to the right-hand rule; r b Is represented by B 1 ～B 6 The radius of the determined circle is called as the radius of the virtual circle of the Hooke's hinge; O OB 1 ～ O OB 6 ： O OB i the position vector of the Hooke's joint is expressed, specifically, the ith Hooke's joint origin B is expressed by taking the origin of the base coordinate system as the starting point i I = 1-6 as the vector of the terminal point, and the reference coordinate system is a base coordinate system;
β i i =1 to 6 is a hook hinge offset angle, and represents O OB i An angle to the Y-axis of the base coordinate system { O };
R Q the radius is called as the virtual circle radius of the crossed shaft and represents the radius value of a circle determined by the original points of the three crossed shaft components;
Q i i = 1-3 is the axle ear origin of the cross axle assembly, and the axle ear is connected with U i I =1 to 3 corresponds to the overlapping point and is set as Q i ，i＝1～3；
{Q i I = 1-3 represents an axis ear coordinate system, and the origin of the coordinate system is fixedly connected with the origin Q of the axis ear i ，{Q i The z axis of the hinge is along the axis direction of the shaft part of the shaft lug, the y axis is along the connecting line direction of two points of the hinge of the pin shaft, and the x axis is determined according to the right-hand rule;
U i i = 1-3 is the origin of the crossed axis, two circles of the crossed axis partThe axes of the cylindrical surfaces form an intersection point;
{U i i =1 to 3, and represents a cross-axis coordinate system whose origin is a cross-axis origin U i The z-axis is along the axial direction of the shaft part of the shaft lug, the y-axis is along the axial direction of the central shaft, and the x-axis is determined according to the right-hand rule;
{ P } is a moving platform coordinate system, and the origin P of the coordinate system { P } is located at U i I = 1-3 on a plane defined by three U' s i Determining the center position of the circle; the y-axis of the coordinate system { P } is set as: u shape 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 is determined by a right-hand rule;
Figure FDA0003364332150000021
distribution angle representing pivot ear origin
Figure FDA0003364332150000022
O OP position of the movable platform, which represents the position vector of the origin P of the movable platform coordinate system { P } relative to the origin O of the stationary platform coordinate system;
O R P representing a rotation matrix of a movable platform coordinate system { P } relative to a static platform coordinate system { O } for the attitude of the movable platform;
A 1 ～A 6 is the hinge center of the pin shaft, A 2 And A 3 Corresponding to the first cross-shaft assembly, A 4 And A 5 Corresponding to the second cross-shaft assembly, A 6 And A 1 Corresponding to the third cross shaft assembly;
Ο ΒΑ i representing the position vector of the electric cylinder, and taking a base coordinate system { O } as a reference system;
s2, on the cross shaft of the second hook joint component, using the center B of the cross shaft 2 Establishing a Hooke's hinge coordinate system { B2} for an origin, wherein the origin is fixed at the center of the cross shaft, namely the intersection point of the axis of the fixed shaft part and the axis of the swinging shaft part, the y-axis of the Hooke's hinge coordinate system { B2} is along the axis of the fixed shaft part and points to a Hooke's hinge component at the right end, the z-axis is the same as the z-axis of { O }, and the x-axis is the same as the z-axis of the { O }The axis is obtained by right hand rule;
s3, establishing an electric cylinder coordinate system { L2} on a Hooke joint upper base of the second Hooke joint component, wherein the origin of the electric cylinder coordinate system is superposed with the origin of the Hooke joint coordinate system { B2}, the z axis is vertical to a plane determined by the axis of the fixed shaft part and the axis of the swinging shaft part of the second Hooke joint component and faces upwards, the x axis faces the same direction as the x axis of the { B2} along the axis of the swinging shaft part, and the y axis can be obtained by right-hand rule;
s4, center B of second hook joint component 2 From the center B of the third Hooke's hinge component 3 Is denoted by b 23 ：
Figure FDA0003364332150000031
S5, solving the pose of the { B2} coordinate system by taking the { O } as a reference system: O P B2 indicates the position of the origin of B2, O R B2 the attitude of B2 is represented, O T B2 representing a pose matrix;
Figure FDA0003364332150000032
s6, solving the pose of the electric cylinder coordinate system (L2) by taking (O) as a reference system, B2 R L2 indicating the attitude of L2 with respect to B2, O T L2 representing a pose matrix:
Figure FDA0003364332150000033
Figure FDA0003364332150000041
O T L2 and the 1 st to 3 rd rows and the 1 st to 3 rd columns of O R L2 ；
S7, using { O } as reference system, solving A 2 Position of the point:
Figure FDA0003364332150000042
s8, solving A by taking { O } as a reference system 3 Position of the point:
Figure FDA0003364332150000043
s9, solving for { Q 1 Pose with respect to { O }, using O T Q1 It is shown that, L2 N 23 the vector indicating the point A2 points to the point A3, using { L2} as the reference system,
L2 N 23 ＝ L2 P A3 - L2 P A2 ；
solving a rule according to a normal vector of the two-dimensional vector, and L2 N 23 the unit vector of the vertical is L2 N ⊥23 ；
α 23 To represent L2 N 23 And z-axis of { L2}, i.e. vector z L2 ＝[0 0 1] T An included angle value;
L2 A o23 is represented by A 2 Point sum A 3 A center point position vector of the point;
L2 P Q1 a position vector representing the origin of { Q1} in a { L2} coordinate system;
Figure FDA0003364332150000051
s10, solving { U 1 Pose with respect to { O }, using O T U1 Represents:
Figure FDA0003364332150000052
Q1 P U1 ＝[0 0 0]
Figure FDA0003364332150000053
s12, solving for { P 1 Pose with respect to { O }, using O T P1 It is shown that,
Figure FDA0003364332150000054
s13, solving O OP and O R P ：
P1 P P ＝[-R Q 0 0]
Figure FDA0003364332150000055
Figure FDA0003364332150000056
O T P the matrix formed by the 1 st to 3 rd rows and the 1 st to 3 rd columns is O R P ， O T P The vector formed by the 1 st to 3 rd lines and the 4 th column of (A) is O OP。
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